evropský
sociální fond v ČR
EVROPSKÁ UNIE
MINISTERSTVO ŠKOLSTVÍ, MLÁDEŽE A TĚLOVÝCHOVY
OP Vzdělávání pro konkurenceschopnost
INVESTICE DO ROZVOJE VZDĚLÁVÁNÍ
Tento učební text vznikl za přispění Evropského
sociálního fondu a státního rozpočtu ČR
prostřednictvím Operačního programu
Vzdělávání pro konkurenceschopnost v rámci projektu Univerzitní výuka matematiky v měnícím
se světě (CZ.1.07/2.2.00/15.0203).
Obsah:
1. Úvod do SAS EG 4
2. Pokročilé programování v SAS 51
3. Pokročilé programování v SAS - indexy,... 173
4. Credit scoring (CS) - historie, základní pojmy. 305
5. Metodologie vývoje scoringových funkcí. 347
6. Příprava dat II. 419
7. Úvod do shlukové analýzy. Hiearchické shlukování. 467
8. Vývoj CS modelu. 530
9. Úvod do analýzy přežití. 586
10. Coxova regrese. 637
11. Evaluace modelu II. 653
12. Stanovení cut-off. RAROA, CRE. Monitoring. 713
13. Reference. 749
1. Úvod do SAS EG
Introduction to SAS Enterprise Guide
•SAS Enterprise Guide provides a point-and-click interface for managing data and generating reports.
Summary Statistics for S:\workshop\customers.sas7bdat
Data Statistics Basic
Percentiles Additional
Plots
Results
Titles
Properties
Data source: S:\workshop\custonners.sas7bdat Task filter: None
Variables to assign:
Name
CustomerJD ^ Customer_Country ^ Customer_G ender
Customer_N ame ^ Customer_FirstName ^ Customer_LastName
Customer_BirthDate ^ Customer_Age_G roup
Customer_Type ^ Customer_G roup (2> Customer_Age
	Analysis variables
	Customer_Age
	FH Classification variables
	^RuS Custorner_Type
	Frequency count (Limit: 1)
	ffil Relative weight (Limit: 1)
	B Copy variables
	B Group analysis by
H	
Class level Customer_ Sort by:
Unformatted values
Ascending
Missing values:
I  I Allow multi-label for
The variables that you assign to this role are character or discrete numeric variables that are used to divide t data into categories or subgroups. The statistics will be calculated on all selected analysis variables for e. combination of classification variables.
Bar Chart for S:\workshop\orion_profit.sas7bdat
3 of A      Specify appearance
§sas
0 3D chart Colors -
Sample chart:
Color bars by:
Labels
I Bar category
Preview code
HE
t\ae t eachl
3
I  I Legend: 0Data labels:
Lines and ticks
South
Sum
Anis Labels
W] Use reference lines [^1 Tick marks
SAS Enterprise Guide Interface
SAS Enterprise Guide also includes a full programming interface that can be used to write, edit, and submit SAS code.
^ SAS Enterprise Guide
File     Edit     View Tasks
Project Tree
Q S^n Process Flow
3'"i^l orion_profit
fe|$ Bar Chart customers □~CD Programs
jM ep02d01
Program Tools T x    ep02d01 -
Help "a-&T
¥^ R=) CB X I W> l3< I □ " I     Process Flow
Output Data (2)
Program
y 5ave "  w Run  "       itop   5elect 5erver    Export " 5end To - Create " | [?] Properties
libnarne orion "s:\workshop'
set orion.customers;
if Customer_Type_ID = 3010
then output work.nonelub; else output work. clubrnembers;
1
2
3 13 data work. c lubrnembers work. none lub;
4
5
6
7
8
9
lOBproc print data=work.nonelub noobs; 11 title  "Non Club Members";
var Country Gender Custorner_Name;
13 run;
14
run;
SAS Enterprise Gu
ide Interface: The Project
A project serves as a collection of
• data sources
• SAS programs and logs
• tasks and queries
• results
• informational notes for documentation.
SAS Enterprise Guide - e101a01.egp
File     Edit     View     Tasks     Program Tools
Q       Process Flow
S El 0RI0N_PR0FIT
H Product Frequencies Wi Profit by Category Pie Chart |; 1 Hrotit by Countiy/Agebioup Report Q 53* Create Format ($CntryFmt ■ Local)
Link to Create Orion_Profit Q Cj Programs
E) j|J Create Orion_Profit B Qi) Cuslom Reports ^ Report
Help "Ü - reprocess Flow -
C|^| [fa,  X I       CM I      Process Flow
> Run -r  Q Export ▼ Schedule - | Zoom - | ^ Project Log  | [7] Properties
Tasks by Category
Sw.
Filter and Sort Query Builder Append Table !d Create Imported Format Sort Data
J Create Format
Ready
You can control the contents, sequencing, and updating of a project.
SAS Programs
data work.clubmembers work.nonclub;^ set orion.customer; if Customer_Type_ID = 3010
then output work.nonclub; else output work.clubmembers;
run;
print data=work.nonclub; title "Non Club Members"; var Country Gender Customer Name*
run ;
DATA Step
PROC Step
ep02d01.sas
8
PROC PRINT Output
5sa			Enterprise Guide-			
		The Fkruver tftKiww-Non Club Members				
	Obs	Country		Gender	Customer_Name	
	1	DE		M	Ulrich Heyde	
	2	US		M	Tulio Devereaux	
	3	US		F	Robyn. Klera	
	4	us		F	Cynthia Mccluney	
	5	AU		F	Candy Kinsey	
	6	US		M	Phenix. Hill	
	7	IL		M	Avinoam a we ig"	
	8	CA		F	Lauren Marx	
						
Saving SAS Programs
•The SAS program in the project is a shortcut to the physical storage location of the .sas file. Select the program icon and then select File O Save program name to save the program as the same name, or Save program name As... to choose a different name or storage location. ^^^^^^^^^^^^^^^
SAS Enterprise Guide
File
Edit     View     Tasks Program
New "J Open
Close Project
►
►
5ave Project 5ave Project As...
Ctrl+5
y    5ave ep02d01 Ctrl+Shift+S
IE
Save ep02d01 As...
10
Embedding Programs in a Project
•A SAS program can also be embedded in a project so that the code is stored as part of the project .epg file.
•Right-click on the Code icon in a project and select Properties O Embed.
Properties for ep02d01
Results Prompts Summary
Label: ep02d01
Code will run on server:
Local
Last Execution Time:
2 seconds
File path:
Change..
Location:
My Computer
Embed
1¥
Save As..
Embeds the code in the SAS Enterprise Guide project so that any changes that you make to the code in SAS Enterprise Guide are not applied to the original code file. This option is available only for existing code files that you have inserted into yr^r "'"^j
□ K
Cancel
How Do You Include Data in a Project?
File
Edit     View     Tasks Program
'=1 New
Tools     Help    I HI -Process Flow
[?=t Open
Close Project
5ave Project 5ave Project As. 5ave
F
igfl  Project Ctrl+O
SAS Enterprise Guide
Ctrl+
File Edit
View
Tasks     Program Tools
Selecting File ■=> Open o Data
adds a shortcut to a SAS data source in the project.
Project Tree
Process FlowA
□ S^c Process Flow order_itern
Pun Stop
												
												
												
order_itern												
												
												
												
												
												
												
12
Assigning a Libref
•You can use the Assign Project Library task to define a SAS library for an individual project.
SAS Enterprise Guide																																				
File     Edit     View     Tasks Program		Tools		Help |H~|^r^&|											=) Oi ?\ I             I n» | E^g Process Flow ^																					
Project Tree ^		D	Add-In																																	
□ S^g Process Flow			Create HTML Document... Style Manager												" I Zoom "   "^Project Log | [^Properties »																					
U   1_1	i luyiain-^ ep02d01																																			
																																				
	£J ep02d02																																			
		Assign Project Library...																																		
																																				
																																				
			JMP Stored Process Packager.. Project Maintenance.., View Open Data Sets...																																	
																																				
																																				
																																				
																																				
																																				
																																				
		■_■ i ■_■ i ij																																		
																																				
																																				
																																				
																																				
											HTML ep02d0																									
																																				
												1																								
Browsing a SAS Library
Server List
H~W LLB Inventory Local Ö-|3) Libraries
+
$■ (=)■
•During an interactive SAS Enterprise Guide session, the Server List window enables you to manage your files in the windowing environment.
In the Server List window, you can do the following:
■ view a list of all the servers and libraries available during your current SAS Enterprise Guide session
■ drill down to see all tables in a specific library
■ display the properties of a table
■ delete tables
■ move tables between libraries
GISMAPS MAPS MYDATA ORION
TJ ALL_SUPPLIERS
AUSTRALIA_SUPPLIERS QJ COMBINED_PRODUCT [3 CUSTOMER [3 CUSTOMER_PROFIT jJJ CUSTOMER_TYPE [3 EMPLOYEE_CELL |3 EMPLOYEEJHOME |3 MNTH7_2007 [3 MNTHS_2007 [3 MNTH9_2007 TJ NONSALES
jg NORTH_AMERICAN_SUPPLIERS
14
Applying Formats
Display formats can be applied in a SAS Enterprise Guide task or query by modifying the properties of a variable.
Task roles:
I
List variables ^) EmploiieeJD ■jfci. First_Nanne ■jfä^ Last_Name (;Ti) ff^JB'111 (j3) Bonus ^) Compens ^) BonusMq
Group analysl | ^ | Page by (LirrJP Total of Subtotal of Identifying laBeT
Remove from Role 5ort Columns
Show Names 5how Labels
Properties
Ír
Categories:
Formats:
None Numeric
Time
Date/Time Currency User Defined All
MMDDYYSw.d_ai|	
MMDDYYw.d	
MMYYCw.d	
MMYYDw.d	
MMYYNw.d	._■
MMYYPw.d	
MMYYSw.d	
MMYYw.d	
■Attributes -Overall width:
Decimal places:
|Š~~ 3J Min: 2 Max: 10 |Ö~~ ~~3 Min: 0    Max: 7
"Description date values
"Example Value:
14245 (01Jan1999]
Output:	0	1	/	0	1	/	9	9	
OK
Cancel
15
Query Builder Join
•When you use the Query Builder to join tables in SAS Enterprise Guide, SQL code is generated.
SQL does not require sorted data.
SQL can easily join multiple tables on different key variables.
SQL provides straightforward code
to join tables
based on a non-equal
comparison of common columns
(greater than, less than,
between).
"!:: Query Builder for Local: ORION. ORD ERJTEM
Query name:   Join for Product List]
Output name:   |SASUSER.QUERY_FOR_ORDER_IT | | Change...
H] Computed Columns | @ Prompt Manager    Tc^ Preview | Tools
Options "
} Add Tables  X Delete       Join Tables
■ © o © ©
©
■ ©
© © ©
ORDERJTEM) □ rder_ID Order_ltem_Num Product_ID Quantity
Total_Retail_Price CostPrice_Per_U nit Discount
PRODUCTJJST )
Product_ID Product_Name Supplier_ID Product_Level Product Ref ID
Select Data | Filter Data| Sort Data]
Column Name	Input	Summary	
® OrderJD [Order...	tl.OrderJD	H	
@ Order_ltem_Num...	t1 .OrderJtem_Num		
® ProductJD (Pro...	H.Product ID		
® Quantity (Quantit...	H .Quantity		
*f* Total_Retail_Pri...	H.Total Retail Price		
^ CostPrice_Per_...	tl.CostPrice Per ...		
@ Discount (Disco...	tl .Discount		
© ProductJD 1 (Pr...	t2. ProductJD		
^ ProductJJame (...	t2.Product_Name		
© SupplierJD (Sup...	t2. SupplierJD		
@ ProductJ_evel (...	t2.Product Level		
@ Product_Ref_ID ...	t2.Product Ref ID		
			
		>	
Ml
m
a
I  I Select distinct rows only
Run
Save and Close
Cancel
Help
16
Sort Data Task
•The Sort Data task enables you to create a new data set sorted by one or more variables from the original data.
Ü Sort Data for Local:ORION.PRODUCT_L 1ST
Options Results Properties
Data
Data source: Local:ORION.PRODUCTJJST Task filter: None
Edit..
Columns to assign:
Task roles:
ProductJD sort order:
Name
® ProductJD $1 Product_Narne © SupplierJD ® Product_Level ® Product_Ref_ID
| Sort by
■@ ProductJD
| Columns to be dropped (Limit: A
l±J
Ascending
O Sort Data for Local:ORION.PRODUCT LIST
Data Options Results Properties
Results
(^Location to save output data-
Local: WORK. SORT PRODUCT
Browse...
Business Scenario
•Orion Star wants to send information about a specific promotion to female customers in Germany. The report can be created by querying the or ion. customer data set to include only the desired customers, and then by producing a report with the List Data task.
CU5TKiMEF[
remale German
F_G ermanv
List
Da:a
HTML
Female Customers in Germany
Customer Country	Customer First Name	Customer Last Name	Customer Birth □ate
DE	Co rnelia	Krahl	27FEB1974
DE	Elke	iallstab	16AUG1974
DE	Ines	Deisser	20JUL1969
			
Business Scenario
•The same report can be generated more efficiently by subsetting the data directly within the List Data task. This requires modification of the code generated by SAS Enterprise Guide.
CUSTOMER
List
Data
-HTMM-List Data
2 7 □ PRÜC PRIHT DATA=WORK. SORTTempTableSorted
2 8 NOOBS
29 LABEL
30 ;
31 _
32
33
34
35
3 6 VAR Country Customer_FirstName Customer_LastWame Birth_Date; 3 7 RUH;
/* Start of custom user code. */ where Country =   1DE1   and Gender =   1F1;
/* End of custom user code. */
38 /*------------------
39 End of task code.
40
41 RUH; QUIT;
19
Understanding Generated Task Code
•There are many situations where task results created by SAS Enterprise Guide can be further enhanced or customized by modifying the code.
•However, before you can effectively modify the code, you must first understand the code that SAS Enterprise Guide generates.
List Data Task
H List Data for Local:ORION.CUSTOMER
Data
Options
Titles
Properties
Preview code
Data
Data source: Task filter:
LocahORION.CUSTOMER None
Edit..
Variables to assign:
Task roles:
Gender sort order:
Name
1^3) Custorner_ID fy. Country ^.Gender ^PersonalJD fy. Custorner_Name fy. Custorner_FirstName fy. Customer_LastName Q Birth_Date fy> Custorner_Address © StreetJD $L Street_N umber @) Custorner_Type
When yo^assign one or is gendered for each dis
List variables Country
Customer_FirstName Customer_LastName -H Birth_Date Group analysis by
Page by (Limit: 1 ] Total of
Subtotal of (Limit: 1] Identifying label
Ascending
0 Sort by variables
The Preview code button enables you to view and modify the code generated by the task.
ng
Run
Save
Cancel
Help
List Data Task - Code Preview
Code Preview For Task
Insert Code..
I
Code generated by SAS Task
Generated on: Wednesday, April 29, 2009 at 11:12:29 AH By task:   List Data
Input Data:   ORION.CUSTOMER Server: Local
%  eg coitd±t±oital diopds (WORK. SORTTempTab leSorted) ;
/*-------------------------------------------------------------------
Sort data set ORION.CUSTOMER
------------------------------------------------------------------- */
□ PROC SORT
DATA=ORION. CUSTOMER (KEEP = Country Custorner_FirstNaroe Customer_LastName Bin OUT=UORK. SORTTempTableSorted
BY Gender;
RUM;_
TITLE;
TITLE 1  "Report Listing"; FOOTNOTE;
TT" TT,TT"TT" H FFf1
Using the List Data Task to Generate Code
•This demonstration illustrates building a List Data task and examining the code generated by SAS Enterprise Guide.
Customer Listing
Customer Gender=F
Customer  Customer First  Customer Last Name Customer Birth
Country         Name Date
US                Sandrina           Stephano 09JUL1979
DE                Cornelia           Krahl 27FEB1974
US               Karen                Ballinger 1BOCT19B4
DE                 Elke                     Wallstab 16AUG1974
Customer Gender=M
Customer Country	Customer First Name	Customer Last Name	Customer Birth □ate
US	James	Kvarniq	27JUN197 4
us	David	Black	12APR1969
DE	Markus	Sepke	21JUL1988
DE	Ulrich	Heyde	16JAN193 9
			
23
List Data Task - Generated Code
•The initial comment block shows information about the task.
/*----------------------------------------------------------
Code generated by SAS Task
Generated on:   Wednesday,   April 29,   2009 at  1:13:33 PH By task:   List Data
Input Data:   ORION.CUSTOMER Server: Local
------------------------------------------------------- */
24
List Data Task - Generated Code
•The first line uses a macro to delete temporary tables or views if they already exist. If the Group by role is used in the task, the data must be ordered by the grouping variable. PROC SORT is used by default. Only variables assigned to roles are kept in the new data set.
h  eg cofldl t± on a Id ±op d & (WORK ■ S ORTTernp Tab leSorted) ;
/*---------------------------------------------------------
Sort  data set  ORION.CUSTOMER
------------------------------------------------------ V
PROC SORT
DATA=ORION. CUSTOMER (KEEP = Country Custonier_FirstName
Custonier_LastName Birth_Date Gender)
OUT=UORK.SORTTempTataleSorted
■
BY Gender;
RU1I;
List Data Task - Generated Code
If the Group by role is not used, SQL creates a temporary view of the required data. Again, only variables assigned to roles in the task are included in the view. This comment incorrectly states that sorting occurs.
h  eg aon<l± t± on a Id jop d & (WORK. S ORTTernp Tab leSorted) ;_
/*---------------------------------------------------------
Sort data set ORION.CUSTOMER
------------------------------------------------------ V
PROC SQL;
CREATE VIEW WORK.S ORTTemp TableSorted AS
SELECT T.Country,   T.Customer_FirstName, T. C us t oine r_L as tNaine,   T. E i r t h_D at e FROM ORION.CUSTOMER as T
■
QUIT;
List Data Task - Generated Code
The main part of the code includes the titles, footnotes, and procedure code to generate the report. PROC PRINT is the procedure used with the List Data task.
TITLE;
TITLE 1  "Customer Listing"; FOOTNOTE;
FOOTNOTE1  "Generated toy the  3AS System   (£  SASSERVERNAHEf fiSYSSCPL)
PROC PRINTEDATA= WORK. SORTTempTatoleSorted IUlDUL!j-= "Row number" LABEL
VAR Country Customer_FirstName Customer_LastName Birth_Date; BY Gender;
RUN;
y>    TITLE and FOOTNOTE are examples of global statements and can be included anywhere in a SAS program.
on hTRIM(%QSYSFUNC(DATE(), NLDATE2□.)) at  % TRIM(% SYSFUNC(TIME[) f   NLTIHAP2□.) )
rr .
27
List Data Task - Generated Code
•At the end, the final lines of code delete any temporary tables created to build the task, and delete any assigned titles and footnotes.
/*---------------------------------------------------------
End of task code.
------------------------------------------------------ */
RUN; QUIT;
%_eg_cojidit±onal_djropds (WORK. SORTTempTab leSorted) ; TITLE; FOOTNOTE;
28
Techniques to Modify Code
•Three methods can be used to modify code generated by SAS Enterprise Guide:
1. Edit the last submitted task code in a separate Code window.
2. Automatically submit custom code before or after every task and query.
3. Insert custom code in a task.
29
Edit Last Submitted Code
•After a task runs, the code can be viewed from either the Project Tree or Process Flow.
SAS Enterprise Guide
File     Edit     View     Tasks     Program     Tools Help
I ,ä ^ ^ XI*
Project Tree
S S^g Process Flow
CUSTOMER
List Data
Process Flow
t> Run " □ 5top    Export - Schedule
Open
i>     Run List Data [TJ    Modify List Data Select Input Data Publish,,,_
I  Open List Data I        Open Last Submitted Code
Zoom
Open Log
Process Flow
b- Run
I Stop I Export T Schedule
CUSTOMER
List Data
■ I Zoom
MTMI -
■ Project Log | [?] Properties
Open
Run
Modify List Data
Run Branch from List Data
T-l--■■ T----
-a
pj   Open List Data
[SI   Open Last Submitted Code
\=M  Open Log
0 HTML - List Data
Edit Last Submitted Code
The task code is read-only and cannot be edited directly. To create a copy of the code from the Last Submitted Code window, select any key while in the SAS program window. SAS Enterprise Guide offers to make a copy.
SAS Enterprise Guide
This code is read-only.
Do you want to create a copy of this code that can be modified?
Yes
No
After the code is copied, there is no link between the task and the new code. Any changes in the task are not reflected in the copied code, and modifications to the code do not affect the task.
Summary of Editing Last Submitted Code
Custom code linked to task?	No
Can be used to modify query code?	Yes
Extent of modification allowed?	Anything in the program can be changed.
Custom code included when exported?	Yes. You must export the edited program and select the option in the Export wizard.
Automatically Submit Custom Code Before or After Every Task and Query
•There are times when you might need to run a SAS statement or program before or after any task or query is executed. The Custom Code option enables you to insert custom code before or after all tasks and queries.
33
Automatically Submit Custom Code Before or After Every Task and Query
•IT
General Project Views Project Recovery Results
Results General
Viewer
SAS Report
HTML
RTF
PDF
Graph
Stored Process Data
Data General Performance Query □ LAP Data Tasks
Tasks General Custom Code
Tasks > Custom Code
■Additional SAS code-
[^1 Insert custom SAS code before task and query code ^ Insert custom SAS code after task and query code
To run code before tasks and queries, select the
first check box and select Edit... to type the code.
Edit
Edit.
34
Automatically Submit Custom Code Before or After Every Task and Query
Global statements or complete program steps can be entered. Example: Set the LOCALE= option to Great Britain.
Edit
/* Insert custom code before task code here */ OPTIONS  LOCALE=en GB;
nsert Code Before or After SAS Programs
•Similar options exist to automatically submit code before or after SAS programs written and submitted in Code windows in SAS Enterprise Guide.
General Project Views Project Recovery Results
Results General
Viewer
SAS Report
HTML
RTF
PDF
Graph
Stored Process
Data
Data General Performance
Query
OLAP Data
Tasks
Tasks General Custom Code Output Library
SAS ProgramsK
Security §
SAS Programs
r General
0 Automatically direct results back to SAS Enterprise Guide 3 Close all open data before running code
Editor Options..
r Additional SAS code
[^1 Insert custom SAS code before submitted code [^1 Insert custom SAS code after submitted code ] Submit SAS code when server is connected
Edit.
Edit...
Edit...
Summary of Submitting Custom Code Before or After Every Task and Query
Custom code linked to task?	Yes
Can be used to modify query code?	Yes
Extent of modification allowed?	Statements can only be submitted before or after the task code.
Custom code included when exported?	Yes, select the option in the Export wizard.
Insert Custom Code in a Task
In most task dialog boxes, you have the ability to insert custom code within the generated SAS program. This technique has the significant benefit that the task interface can still be used to modify the report.
13
w lor Tas
Insert Code..
2 7 □ PROC PRINT DATA= WORK. SORTTempTab leSot^ted
28 OBS="Row number"
29 LABEL
30 ;
3 1
32
33
34
35 3 6
/* Staut of custom usee code. where country="DE"; ^^^En^^of^custo^j^iser^codej^^^
7
VAR Country Customer FirstName Customer LastName Birth Date;
RUH;
.a
37 /*-----------------
38 End of task code
39
Insert Custom Code in a Task
•In the Code Preview window, select Insert Code... to add custom code in predefined locations in the SAS program.
Code Preview For Task
Insert Code.
21
! /*------------------------------------------------------
2 Code generated toy SAS Task
3
4 Generated on:   Thursday,   March 13,   2008 at  10:57:50 PM
5 By task:   List Data
6
7 Input Data:   ORION.CUSTOMER
8 Server: Local
10
HBPROC SQL;
12 %_£A£TA£K_BFtGPDS (WORK. SORTTennpTab leSorted) ;
13 QUIT;
nsert Custom Code in a Task
User Code
Positions where user code may be inserted are indicated by the icons. Double-click on a marked line to add user code or change existing user code.
V
PROCSQL;
CREATE VIEW WORK.SORTTempTableSorted
AS SELECT Country, Custorner_FirstName, Custorner_LastNarne, Birth_Date FROM ORION.fl^BffMER; QUIT; TITLE;
TITLE1 "Report Listing"; FOOTNOTE;
F00TN0TE1 "Generated by the SAS System (&_SAS SERVER NAME, E.S^ffCJfl' oy^ffSFUNC(DATELl EL
i <double dick to insert code}
PROC PRINT DATA=WORK.S0RTTempTableSorted OBS="Row number" LABEL
In any of these predefined
locations, you can double-click on a line to insert
custom code.
\^LS< double-click to insert code}                             f f		
		
<'double-click to insert code}                     r f		
VAR Country Customer_FirstName Customer_LastNaj	^BirthJDate	
^^s<double-chck to insert code}		ill
		
		>
Clear All
OK
Cancel
Help
40
nsert Custom Code in a Task
Some insert points enable custom options to be added to existing statements.
User Code
0®
Positions where user code may be inserted are indicated by the icons. Double-click on a marked line to add user code or change existing user code.
PROC PRINT DATA=W0RK.S□ RTTempTableSorted, □ BS="Row number" LABEL
-Ji, <doub/e-click to insert code}
Insert options in the PRINT statement.
j^l, < do tsb/e - dick f o insert code}
VAR Country Customer_FirstName Customer_LastName Birth_Date Vi, <do ubf g-cfick to insert code}
<doubfe-dick to insert code}
Insert options in the VAR statement.
-1
Insert Custom Code in a Task
•Other insert points enable entire statements to be added inside a step in the program.
User Code
Positions where user code may be inserted are indicated by the icons. Double-click on a marked line to add user code or change existing user code.
PROC PRINT DATA=WORK.S□ RTTerinpTableSorted □BS="Row number" LABEL
< do tib/e - dick fo insert code}
< do ubf e - click fo insert code}
VAR Country Customer_FirstName Customer_LastName Birth.
< do Lib/e - dick f o imerf code}
< do ub/e - cfick f o insert code}
Statements inside the PRINT step
Insert Custom Code in a Task
•Additional locations enable global statements or additional steps to be inserted before or after the main code.
User Code
(n)(x)
Positions where user code may be inserted are indicated by the icons. Double-click on a marked line to add user code or change existing user code.
<doc/if/e-c/fd to /rtseff code}	
1 PROC PRINT DATA=WORK.S0RTTennpTableSorti 1    OBS="Row number" 1 LABEL	
	
Locations for global statements or additional steps	
, <double click to insert code>
RUN;
, <double-dick to insert code>
r
End of task code.
V
RUN;QUIT;
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5
List Data
About the List Data task
The List Data task prints the observations in a SAS data set, using all or some of the variables. You can create a variety of reports, ranging from a simple listing to a highly customized report that groups the data and calculates totals and subtotals for numeric variables.
For example, you can use the Lis report that sums the expenses a sales region, compares these va expenses and revenues for the c number of observations in each ; whole report, and has a customi name of the region.
► Assigning variables to analysis
► Setting listing options
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The task help indicates the procedure name to search in the SAS syntax help.
SAS procedures used	PRINT
Required SAS products	^aase^Ksr^
Recommended additional	none
SAS products	
J
49
Procedure Syntax Help
Jp. SAS Documentation
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9 ft The PLOT Procedure + ft ThePMENU Procedure □ S The PRINT Procedure
\^} Overview: PRINT Procedure
|i] PROC PRINT Statement |] BY Statement ^ ID Statement |] PAGEBY Statement |] SUM Statement D SUM BY Statement ff) VAR Statement \^\ Results: Print Procedure B ft Examples: PRINT Procedure 9       The PRINTTO Procedure + ft The PROTO Procedure + ft The PRTDEF Procedure El ft The PRTEXP Procedure 9 ft TheFWENCODE Procedure B ft The RANK Procedure B ft The REGISTRY Procedure S ft The REPORT Procedure + ft The SCAPROC Procedure B ft The SOAP Procedure + ft The SORT Procedure + CD Ttle SQL Procedure B ft The STANDARD Procedure + ft The SUMMARY Procedure a ft The TABULATE Procedure + ft The TEMPLATE Procedure a ft The TIMEPLOT Procedure B ft The TRANSPOSE Procedure + ft The T RAN TAB Procedure B ft The UNIVARIATE Procedure
Previpus Page  |   Next Page The PRINT Procedure
Syntax: PRINT Procedure
Tip: Supports the Output Delivery System. See Output Delivery System: Basic Concepts in SAS Output Delivery System: User's Guide for details.
Tip: You can use the ATTRIB, FORMAT, LABEL, and WHERE statements. See Statements with the Same Function in Multiple Procedures for details. You can also use any global statements. See Global Statements for a list.
Table of Contents: The PRINT Procedure
PROC PRINT <option(s)>;
BY <DESCENDING> variable-1 <...<DESCENDING> variable-nxNOTSORTEDo;
PAGEBY BY-variable, SUM BY BY-variable,
ID variable(s) <option>: SUM variablefs) <option>, VAR variable(s) <option>;
Task	Statement
Print observations in a data set.	PROC PRINT
I Produce a separate section of the report for    I BY	
2. Pokročilé programování v SAS
Running a SAS Program
What resources are required to run a SAS program? The programmer must perform the following tasks:
determine program specifications
write the program
test the program
execute the program IL^i maintain the program I
Running a SAS Program
• The computer must perform the following actions
• load the required SAS software into memory
• compile the program
• read the data
• execute the compiled program
• store output data files
• store output reports
3^01733473
What Resources Are Used?
CPU
bandwidth
data storage space
54
Understanding Efficiency Trade-offs
• When you decrease the use of one resource, the use of other resources might increase.
• Resource usage is dependent on your data. A specific technique might be more efficient with one data set and less efficient with another.
55
Understanding Efficiency Trade-offs
Data
Space
Decreasing the size of a SAS data set can result in an increase in CPU usage.
56
Understanding Efficiency Trade-offs
il
i/o
Decreasing the number of I/O operations comes at the expense of increased memory usage.
Memory
57
Deciding What Is Important for Efficiency
Your Programs
Your Site
Your Data
58
Understanding Efficiency at Your Site
<c3Copj-L^it L930, 1991, 199? Cwr*]l Urlwrskty {cJCopyf L=ht i3S9-i99L Tin Un la rf hValartd KcJtjjp^rLghl 1388 C*-r»gL* hellem Lkilverttty
Operating Environment
jjLo -Ho. C* 9*3W U.S.A.
ir., !
Ml].
asm
iitVEF: ■ tf09
SSSOPT   ■ -utoolt -rt> -O00> -üW_rt IHH1H - Ajar/^Ij'iiii^/tWtrLbu'iiali/Li^^LocjiL/KllfH/'PwiJ/uSr/lätii s/Cmfg/ un; /=a s/nfiWVtoo [*/ un; /sa irt oo Ls/pun
S     Sw n
Bf Gdk Setup Contrail tUfyMc&u Hdp
j pm] Pis] pis] pit] nej m] reo] raj re?j pa] re*] cu»r| p*2j
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Um. dyllc«tlcn, or dltclc I ■<•! trict lo
Rights For
SAS Environment
forth in Ff* 52.227-19(cHl,2>. You K*ve Mil. SDSOrV   = 609 SBSVER   = «609
SSSOPT   ■ -"tools -ro -000.» -00©_r*
WNPAIH = Aar/»an: /uir/ccntr ih/»an: /cur /1 oca 1 /XJ
ÄToof9/iuri:/;a:/iii609,-'tool:J'«r:/:a:/tool :/«r.
59
B.^
Knowing How Your Program Will Be Used
• The importance of efficiency increases with the following:
• the complexity of the program and/or the size of the files being processed
• the number of times that the program will be executed
60
Knowing How Your Program Will Be Used
• What type(s) of data do you use?
a. SAS data sets
b. External files
c. Data from a relational database - for example, Oracle, Teradata, or SQL Server
d. Excel spreadsheets
e. OLAP cubes
f. Information maps
g. Other
Considering Trade-Offs
• In this class, many tasks are performed using one or more techniques.
• To decide which technique is most efficient for a given task, benchmark, or measure and compare, the resource usage of each technique.
• You should benchmark with the actual data to determine which technique is the most efficient.
The effectiveness of any efficiency technique depends greatly on the data with which you use the technique.
Running Benchmarks: Guidelines
• To benchmark your programming techniques, do the following:
• Turn on the appropriate options to report resource usage.
• Test each technique in a separate SAS session.
• Test only one technique or change at a time, with as little additional code as possible.
• Run your tests under the conditions that your final program
will use (for example, batch execution,
large data sets, and so on).
° continued.,
63
Running Benchmarks: Guidelines
• Run each program several times and base your conclusions on averages, not on a single execution. (This is more critical when you benchmark elapsed time.)
• Exclude outliers from the analysis because that data might lead you to tune your program to run less efficiently than it should.
• Turn off the options that report resource usage after testing is finished, because they consume resources.
In a multi-user environment, other computer activities might \      affect the running of your program.
64
Tracking Resource Usage
65
Tracking Resources with SAS Options
Windows, UNIX
OPTIONS STIMER	NOSTIMER; 1
	
OPTIONS NOFULLSTIMER | FULLSTIMER;
z/OS
Invocation option only
OPTIONS STATS	NOSTATS;
	
OPTIONS NOFULLSTIMER I FULLSTIMER
66
Business Scenario
• You should benchmark to determine the most efficient technique for creating a new variable based on a condition.
• The following methods can be used:
• IF-THEN with an assignment statement
• IF-THEN/ELSE with an assignment statement
• SELECT/WHEN with an assignment statement
67
1.07 Quiz
Open and submit p30iaoia.
Record the user CPU:___
Exit SAS. Start SAS.
Open and submit p30iaoib.
Record the user CPU:___
Exit SAS. Start SAS.
Open and submit p30iaoic. Record the user CPU:
Which technique is most efficient?
69
Sample Windows Log
5	options fullstimerj		
6	data _null_;		
7	length var $ 30;		
8	retain var2-var50 0 var51-var100 'ABC;		
9	do x=1 to 100000000;		
10	var1=10000000*ranuni(x);		
11	if var1>1000000 then var='Greater than 1,000,000';		
12	if 500000<=var1<=1000000 then var='Between 500,000	and	1,000,000';
13	if 100000<=var1<500000 then var='Between 100,000 and 500,000';		
14	if 10000<=var1<100000 then var='Between 10,000 and	100,	000';
15	if 1000<=var1<10000 then var='Between 1,000 and 10,	000'	■ J
16	if varKIOOO then var='Less than 1,000';		
17	end;		
18	run;		
NOTE	: DATA statement used (Total process time):		
	real time               1.26 seconds		
	user cpu time          0.98 seconds		
	system cpu time       0.04 seconds		
	Memory 278k		
	OS Memory 4976k		
	Timestamp                 6/29/2010   12:39:21 PM		
p301a01a
70
Sample UNIX Log
1 options fullstimer;
2 data _null_;
3 length var $30;
4 retain var2-var50 0 var51-var100 'ABC;
5 do x=1 to 10000000;
6 varl=10000000*ranuni(x);
7 if var1>10000000 then var='Greater than 1,000,000';
8 if 500000<=var1<=1000000 then var='Between 500,000 and 1,000,000';
9 if 100000<=var1<500000 then var='Between 100,000 and 500,000';
10 if 10000<=var1<100000 then var='Between 10,000 and 100,000';
11 if 1000<=var1<10000 then var='Between 1,000 and 10,000';
12 if varKIOOO then var='Less than 1,000';
13 end;
14 run;
NOTE: DATA statement used (Total process time)
6.62 seconds 5.14 seconds 0.01 seconds
real time user cpu time system cpu time Memory OS Memory
Timestamp 6/29/2010 Page Faults Page Reclaims Page Swaps
Voluntary Context Switches Involuntary Context Switches Block Input Operations Block Output Operations
526k 5680k 11:55:32 AM 82 0 0 91 48 91 0
p30iaoia
71
Objectives
• List the attributes of a data set page and define how it relates to the structure of SAS data sets.
• Describe how SAS reads and writes data.
SAS Data Set Pages
• A SAS data set page has the following attributes:
• It is the unit of data transfer between the operating system buffers and SAS buffers in memory.
• It includes the number of bytes used by the descriptor portion, the data values, and any operating system overhead.
• It is fixed in size when the data set is created, either
to a default value or to a value specified by the programmer.
74
Using PROC CONTENTS to Report Page Size
proc contents data=orion.sales_history; run;
Partial PROC CONTENTS Output
Engine/Host Dependent Information
16,384*18= 294,912 bytes
Data Set Page Size
Number of Data Set Pages
First Data Page
Max Obs per Page
Obs in First Data Page
Number of Data Set Repairs
File Name
Release Created
Host Created
	
16384	
,18	
1
92 72 0
S: \workshop\sales_history.sas7bdat 9.0201MO XP PRO
75
Reading External Files
Input Raw Data
r
memory
Reading External Files
Input Raw Data
i/o
measured here
o
Caches
Data might be cached in storage devices. On UNIX and Windows, data can also be cached by the OS file system.
memory
Reading External Files
Input Raw Data
i/o
measured here
Caches
Buffers
Input Buffer
memory
Reading External Files
Input Raw Data
measured here
o
Caches
Buffers
Input Buffer
memory
PDV
Data is converted from external
format to SAS format.
ID	Gender	Country	Name
			
79
Reading External Files
Input Raw
i/o
measured here
fr
Buffers
Buffers
Input Buffer
memory
Data is converted from external
format to SAS format.
PDV		1		
	ID	Gender	Country	Name
				
80
Reading External Files
Input Raw
i/o
measured here
fr
Output SAS
i/o
measured here
Buffers
Buffers
Input Buffer
memory
Data is converted from external
format to SAS format.
PDV		1		
	ID	Gender	Country	Name
				
81
Reading a SAS Data Set with a SET Statement
Input SAS
r
memory
82
Reading a SAS Data Set with a SET Statement
Data might be cached in storage devices. On UNIX and Windows, data can also be cached by the OS file system.
memory
Reading a SAS Data Set with a SET Statement
t ir\
Reading a SAS Data Set with a SET Statement
Input SAS
i/o
measured here
No data conversion is necessary.
memory
PDV
ID	Gender	Country	Name
			
85
Reading a SAS Data Set with a SET Statement
Input SAS
i/o
measured here
No data conversion is necessary.
memory
PDV
	ID	Gender	Country	Name
				
86
Reading a SAS Data Set with a SET Statement
Input SAS
i/o
measured here
No data conversion is necessary.
memory
PDV
	ID	Gender	Country	Name
				
87
Reading a SAS Data Set with a SET Statement
i/o
measured here
Input SAS
d Caches -y)
o
o
Output SAS
i/o
measured here
No data conversion is necessary.
memory
PDV
	ID	Gender	Country	Name
				
88
Reading a SAS Data Set with a SET Statement
Chapter 2: Controlling I/O Processin
and Memory
2.1: Controlling I/O
2.2: Controlling Data Set Size
P 2.3: Compressing SAS Data Sets Br^^^F 2.4: Controlling Memory (Self-Study)
I/O (Review)
• SAS programs typically perform the following tasks
• reading data sets sequentially
• performing analysis and data manipulation
• writing data sets sequentially or writing reports
I/O is one of the most important factors for optimizing performance.
Where Is I/O Measured? (Review)
i/o
measured here
here
o
Buffers
* Caches
Output SAS Data
t
Buffers
memory
PDV
ID	Gender	Country	Name
			
i/o
measured here
* Windows and UNIX Only
Using the Operating Environment Cache in Windows and UNIX
• Windows and UNIX use a file-caching mechanism in the background.
• A file cache is an area in memory that holds recently accessed data.
• By default, SAS reads and writes data through the operating environment file cache, not by direct I/O.
• File caching is beneficial if the same data is used more than once.
• File caching adds overhead to sequential I/O.
93
Techniques for Reducing I/O Operations
1. Minimize the number of variables and observations.
2. Reduce the number of times that the data is processed.
3. Create a SAS data file when you process the same raw data file repeatedly.
4. Use the SASFILE statement to process a small SAS data set repeatedly.
5. Minimize the size of the SAS data set.
6. Use appropriate BUFSIZE= and/or BUFNO= options for
random or sequential access. .. ,
^ continued.,
94
Techniques for Reducing I/O Operations
7. Bypass system file caching in Windows and UNIX.
8. Create views in programs that require intermediate temporary SAS data files.
9. Create indexes on variables used for WHERE processing.
Technique 1: Process Only the Necessary Variables and Observations
Simple techniques can conserve I/O. The amount of I/O saved depends on the size of the subset being processed.
• Reduce the number of variables.
DROP or KEEP statements
• DROP= or KEEP= data set options
• Reduce the number of observations.
• WHERE statement
• WHERE= data set option
• OBS= and FIRSTOBS= data set options
96
Subsetting Data
Program 1: Subsetting in the Procedure
One way to create a subset is to use the WHERE statement in a procedure.
data bonus;
set orion.staff;
YrEndBonus=Salary*0.05; run;
proc means data=bonus mean sum;
where Job_Title contains  'Manager';
class Manager_ID;
var YrEndBonus; run;
f     The data set bonus contains 11 variables and 424 observations.
p302d01
97
Subsetting Data
• Program 2: Subsetting in the DATA Step
Because the DATA step is required to create the variable YrEndBonus, it is more efficient to subset in the DATA step.
data bonus(keep=Manager_ID YrEndBonus);
set orion.staff(keep=Job_Titie Salary Manager_ID); where Job Title contains   'Manager';
YrEndBonus=Salary*0.05; run ;
proc means data=bonus mean sum;
I/O savings result from reducing the number of variables and observations in the input and output data sets.
class Manager_ID; var YrEndBonus;
run ;
/S     The data set bonus contains two variables and 41 observations.
p302d01
98
Using the KEEP=/DROP= Options
Input SAS Data
i/o
measured here
I/O measured here
Buffers
I
KEEP=/DROP= data set option on the input data set
memory
Buffers
N^Job ^Yitle	^Salary	Manager ID	YrEnd Bonus
			
KEEP=/DROP= data set option on the output data set (KEEP/DROP statement in the DATA step)
99
Setup for the Poll
p302doi Program 1
data bonus;		
set orion.staff; YrEndBonus=Salary*0.05;		
run ; proc means data=bonus mean sum; where Job Title contains  'Manager'; class Manager ID; var YrEndBonus; run ;	I/O savings results from reducing the number of variables and observations in the input and output data sets.	
p302d01 Program 2		
data bonus(keep=Manager ID YrEndBonus);		
set orion.staff(keep=Job Title Salary Manager ID);		
where Job Title contains  'Manager';		
YrEndBonus=Salary*0.05;		
run ;		
proc means data=bonus mean sum;		
class Manager ID;		
var YrEndBonus;		
run ;		
101
2.01 Multiple Choice Poll
• In addition to the I/O decrease when the DATA step creates bonus, where does Program 2 have additional decrease of I/O?
a. Fewer variables are read into the program data vector from orion.staff in Program 2 because of the KEEP= data set option.
b. The PROC MEANS in Program 2 loads a smaller version of bonus.
c. There is no additional decrease in I/O; all of the decrease in I/O occurs when the data set bonus
is created by the DATA step.
102
2.01 Multiple Choice Poll - Correct Answer
• In addition to the I/O decrease when the DATA step creates bonus, where does Program 2 have additional decrease of I/O?
a. Fewer variables are read into the program data vector from orion.staff in Program 2 because of the KEEP= data set option.
bjhe PROC MEANS in Program 2 loads a smaller version of bonus.
c. There is no additional decrease in I/O; all of the decrease in I/O occurs when the data set bonus is created by the DATA step.
103
Technique 2: Reducing the Number of Times that Data Is Processed
• The following techniques reduce the number of times that data is processed:
• Subset data within a procedure step if possible.
• Create SAS data files. SAS can process SAS data files more efficiently than raw data files.
• Use engines efficiently.
• Use indexes.
• Access data through SAS views.
104
Subsetting Data within a Procedure Step
• Program 1: Subset in the DATA Step
• You can subset in the DATA step first, and then execute the
data big salaries;	
set orion.staff;	
where Salary > 50000;	
run;	
proc means data=big salarj	Les mean sum;
class Manager ID;	
var Salary;	
run;	
p302d02
Subsetting Data within a Procedure Step
• Program 2: Subset in the Procedure
• A better way is to execute only one step and subset in that step.
proc means data=orion.staff class Manager ID; var Salary; where Salary > 50000;	mean sum;	
	I/O savings results from avoiding an extra step for subsetting.	
run;		
		
106
Technique 3: Creating a SAS Data File
Program 1:    Write two programs. Each program should create a temporary
SAS data set to read in the same raw data file and create a report.
data prices;	
infile  'prices.dat1 dlm='*';	
input Product ID  :  12 .  Start Date  :  date9.	End Date  :  date9.
Unit Cost Price:dollar7.2 Unit Sales	Price:dollar7.2;
run ;	
proc print data=prices(obs=5);	
titlel "Prices Data Set";	
run ;	
	
I data prices;
infile  'prices.dat1 dlm='*';
input Product ID  :  12.  Start Date  :  date9.  End Date  : date9.
Unit_Cost_Price:dollar7.2 Unit_Sales_Price:dollar7.2;
run ;
proc means data=prices(keep=Unit_Cost_Price Unit_Sales_Price);
var Unit_Cost_Price Unit_Sales_Price; run ;
p302d03
107
Creating a SAS Data File
Program 2:    Create a permanent SAS data set by reading
in the raw data file one time. Write two programs using the SAS data set to create a report.
data orion.prices;
infile  fprices.datf dlm=f*f;
input Product_ID  :   12. Start_Date End_Date  : date9. Unit_Cost_Price  : dollar7.2 Unit_Sales_Price  :  dollar7.2
run ;
proc print data=orion.prices(obs=5);
titlel  "Prices Data Set"; run ;
date9.
I/O savings from reading the raw data once
proc means data=orion.prices
(keep=Unit_Cost_Price Unit_Sales_Price); var Unit_Cost_Price Unit_Sales_Price; run ;
108
Technique 4: SASFILE Global Statement
If your program uses the same data set multiple times, the SASFILE statement can reduce I/O resources.
• The SASFILE statement loads the SAS data set into memory in its entirety, instead of a few pages at
a time.
• After it is loaded, the data set is held in memory for subsequent DATA and PROC step processing.
• A second SASFILE statement closes the file and frees the SAS buffers.
• It is useful for data sets that fit entirely into memory.
• The SASFILE statement should not be used if the data set is larger than available physical memory.
The reduction in I/O resources comes at the cost of increased memory usage.
109
Business Scenario
Create reports using the PRINT, TABULATE, MEANS, and FREQUENCY procedures against a single SAS data set.
sasfile orion.customer dim load;
proc freq data=orion.cus
tables Customer_Country Customer_T; run;
proc print data=orion.customer_dim no< where Customer_Type=1 Orion Club Go var Customer_ID Customer_Name Cust<
run;
proc means data=orion.customer_dim me
var Cu s tome r_Age;
clas s Customer_Group; run;
proc tabulate data=orion.customer_dim class Customer_Age_Group Customer_ table Customer_Type All=Total,
Customer_Age_Group*n=1   1 All
run;
sasfile orion.customer dim close;
The orion.customer_dim data set is read into memory only once instead of four times. This results
in one-fourth as many I/O operations, which can also reduce elapsed time. However, it comes at the expense of increased memory
usage.
=Total*n=' '/rts=45;
p302d04
no
SASFILE Global Statement
• General form of the SASFILE statement:
SASFILE <libref.>member-name
< (password-data-set-option(s)) > OPEN | LOAD | CLOSE;
• When the SASFILE statement executes, SAS allocates the number of buffers based on the number of pages in the SAS data set and index file.
• If the file in memory increases in size during processing by editing or appending data, the number of buffers also increases.
in
2.2: Controlling Data Set Size
2.3: Compressing SAS Data Sets
2.4: Controlling Memory (Self-Study)
r
Objectives
• List techniques to reduce data storage.
• Describe how SAS stores numeric values.
• Describe how to safely reduce the space required to store numeric values in SAS data sets.
Techniques for Reducing Data Set Size
1. Store integers as reduced-length numerics.
2. Compress the data set.
• /f Reducing the size of a SAS data set reduces the I/O required to process it.
114
Characteristics of Numeric Variables
• Numeric variables have the following characteristics:
• are stored as floating-point numbers in real-binary representation
• store multiple digits per byte
• use a minimum of one byte to store the sign and exponent of the value (depending on the operating environment) and use the remaining bytes to store
the mantissa of the value
take 8 bytes of storage per variable, by default, but can be reduced in size
• always have a length of 8 bytes in the PDV
115
Default Length of Numeric Variables
The number 35,298 can be written as follows:
^P-3529Q* ( ip* * ^) Sign Mantissa Base Exponent
SAS stores numeric variables in floating-point form:
/
Exponent
Mantissa
116
Assigning the Length of Numeric Variables
You can use a LENGTH statement to assign a length from 2 to 8 bytes to numeric variables.
data emps_short;
length Street_ID 6
Employee_ID Manager_ID 5 Street_Number Employee_Hire_Date Employee_Term_Date Birth_Date Salary 4 Dependents 3; merge employee_addresses
employee_organization employee_payrol1 employee_phones; by Employee_ID; run;
If the variable is numeric, the length applies only to the output data set. If the variable is character, the length applies to the program data vector and the output data set.
p302d05
117
Comparing Results
• To determine whether the data sets emps_short and emps are equivalent, you can use the COMPARE procedure.
proc compare data=emps compare=emps_short; run;
118
Comparing Data Sets
The COMPARE Procedure Comparison of WORK.EMPS with WORK.EMPS_SHORT
(Method=EXACT)
Observation Summary
Observation        Base Compare
First Obs 1 1
Last   Obs 923 923
Number of Observations in Common: 923.
Total Number of Observations Read from WORK.EMPS: 923.
Total Number of Observations Read from WORK.EMPS_SHORT: 923.
Number of Observations with Some Compared Variables Unequal: 0. Number of Observations with All Compared Variables Equal: 923.
NOTE: No unequal values were found. All values compared are exactly equal.
119
Possible Storage Lengths for Inte Values
• Windows and UNIX
Length (bytes)	Largest Integer Represented Exactly
3	8,192
4	2,097,152
5	536,870,912
6	137,438,953,472
7	35,184,372,088,832
8	9,007,199,254,740,992
Possible Storage Lengths for Inte Values
Length      Largest Integer (bytes)      Represented Exactly
2	256
3	65,536
4	16,777,216
	4,294,967,296
6	1,099,511,627,776
7	281,474,946,710,656
8 72,057,594,037,927,936
Assigning the Length of Numeric Variables
• The use of a numeric length less than 8 bytes does the following:
• causes the number to be truncated to the specified length when the value is written to the SAS data set
This reduces the number of bytes available for the mantissa, which reduces the precision of the number that can be accurately stored.
• causes the number to be expanded to 8 bytes in the PDV when the data set is read by padding the mantissa with binary zeros
f   Numbers are always 8 bytes in length in the PDV.
122
Dangers of Reduced-Length Numeric Variables
• It is not recommended that you change the length of non-integer numeric variables.
data test;
length x 4;
X=l/10;
Y=l/10; run ;
data _null_;
set test;
put X=;
put Y=; run ;
p302a01
123
2.02 Poll
Open the program p302aoi and submit it. Look at the log.
Are the values of X and Y equal?
O Yes O No
2.02 Poll - Correct Answer
Open the program p302aoi and submit it. Look at the log.
Are the values of X and Y equal?
O Yes
umeric Precision
Partial SAS Log (Windows)
7     data test;		
8          length x 4;		
9 X=1/10;		
10 Y=1/10;		
11 run;		
NOTE: The data set WORK.TEST has 1 observations and 2 variables.		
NOTE: DATA statement	used	(Total process time):
real time		0.00 seconds
cpu time		0.00 seconds
12		
13    data _null_;		
14        set test;		
15         put X=;		
16         put Y=;		
17 run;		
x=0.0999999642		
y=0.1		
NOTE: There were 1 observations read from the data set WORK.TEST.		
NOTE: DATA statement	used	(Total process time):
real time		0.03 seconds
cpu time		0.00 seconds
127
Dangers of Reduced-Length Numeric Variables
• It is not recommended that you reduce the length of integer numeric variables inappropriately or that you reduce the length of variables that hold large integer numeric values. This example illustrates the effect of inappropriately reducing integer values.
data test;
length X 3;
X=8193; run;
data _null_;
set test;
put X=; run;
p302d07
128
Numeric Precision
120 data test;
121 length X 3;
122 X=8193;
123 run;
NOTE: The data set WORK.TEST has 1 observations and 1 variables. NOTE: DATA statement used (Total process time):
real time 0.00 seconds
cpu time 0.00 seconds
124
125 data _null_;
126 set test;
127 put X=;
128 run;
x=8192
NOTE: There were 1 observations read from the data set WORK.TEST. NOTE: DATA statement used (Total process time):
real time 0.00 seconds
cpu time 0.00 seconds
129
Advantages and Disadvantages
of Reduced-Length Numeric Variables
Advantages	Disadvantages
Conserves data storage        Uses additional CPU to read space	
Requires less I/O to read	Can alter high-precision values such as non-integer and large integer values
130
2.1: Controlling I/O
2.2: Controlling Data Set Size
2.3: Compressing SAS Data Sets
Objectives
• Define the structure of a compressed SAS data file.
• Create a compressed SAS data file.
• List the advantages and disadvantages of compression.
Simplified Uncompressed Data File Structure
	24/40 byte OH	Obs 1	Obs 2	Obs 3	Obs 4	Obs 5	*	1 bit/ obs OH		Descriptor		
	24/40 byte OH	Obs 6	Obs 7	Obs 8	Obs 9	Obs 10	Obs 11		Obs 12		*	1 bit/ obs OH
	■ ■ ■	■ ■ ■	■ ■ ■	■ ■ ■	■ ■ ■	■ ■ ■	■ ■ ■		■ ■ ■		■ ■ ■	■ ■ ■
	24/40 byte OH	Obs X	Obs y	Obs z	*	Unused space						1 bit/ obs OH
Uncompressed SAS Data File
The following are features of uncompressed SAS data files:
• All observations use the same number of bytes.
• Each variable occupies the same number of bytes in every observation.
• Character values are padded with blanks.
• Numeric values are padded with binary zeros.
• The descriptor portion of the data set uses part
of the first data set page.
r ° continued...
134
Uncompressed SAS Data File
• There is a 24-byte overhead at the beginning of each page on 32-bit systems.
• There is a 40-byte overhead at the beginning of each page on 64-bit systems.
• There is a l-bit per observation overhead, rounded up to the nearest byte.
• New observations are added at the end of the file. If a new page is needed for a new observation,
a whole data set page is added.
• Deleted observation space is never reused, unless the entire data file is rebuilt.
135
Simplified Structure of a Compressed Data Set
12 I 24 bytes/
obs
OH
Obs 7
Obs 6
Obs 5
O b s 4
Obs 3
Obs 2
0 b s
1
Descriptor
12 I 24 bytes/ obs OH
Obs 16
O b s
15
Obs 14
Obs 13
Obs 12
O b s 11
Obs 10
Obs 9
O b s 8
Page
24 I 40 byte OH
12 I 24 bytes/ obs OH
O b s
Obsz
Unused space
136
Compressed SAS Data File
Features of compressed SAS data files:
• Each observation is a single string of bytes. Variable types and boundaries are ignored.
• Each observation can have a different length.
• Consecutive repeating characters and numbers are collapsed into fewer bytes.
• If an updated observation is larger than its original size, it is stored on either the same data set page or on a different page with a pointer to the original page.
• The descriptor portion of the data set is stored at the end of the first data set page. continued.
137
Compressed SAS Data File
• There is a 24-byte overhead at the beginning of each page on 32-bit systems.
• There is a 40-byte overhead at the beginning of each page on 64-bit systems.
• There is a 12-byte-per-observation overhead on 32-bit systems.
• There is a 24-byte-per-observation overhead on 64-bit systems.
• Deleted observation space can be reused if the REUSE=YES data set or system option was turned
on when the SAS data file was compressed.
Compressing SAS Files
There are two different algorithms that can be used to compress files:
• the RLE (Run Length Encoding) compression algorithm (COMPRESS=YES | CHAR)
• the RDC (Ross Data Compression) algorithm /\ (COMPRESS=BINARY)
The optimal algorithm depends on the characteristics of your data.
139
Creating a Compressed Data File
• To create a compressed data file, use the COMPRESS= output data set option or system option.
• General forms of the COMPRESS= options:
SAS-data-set(COMPRESS=NO | YES | CHAR | BINARY) OPTIONS COMPRESS=NO | YES | CHAR | BINARY;
140
Comparing Compression Method!
• COMPRESS=YES | CHAR
• is effective with character data that contains repeated characters (such as blanks).
• COMPRESS=BINARY
• takes significantly more CPU time to uncompress than COMPRESS=YES | CHAR
• is more efficient with observations greater than a 1000 bytes in length
• can be very effective with numeric data
• can be effective with character data that contains patterns, rather than simple repetitions.
2.04 Quiz
Open the program p302ao2.
1. Change the data set name to empchar. Add the
COMPRESS=CHAR data set option to the DATA
step and submit the program.
By what percentage was the data set reduced or
increased?
2. Change the data set name to empbin. Add the
COMPRESS=BINARY data set option to the DATA
step and submit the program.
By what percentage was the data set reduced or
increased?
2.04 Quiz - Correct Answer
Open the program p302ao2.
l. Change the data set name to empchar. Add the
COMPRESS=CHAR data set option to the DATA
step and submit the program.
By what percentage was the data set reduced or
increased?
data empchar(compress=char); merge employee_addresses
employee_organization employee_payroll employee_phones; by Employee_ID; run ;
continued.,
144
Using the COMPRESS=CHAR Option
• Partial SAS Log (Windows)
44
45 data empchar(compress=char);
46 merge employee_addresses employee_organization
47 employee_payroll employee_phones;
48 by Employee_ID;
49 run;
NOTE: There were 424 observations read from the data set WORK.EMPLOYEE_ADDRESSES. NOTE: There were 424 observations read from the data set WORK.EMPLOYEE_ORGANIZATION. NOTE: There were 424 observations read from the data set WORK.EMPLOYEE_PAYROLL. NOTE: There were 923 observations read from the data set WORK.EMPLOYEE_PHONES. NOTE: The data set WORK.EMPCHAR has 923 observations and 21 variables. NOTE: Compressing data set WORK.EMPCHAR decreased size by 60.71 percent.
Compressed is 11 pages; un-compressed would require 28 pages. NOTE: DATA statement used (Total process time):
real time 0.04 seconds
cpu time 0.01 seconds
145
2.04 Quiz - Correct Answer
Open the program p302ao2.
2. Change the data set name to empbin. Add the
COMPRESS=BINARY data set option to the DATA
step and submit the program.
By what percentage was the data set reduced or
increased?
data empbin(compress=binary); merge employee addresses
employee employee employee
organization payroll phones;
by Employee ID
run;
Using the COMPRESS=BINARY Option
• Partial SAS Log (Windows)
50	data empbin(compress=binary);	
51	merge employee_addresses employee_organization	
52	employee_payroll employee_phones;	
53	by Employee_ID;	
54	run;	
note:	There were 424 observations read from the data set W0RK.EMPL0YEE_	addresses.
note:	There were 424 observations read from the data set W0RK.EMPL0YEE_	"organization.
note:	There were 424 observations read from the data set W0RK.EMPL0YEE_	"payroll.
note:	There were 923 observations read from the data set W0RK.EMPL0YEE_	>H0NES.
note:	The data set work.empbin has 923 observations and 21 variables.	
note:	Compressing data set work.empbin decreased size by 57.14 percent	■
	Compressed is 12 pages; un-compressed would require 28 pages.	
note:	data statement used (Total process time):	
	real time               0.03 seconds	
	cpu time                 0.03 seconds	
147
Summary of Compression Results
Data Set	Option	Algorithm	Number	Decreased
	Used	Used	of Bytes	Size
employees	None	None	458,752	0%
empchar	YES|CHAR		180,224	60.71%
empbin	BINARY	RDC	196,608	57.14%
• f   Your results might differ, depending on SAS option settings and the operating system.
148
How SAS Compresses Data
A SAS data file has these variables:
Name
LastName FirstName
Type
Character Character
Length
20 15
• In uncompressed form, all observations use 35 bytes for these two variables.
Input Buffer 1 2
1	2	3	4	5	6	7	8	9	0	1	2	3	4	5	6	7	8	9	0	1	2	3	4	5
A	D	A	M	S																B	i	1	1	
3 5
LastName
FirstName
149
YES
Using COMPRESS=CHAR
• In run-length encoding compressed form, the LastName and FirstName values for this observation use only 13 bytes.
1
123456789 0123
e	A	D	A	M	S	#	e	B	I	L	L	#
FirstName
The @ is a symbol that indicates how many uncompressed characters follow.
The # is a symbol that indicates the number of blanks repeated at this point in the observation.
Using COMPRESS=BINARY
• Ross Data Compression uses both run-length encoding and sliding window compression.
A SAS data set has these variables:
Name Type Length
Answerl Numeric 8
Answer200        Numeric 8
• In uncompressed form, the SAS data file resembles this:
Answerl	Answer2       Answer3 Answer4			Answer5 Answer6		...	Answer200
1	2 1		2	1 1	2	...	2
1	1	1	1	1	1	...	1
2	2	2	2	2	2	...	2
151
Using COMPRESS=BINARY
• In Ross Data Compression form, the first observation in the data file resembles this:
123456 789
	+				+			
@		1	#	@		2	#	O, "O
	1				1			
• The @ is a symbol that indicates how many uncompressed characters follow.
• The # is a symbol that indicates the number of binary zeros repeated at this point in the observation.
• The % is a symbol that indicates how many times these values are repeated.
Compression Dependencies
/i\ Some data sets do not compress well or at all.
• Because there is higher overhead for each observation, a data file can occupy more space in compressed form than in uncompressed form if the file has the following characteristics:
• few repeated characters
• small physical size
• few missing values
• short text strings
153
Compression Dependencies
1 data orders(compress=yes);
2 set orion.orders;
3 run;
NOTE: There were 490 observations read from the data set ORION.ORDERS. NOTE: The data set WORK.ORDERS has 490 observations and 6 variables. NOTE: Compressing data set WORK.ORDERS decreased size by 0.00 percent.
Compressed is 7 pages; un-compressed would require 7 pages. NOTE: DATA statement used (Total process time):
real time 1.04 seconds
cpu time 0.12 seconds
55    data orders(compress=binary);
56        set orion.orders; 57 run;
NOTE: There were 490 observations read from the data set ORION.ORDERS. NOTE: The data set WORK.ORDERS has 490 observations and 6 variables. NOTE: Compressing data set WORK.ORDERS increased size by 28.57 percent. Compressed is 9 pages; un-compressed would require 7 pages. NOTE: DATA statement used (Total process time): real time 0.09 seconds
cpu time 0.09 seconds p302d08
Compression Dependencies
• When you use the COMPRESS= data set option or the COMPRESS= system option, SAS knows the following:
• the size of the overhead introduced by compression
• the maximum size of an observation
• If the maximum size of the observation is less than the 12-byte (32-bit systems) or 24-byte (64-bit system) overhead introduced by compression, SAS does the following:
• disables compression
• creates an uncompressed data set
• issues a note stating that the file was not compressed
155
Compression Dependencies
SAS Log (Windows)
18 data test(compress=yes);
19 x=1;
20 run;
NOTE: Compression was disabled for data set WORK.TEST because
compression overhead would increase the size of the data set.
NOTE: The data set WORK.TEST has 1 observations and 1 variables.
NOTE: DATA statement used (Total process time): real time 0.00 seconds
cpu time 0.00 seconds
p302d09
156
Compression Trade-Offs
Uncompressed	Compressed
Usually requires more disk	Usually requires less disk
storage	storage
Requires less CPU time to	Requires more CPU time to
prepare an observation for I/O	prepare an observation for I/O
Uses more I/O operations	Uses fewer I/O operations
The savings in I/O operations greatly outweigh the increase in CPU time.
continued...
157
Compression Trade-Offs
Uncompressed	Compressed
An updated observation fits in     An updated observation might its original location.                 be moved from its original location.	
Deleted observation space is never reused.	Deleted observation space can be reused.
New observations are always When REUSE=YES, new inserted at the end of the data observations might not be file. inserted at the end of the data
file.
158
2.1: Controlling I/O
2.2: Controlling Data Set Size
2.3: Compressing SAS Data Sets
2.4: Controlling Memory (Self-Study)
Objectives
• Investigate techniques for controlling memory.
• Use system options to specify the amount of available memory.
Comparing Memory, I/O, and CPU Resources
• The techniques that reduce CPU and I/O can increase memory usage.
• Efficient use of the I/O subsystem uses larger buffers and/or multiple buffers.
• These buffers share memory space with the other memory demands of your SAS session.
Benchmark carefully to balance the need to conserve memory with the need to reduce CPU and I/O.
161
Reducing Memory Usage
• Use small data set page sizes when you create data sets that will be accessed in a sparse, random pattern.
Use a single read buffer when the data is accessed randomly instead of sequentially.
• Use BY-group processing instead of CLASS statements in those procedures that support both, especially where you have pre-sorted data or can
use an existing index.
162
Using the BY Statement
• Instead of using a CLASS statement to group data, you can use the BY statement to specify the variables whose values define the subgroup combinations for an analysis by a SAS procedure.
163
Using the BY Statement
What are the differences between using a BY statement and using a CLASS statement in a procedure?
BY Statement	CLASS Statement
The data set must be sorted or       The data set does not need to be indexed on the BY variables.          sorted or indexed on the CLASS variables.	
BY-group processing holds only one BY group in memory at a time.	The CLASS statement accumulates aggregates for all CLASS groups simultaneously in memory.
A percentage for the entire report     A percentage for the entire report cannot be calculated with can be calculated with procedures
procedures such as the REPORT such as the REPORT or or TABULATE procedures. TABULATE procedures.
164
PROC MEANS with a BY Statement
proc means data=orion.or	rder fac	:t mean me	m
maxdec=2;			
format Order Date yea	Lr4 . ;		
by Order Date;			
var Quantity CostE	>rice P€	*r Unit;	
run;			
p302dl0
165
PROC MEANS with a BY Statement
Partial PROC MEANS Output with a BY Statement
Date Order was placed by Customer=2003-The MEANS Procedure
Variable
Label
Mean
Median
Quantity
Total_Retail_Price CostPrice Per Unit
Quantity Ordered
Total Retail Price for This Product Cost Price Per Unit
1.82 177.59 42.72
2.00 105.95 31 .80
Variable
--- Date Order was placed by Customer=2004 Label
Mean
Median
Quantity
Total_Retail_Price CostPrice Per Unit
Quantity Ordered
Total Retail Price for This Product Cost Price Per Unit
1.69 146.13 37.10
1 .00 85.65 25.68
166
PROC MEANS with a CLASS Statement
proc i	neans data=orion.ox	rder fac	:t mean me	m
	maxdec=2;			
	rmat Order Date yea	Lr4 . ;		
cl<	ass Order Date;			
va:	c Quantity CostE	>rice	*r Unit;	
run ;				
p302dl0
167
PROC MEANS with a CLASS Statement
The MEANS Procedure
Date Order was placed
by N
Customer	Obs	Variable	Label			Mean	Median
2003	128	Quantity Total_Retail_Price Cost Price_Pe r_Unit	Quantity Ordered Total Retail Price for Cost Price Per Unit	This	Product	1 .82 177.59 42.72	2.00 105.95 31 .80
2004	108	Quantity Total_Retail_Price Cost Price_Pe r_Unit	Quantity Ordered Total Retail Price for Cost Price Per Unit	This	Product	1 .69 146.13 37.10	1 .00 85.65 25.68
2005	90	Quantity Total_Retail_Price Cost Price_Pe r_Unit	Quantity Ordered Total Retail Price for Cost Price Per Unit	This	Product	1 .70 187.20 49.45	1 .00 77.00 25.20
2006	143	Quantity Total_Retail_Price Cost Price_Pe r_Unit	Quantity Ordered Total Retail Price for Cost Price Per Unit	This	Product	1 .57 149.70 44.25	1 .00 92.80 29.95
2007	148	Quantity Total_Retail_Price Cost Price_Pe r_Unit	Quantity Ordered Total Retail Price for Cost Price Per Unit	This	Product	1 .93 157.49 37.53	2.00 80.95 21 .35
168
Using Memory System Options
• The operating environment will use disk-based virtual memory when physical memory is depleted. This adversely affects performance.
• Use these SAS system options to limit the amount of memory used by SAS:
• REALMEMSIZE=
• MEMSIZE=
/A   Set the REALMEMSIZE= and MEMSIZE= options
to values below the amount of available physical memory to prevent page thrashing or memory swapping.
169
Using System Options to Control Memory
• The total amount of memory that a SAS job can consume is limited by the MEMSIZE= invocation system option.
-MEMSIZE=n | n K | n M | n G | hexX | MIN | MAX I
170
Using the MEMSIZE= Option
• The MEMSIZE= option places a limit on the total amount of memory that SAS dynamically allocates at any time. This memory is supported by a combination of real memory and space for utility files on disk.
• Increase this option s value in small increments until you find your optimal value.
f       SAS does not automatically reserve or allocate the amount of memory that you specify in the MEMSIZE= system option. SAS will use only as much memory as it needs to complete a process.
171
Using the REALMEMSIZE= System Option
• Some SAS procedures use the REALMEMSIZE= invocation option to specify how much memory * the procedure can allocate and use without inducing excessive page swapping.
-REALMEMSIZE=n | nK | nM | nG | hexX | MIN | MAX
• The REALMEMSIZE= option should never be set beyond the amount of real memory.
• In UNIX and z/OS, REALMEMSIZE= specifies real (physical) memory In Windows, REALMEMSIZE= specifies virtual memory
172
3. Pokročilé programování v SAS - indexy,...
173
3.2 Using an Index
V
s
3.3 Creating a Sample Data Set (Self-Study)
Objectives
• Define indexes.
• List the uses of indexes.
• Use the DATA step to create indexes.
Use PROC DATASETS to create and maintain indexes.
• Use PROC SQL to create and maintain indexes.
Simplified Index File
The index file consists of entries that are organized in a tree structure and connected by pointers.
Partial Listing of orion.saleshistory
Simplified Index
Customer ID	Employee ID	
14958	121031	
14844	121042	
14864	99999999	
14909	120436	
14862	120481	
14853	120454	
14838	121039	
14842	121051	
14815	99999999	
14797	120604	
•	•	
Customer ID Key Value	Record Identifier (RID) Page(obs, obs, ...)
4006	17(85)
4021	17(89)
4059	17(90)
4063	17(80, 86)
•	
14958	1(1, 24)
14972	1(14)
•	
The Purpose of Indexes
• Indexes can provide direct access to observations in SAS data sets to accomplish the following:
• yield faster access to small subsets (WHERE)
• return observations in sorted order (BY)
• perform table lookup operations (SET with KEY=)
• join observations (PROC SQL)
• modify observations (MODIFY with KEY=)
Why Use an Index?
• How is data processed if the input data is not indexed?
data customerl4958;
set orion.sales_history;
where Customer_ID=14958; run ;
178
Reading SAS Data Sets without an Index
Input SAS
r
179
Reading SAS Data Sets without an Index
Input SAS
\
Buffers
Data pages are loaded.
y The number of buffers available affects the I/O.
180
Reading SAS Data Sets without an Index
Input SAS
\
1
Buffers
Data pages are loaded.
The WHERE statement selects observations by reading data sequentially.
181
Reading SAS Data Sets without an Index
Input SAS
\
1
Buffers
Data pages are loaded.
The WHERE statement selects observations by reading data sequentially.
PDV
ID	Gender	Country	Name
			
182
Reading SAS Data Sets without an Index
Input SAS
Buffers
Buffers
The WHERE statement selects observations by reading data sequentially.
PDV
	ID	Gender	Country	Name
				
183
Reading SAS Data Sets without an Index
Input SAS
Buffers
Output SAS
Buffers
The WHERE statement selects observations by reading data sequentially.
PDV
	ID	Gender	Country	Name
				
184
Why Use an Index?
• How is data processed if the input data is indexed?
data customerl4958;
set orion.sales_history;
where Customer_ID=14958; run ;
185
Reading SAS Data Sets with an Index
I-------
Index
Input SAS
186
Reading SAS Data Sets with an Index
n
Index
Input SAS
The index file is checked.
187
Reading SAS Data Sets with an Index
n
Index
Input SAS
Buffers
Only necessary pages are loaded.
The index file is checked.
18
Reading SAS Data Sets with an Index
n
Index
Input SAS
Buffers
Only necessary pages are loaded.
The index file is checked.
The WHERE statement selects observations by using direct access.
189
Reading SAS Data Sets with an Index
n
Index
Input SAS
Buffers
Only necessary pages are loaded.
The index file is checked.
The WHERE statement selects observations by using direct access.
PDV
ID	Gender	Country	Name
			
190
Reading SAS Data Sets with an Index
n
Index
Input SAS
Buffers
Only necessary pages are loaded.
Buffers
The index file is checked.
The WHERE statement selects observations by using direct access.
PDV
	ID	Gender	Country	Name
				
191
Reading SAS Data Sets with an Index
n
Index
Input SAS
Output SAS
Buffers
Only necessary pages are loaded.
Buffers
The index file is checked.
The WHERE statement selects observations by using direct access.
PDV
	ID	Gender	Country	Name
				
192
How Is the Index File Checked?
Index
Output SAS
^ ___' Input	^^^^^^ L	Buffers
SAS M>ata-^	r 1	
Buffers
	
The index file is checked.	
When an index is used, a binary search is done on the index file.
PDV
	ID	Gender	Country	Name
				
193
Using a Binary Search
Partial Listing of
23
24
25
	orion.sales	history	
RID	Customer I D	Employee ID	
1	14958	121031	
2	14844	121042	
3	14864	99999999	
4	14909	120436	
•	•	•	
		
14844	121042	
14958	121031	
14821	120918	
		
Simplified Index File
where Customer ID=14958;
Customer ID Key Value	Record Identifier (RID) Page(obs, obs, ...)
4006	17(85)
4021	17(89)
4059	17(90)
4063	17(80, 86)
•	
14958	1(1, 24)
14972	1(14)
•	
194
Using a Binary Search
23
24
25
Partial Listing of orion.sales history
		
14844	121042	
14958	121031	
14821	120918	
		
Simplified Index File
where Customer ID=14958;
Customer ID Key Value	Record Identifier (RID) Page(obs, obs, ...)
4006	17(85)
4021	17(89)
4059	17(90)
> 4063	17(80, 86)
•	
14958	1(1, 24)
14972	1(14)
•	
195
Using a Binary Search
23
24
25
Partial Listing of orion.sales history
Simplified Index File
where Customer ID^?4958;
		
14844	121042	o
14958	121031	
14821	120918	
		
Customer ID Key Value	Record Identifier (RID) Page(obs, obs, ...)
4006	17(85)
4021	17(89)
4059	17(90)
4063	17(80, 86)
	
14958	1(1, 24)
14972	1(14)
•	
196
Using a Binary Search
Partial Listing of
23
24
25
	orion.sales	history	
RID	Customer I D	Employee ID	
1 ^	14958	121031	
2	^^4844	121042	
3	14864^	^99999999	
4	14909	1*8436	
•	•	•	
where Customer ID=1
		
14844	121042	
14958	121031	
14821	120918	
		
Simplified Index File
8;
Customer ID Key Value	Record Identifier (RID) Page(obs, obs, ...)
4006	17(85)
4021	17(89)
4059	17(90)
4063	17(80, 86)
•	
14958	sfd J24)
14972	1(14)
•	
197
Using a Binary Search
Partial Listing of
Simplified Index File
RID
1
2
3
4
Customer I D	Employee ID	
14958	121031	
14844	121042	
14864	99999999	
14909	120436	
•	•	
23
24
25
where Customer ID=14958;
		
14844	121042	
		
		
14821	120918	
		
Customer ID Key Value	Record Identifier (RID) Page(obs, obs, ...)
4006	17(85)
4021	17(89)
4059	17(90)
4063	17(80, 86)
•	
^    14958 J	1(1, I2^\
	\ J
14972	1(14)
•	
198
3.02 Multiple Choice Poll
If a WHERE statement uses an index to retrieve a small subset of data, which of these resources is conserved?
a. I/O
b. Disk space
c. Memory
d. Programmer time
200
3.02 Multiple Choice Poll - Correct Answer
• If a WHERE statement uses an index to retrieve a small subset of data, which of these resources is conserved?
(a)/0
b. Disk space
c. Memory
d. Programmer time
Business Scenario
•The SAS data set orion.sales_history is often queried with a WHERE statement.
Partial Listing of orion.sales history
Customer ID		Order ID	Order_ Type	ProductJD		Product_ Group	
14958		1230016296	l	210200600078		N.D.  Gear, Kids	
14844		1230096476	l	220100100354		Eclipse Clothing	
14864		1230028104	2	240600100115		Bathing Suits	
14909		1230044374	1	240100200001		Darts	
14862		1230021668	1	240500200056		Running Clothes	
14853		1230021653	1	220200200085		Shoes	
14838		1230140184	1	220100300042		Knitwear	
14842		1230025285	1	240200100053		Golf	
14815		1230109468	3	230100700004		Tents	
14797		1230168587	1	220101000004		Shorts	
202
Business Scenario
•You need to create three indexes on the most frequently used subsetting columns.__
Index Name	Index Variables
Customer ID           Customer ID	
Product Group	Product Group
SalelD Order_ID
Product ID
Partial Listing of orion.sales history
Customer ID	-	Order ID	" 1 Order Type	■ Product_ID k-		Product Group	
14958		12^0016296	1	210100600078		N.D.  Gear, Kids	
14844		1230096476	Y 1	220100100354		Eclipse Clothing	
Creating an Index
Cus tomer_ID
Order_ID Product_ID Product Group
Cus tomer_ID Product_Group SalelD
Key variables in orion.sales history
Indexes in the index file for orion.sales history
sales_history.sas7bdat       sales_history.sas7bndx
Directory-based Index File Naming Conventions
Index Name    Index Variables   Index Type
Cus tomer_ID Product_Group
Customer ID
Product Group
SalelD
Order_ID Product ID
Composite
204
Index Terminology
• There are two types of indexes.
Type	Based On	Name	Example
Simple	the value of only      automatically       Customer ID one variable           given the same    _    ,    . ~ ^         .. .        Product Group name as its key                 — * variable		
Composite	the values of more than one variable concatenated to form a single value	must be given a name that is not the same as any variable or existing index	SaleID= (Order ID Product ID)
205
ndex Terminology
• Index options include the following:
UNIQUE
Values of the key variable(s) must be unique. This option prevents an observation with a duplicate value for the key variable(s) from being added to the data set.
Partial Listing of orion.sales_history
Customer _ID	Employee ID	.   .   . Order_ID		Order Type	Product ID J	Quantity	
14958	121031		1231016296	1	21020^600078	1	
14844	121042		1230098478			1	
14864	99999999		1230028104	Y 2	240600100115	1	
14909	120436		1230044374	1	240100200001	1	
14862	120481		1230021668	1	240500200056	1	
14853	120454		1230021653	1	220200200085	3	
14838	121039		1230140184	1	220100300042	4	
The concatenation of the values for Order_ID and Product_ID forms a unique identifier for a row of data.
Index Terminology
Index options include the following:
excludes all observations with missing values from the index. Observations with missing values can still be read from the data set, but not using the index.
• If there is a large number of missing values for the key variable (s), the NOMISS option can create a smaller index file.
• An index created with the NOMISS option is not used for the following processing:
• a BY statement
• a WHERE expression satisfied by missing values
/\ NOMISS cannot be used when you create indexes using PROC SQL.
3.03 Multiple Answer Poll
On which of these indexed variables can you assign the UNIQUE option?
a. Customer_ID in an orders data set where a customer can place multiple orders
b. Order_Date in an orders data set
c. Employee_ID in a data set containing each individual employee and the family members' names stored in variables Dependenti -Dependentio
d. Product_ID in a data set containing the product identifier and the product description
3.03 Multiple Answer Poll - Correct Answers
On which of these indexed variables can you assign the UNIQUE option?
a. Customer_ID in an orders data set where a customer can place multiple orders
b. Order_Date in an orders data set
^^mployee_ID in a data set containing each individual employee and the family members' names stored in variables Dependenti -Dependentio
^^roduct_ID in a data set containing the
product identifier and the product description
Creating Indexes
• To create indexes at the same time that you create
a data set, use the INDEX= data set option on the output data set.
• To create or delete indexes on existing data sets, use one of the following:
• DATASETS procedure
• SQL procedure
211
Creating Indexes
• When you create the index, do the followin
• designate the key variable(s)
• specify the UNIQUE and/or the NOMISS index option if appropriate
• select a valid SAS name for the index (composite index only)
• A data set can have these index features:
• multiple simple and composite indexes
• character and numeric key variables
Creating an Index with the INDEX= Data Set Option
options msglevel=i;
data orion.sales_history(index=
(Customer_ID Product_Group SaleID=(Order_ID Product_ID)/unique)); set orion.history;
Value_Cost=CostPrice_Per_Unit*Quantity; Year_Month=mdy(Month_Num,  15,  input(Year_ID, 4 .) ); format Value_Cost dollarl2.
Year_Month monyy7.; label Value_Cost="Value Cost" Year_Month=f'Month/Year";
run;
• The following code would delete the indexes:
data   orion.sales_history ;
set orion.sales_history; run ;
p303d01
213
Creating an Index with the INDEX= Data Set Option
• General form of the INDEX= data set option:
SAS-data-file-name (INDEX =
{index-specification-1</option > </option> ...<index-specification-n</option> </option> >));
• jf    For increased efficiency, use the INDEX= option to create indexes when you initially create a SAS data set.
214
Viewing Information about Indexes
• To display information in the log concerning index creation or index usage, change the value of the MSGLEVEL= system option from its default value
of N to I.
• General form of the MSGLEVEL= system option:_
OPTIONS MSGLEVEL=N | I;
11 options msglevel=i;
12 data orion.sales_history(index=
13 (Customer_ID Product_Group
14 SaleID=(Order_ID
15 Product_ID)/unique));
16 set orion.sales_history;
17 run;
NOTE: There were 1500 observations read from the data set ORION.SALES_HIST0RY. NOTE: The data set ORION.SALES_HIST0RY has 1500 observations and 22 variables.
NOTE: Composite index SalelD has been defined. I_
NOTE: Simple index Product_Group has been defined. NOTE: Simple index Customer_ID has been defined.
215
Creating an Index with the INDEX= Data Set Option
Advantages	Disadvantages
You can create the data set    To create an additional index, and the index in one step.      you must re-create the existing indexes.	
SAS only reads the data once.	You need to know in advance that indexes are needed.
216
Managing Indexes with PROC

DATASETS
options msglevel=n;
proc datasets library=orion nolist; modify sales_history;
index create Customer_ID; index create Product_Group; index create SaleID=(Order ID
• The following code would delete the indexes:
proc datasets library=orion nolist; modify sales_history;
index delete Customer ID
Product ID)/unique;
quit;
Product Group SalelD;
p303d02
quit;
Managing Indexes with PROC
DATASETS
• You can use the DATASETS procedure on existing data sets to create or delete indexes.
• General form of the PROC DATASETS step to delete or create indexes:
PROC DATASETS LIBRARY=//27/-e/rNOLIST; MODIFY SAS-data-set-name, INDEX DELETE index-name,
INDEX CREATE index-specification
< / options>)
QUIT;
218
3.04 Quiz
• Open and submit the program p303aoi.
• What error messages are in the log?
options msg]	.evel=n ;
proc dataset	:s library=orion nolist;
modify Sc	lies history;
index	create Customer ID;
index	create Product Group;
index	create SaleID=(Order ID
	Product ID)/unique;
quit ;	
p303a01
3.04 Quiz - Correct Answer
1	options msglevel=n;
2	proc datasets library=orion nolist;
3	modify sales_history;
4	index create Customer ID;
ERROR: An index named Customer ID with the same definition already exists for	
	file ORION.SALES_HIST0RY.DATA.
5	index create Product_Group;
6	index create SaleID=(Order_ID
7	Product_ID)/unique;
8	quit;
NOTE	: Statements not processed because of errors noted above.
NOTE	: The SAS System stopped processing this step because of errors.
NOTE	: PROCEDURE DATASETS used (Total process time):
	real time                0.48 seconds
	cpu time                 0.09 seconds
^ If an index exists, it must be deleted before it can
be re-created.
221
Managing Indexes with PROC
DATASETS
Advantages	Disadvantages
Additional indexes can be created without re-creating the original indexes.	You can only create indexes on existing SAS data sets and existing variables.
One or more indexes can be          PROC DATASETS cannot perform deleted without deleting all of the     data manipulation, indexes on the data set.	
If an index exists, it must be deleted before it can be re-created.
Managing Indexes with PROC SQL
Name of Index
Variable Name
on orion.sales_history(Product_Group); create unique index SalelD
on orion.sales_history(Order_ID,  Product_ID);
quit;
• The following code would delete the indexes:
proc sql;
drop index Customer_IDf  Product_Groupf SalelD from orion.sales_history;
quit;
p303d03
223
Managing Indexes with PROC SQL
• You can use PROC SQL on existing data sets to create or delete indexes.
• General form of the PROC SQL step to create or delete indexes:
PROC SQL;
DROP INDEX index-name
FROM table-name, CREATE <option> INDEX index-name ON table-nametcolumn-name-l,...
column-name-n);
QUIT;
224
Managing Indexes with PROC SQL
Advantages	Disadvantages
Additional indexes can be created    You can only create indexes on without re-creating the original        existing SAS data sets and existing indexes. variables.	
One or more indexes can be deleted without deleting all of the indexes on the data set.	The CREATE INDEX statement cannot perform data manipulation.
If an index exists, it must be deleted before it can be re-created.
225
Comparing Techniques for Index Creation
INDEX= Data Set Option	PROC DATASETS	PROC SQL
You can create the SAS data set at the same time that the index is created.	You can only create indexes on existing SAS data sets and existing variables.	You can only create indexes on existing SAS data sets and existing variables.
To create an additional index, you must re-create the existing indexes.	Additional indexes can be created without re-creating the original indexes.	Additional indexes can be created without re-creating the original indexes.
The DATA step can perform data manipulation at the same time that the index is created.	PROC DATASETS cannot perform data manipulation.	The CREATE INDEX statement cannot perform data manipulation.
To delete one or more indexes, you must re-create the other required indexes.	One or more indexes can be deleted without deleting all of the indexes on the data set.	One or more indexes can be deleted without deleting all of the indexes on the data set.
An existing index can be recreated without first deleting it.	If an index exists, it must be deleted before it can be recreated.	If an index exists, it must be deleted before it can be recreated. 226
Documenting Indexes
• The following can be used to document indexes
• SAS Explorer
• PROC CONTENTS
• PROC DATASETS
• SAS Management Console
Properties Window in SAS Explorer
:p Orion.Sales_history Properties
General ] Details | Columns!) Indexes | Integrity ] Passwords ]
Index
Unique |      Missing    Owned by IC
5aleID
Product_Group Customer ID
Yes No No
Yes Yes Yes
No No No
Columns
Order_IDj Product_ID Product_Group Customer ID
OK    I    Cancel |
228
ndex Documentation
proc contents data=orion.sales_history; run ;
proc datasets lib=orion nolist;
contents data=sales_history; quit;
Partial PROC DATASETS Output
These two steps produce identical output.
	Alphabetic List of		Indexes and	Attributes
			# of	
		Unique	Unique	
#	Index	Option	Values	Variables
1	Customer_ID		1046	
2	Product Group		56	
3	SalelD	YES	1500	0rder_ID Product_ID
p303d04
229
Chapter 3: Accessing Observations
3.1 Creating aurifcdex (S^JJKg^^^f'^Si
I m ^^w|L|Ct tar ™
3.2 Using an Index
230
Objectives
• Describe when an index is used for WHERE statement processing.
• Describe when an index is not used for WHERE statement processing.
231
Index Usage Possible
• An index might be used when a WHERE expression references one of the following:
• a simple index key variable
• the primary key variable of a composite index
Although a WHERE expression can consist of multiple conditions that specify different variables, SAS uses only one index to process the WHERE expression.
Index Usage Possible
• A WHERE condition might possibly use an index, provided the condition contains any one of the following:
• a comparison operator or the IN operator
• the NOT operator
• the special WHERE operators (CONTAINS, LIKE, IS NULL| IS MISSING, and BETWEEN...AND)
• the TRIM or SUBSTR functions (if the second argument of the SUBSTR function is 1)
233
Setup for the Poll
The following indexes were created on the orion.sales_history data set.
Partial PROC DATASETS Output
	Alphabetic List of	Indexes	and Attributes
		# of	
	Unique	Unique	
#	Index Option	Values	Variables
1	Customer_ID	1046	
2	Product Group	56	
3	SalelD YES	1500	Order ID Product ID
			
3.05 Multiple Answer Poll
• Which of the following WHERE conditions could possibly use an index?
a. where Product_ID=220100300042;
b. where Customer_ID ne 3245;
c. where Customer_ID=15020 or Customer_ID=14853;
d. where Order_ID=1230036183;
e. where Customer ID=1 3245 1 ;
236
3.05 Multiple Answer Poll - Correct Answers
• Which of the following WHERE conditions could possibly use an index?
a. where Product_ID=220100300042;
'where Customer_ID ne 3245;
(where Customer_ID=15020 or Customer_ID=14853;
^d)where Order_ID=1230036183;
e. where Customer ID=1 3245 1 ;
237
When Is an Index Not Used?
• An index is not used in the following circumstances
• with a subsetting IF statement in a DATA step
• with particular WHERE expressions
• if SAS determines that all observations will satisfy the WHERE expression
• if SAS determines that it is more efficient to read the data sequentially
No Index Usage
• SAS does not use an index when a WHERE expression references an indexed variable if the following conditions exist:
• No single index can supply all required observations.
• Any function other than TRIM or SUBSTR appears in the WHERE expression.
• The SUBSTR function does not search a string beginning at the first position.
• The SOUNDS-LIKE operator (=*) is used.
239
Compound Optimization
A WHERE expression that references multiple variables can take advantage of a composite index.
compound optimization
use of a composite index to optimize some WHERE expressions that involve multiple variables
where Order_ID=240200100038 and
Product ID=1230151326;
240
Compound Optimization
• For compound optimization to occur, all of the following must be true:
• At least the first two key variables in the composite index must be used in the WHERE conditions.
• The conditions must be connected using the AND operator.
• At least one condition must use the EQ, equal sign (=), or IN operator.
241
3.07 Multiple Choice Poll
• Which of the following WHERE statements can use the composite index SalelD for compound optimization?
a. where Order_ID=240200100038 or Product_ID=l230151326;
b. where Order_ID=. and Product_ID=l230151326;
c. where int(Order_ID/1000000000)=240 and Product_ID=1230151326;
d. where Order_ID>240000000000 and Product ID<1240000000;
243
3.07 Multiple Choice Poll - Correct Answer
• Which of the following WHERE statements can use the composite index SalelD for compound optimization?
a. where Order_ID=240200100038 or Product ID=1230151326;
b^here Order_ID=. and Product_ID=l230151326;
c. where int(Order_ID/1000000000)=240 and Product_ID=1230151326;
d. where Order_ID>240000000000 and Product ID<1240000000;
WHERE Expression Index Usage
• SAS uses the following steps to decide whether to evaluate a WHERE expression using a sequential read or using an index:
• Determine whether the WHERE expression can be satisfied by an existing index.
• Select the best index, if several indexes are available.
• Estimate the number of observations that qualify
• Compare the probable resource usage for both methods.
f   SAS estimates the I/O operations for indexed access based on the subset size and sort order.
245
Subset Size
33.3%
3% 0%
Data Set
SAS will use an index.
246
Subset Size
33.3%
3% 0%
SAS Will
probably use an index.
Data Set
SAS will use an index.
247
Subset Size
33.3%
3% 0%
SAS might use an index,
Data Set
SAS will probably use an index,
SAS will use an index,
248
Subset Size
• The SAS index includes cumulative percentiles or centiles. By default, SAS stores 21 centiles or every
centiles
provide information about the distribution of values in an index.
249
3.08 Multiple Choice Poll
• Which of the following is used to determine the I/O to read a SAS data set sequentially?
a. the page size of the input data set and the number of buffers available
b. the number of observations and the number of variables
c. the page size of the output data set and the number of output buffers available
251
3.08 Multiple Choice Poll - Correct Answer
• Which of the following is used to determine the I/O to read a SAS data set sequentially?
cLy the page size of the input data set and the number of buffers available
b. the number of observations and the number of variables
c. the page size of the output data set and the number of output buffers available
252
Review of Factors Affecting I/O
• The following factors affect I/O:
• size of the subset relative to the size of the data file
• order of data with regard to the chosen index
• page size of the data file
• number of buffers allocated
• cost to uncompress a compressed file for a sequential read
Data Order
Obs	Customer_ID
AQ3Q	
8940	70175
8941	74667
	
39548	89619
32549	70187
32550	76278
)
	QylOQO
45776	70201
45777	20209
For data that is sorted and indexed on the same variable(s), retrieval time through the index is much faster than either sorted or indexed data alone.
where Customer_ID in (70201,  70187,  70175) ;
Fewer pages are copied into memory if the data is sorted.
Unsorted data
Obs	Customer_ID
51050	70175
51051	70177
51052	70180
51053	70181
51054	70183
51055	70184
51056	70186
51057	70187
51058	70188
51059	70191
51060	70192
51061	70193
51062	70194
51063	70195
51064	70197
51065	70199
51066	70200
I51067	70201
■	
Sorted data
254
Controlling WHERE Processing Index Usage
• You can control index usage for WHERE processing with these data set options:
IDXWHERE=YES
IDXWHERE=NO
IDXNAME=/ndex-na/77e
tells SAS to choose the best index to optimize a WHERE expression and to disregard the possibility that a sequential search of the data set might be more resource efficient.
tells SAS to ignore all indexes and satisfy the conditions of a WHERE expression with a sequential search of the data set.
directs SAS to use a specific index.
A
Use the IDXWHERE=NO option when you know
an available index will not optimize WHERE clause processing.
255
Using the IDXWHERE= Option
• To ensure that SAS uses an index when printing the data for Customer_ID in (14844,4983,5862,10032) and Product_Group contains 'Shoes', use the following code:
options msglevel=i;
proc print data=orion.sales_history(idxwhere=yes);
where Customer_ID in (14844,4983,5862,10032) and Product_Group contains   f Shoes f;
var Customer_ID Product_ID Product_Group ;
title  fWith an Index1; run ;
p303d05
256
Using the IDXWHERE= Option
Partial SAS Log
1669 options msglevel=i;
1670 proc print data=orion.sales_history(idxwhere=yes);
1671 where Customer_ID in (14844,4983,5862,10032)
1672 and Product_Group contains "Shoes';
INFO: Data set option (IDXWHERE=YES)forced an index to be used rather
than a sequential pass for where-clause processing.
INFO: Index Customer_ID selected for WHERE clause optimization.
1673 var Customer_ID Product_ID Product_Group ;
1674 title 'With an Index';
1675 run;
257
Using the IDXNAME= Option
• Because using the index on Customer_ID returns a smaller subset than would the index on Product_Group, the IDXNAME= data set option can be used.
options msglevel=i;
proc print data=orion.sales_history(idxname=Customer_ID); where Customer ID in (14844,4983,5862,10032)
and Product_Group contains  1 Shoes 1; var Customer_ID Product_ID Product_Group title  'With an Index1;
run;
Use the IDXNAME= option when you know the better index so SAS does not need to do the evaluation.
p303d06
258
Using the IDXNAME= Option
Partial SAS Log_
92   options msglevel=i;
193 proc print data=orion.sales_history(idxname=Customer_ID);
194 where Customer_ID in (14844,4983,5862,10032)
195 and Product_Group contains "Shoes';
INFO: Index Customer_ID selected for WHERE clause optimization.
196 var Customer_ID Product_ID Product_Group ;
197 title 'With an Index';
198 run;
NOTE: There were 3 observations read from the data set ORION.SALES_HISTORY.
WHERE Customer^ID in (4983, 5862, 10032, 14844) and Product_Group contains 'Shoes'; NOTE: PROCEDURE PRINT used (Total process time):
real time 0.15 seconds
cpu time 0.01 seconds
259
Maintaining Indexes
Data Management Tasks	Index Action Taken
Copy the data set with the      Index file constructed for new COPY procedure or the        data file DATASETS procedure	
Move the data set with the MOVE option in the COPY procedure	Index file deleted from IN= library; rebuilt in OUT= library
Copy the data set with a        Index file constructed for new drag-and-drop action in SAS file
Explorer continued...
260
Maintaining Indexes
Data Management Tasks
Rename the data set
Add observations
Index Action Taken
Index file renamed
Variable renamed to new name in index file
Value/Identifier pairs added
Value/Identifier pairs deleted; space recovered for re-use
Update observations
Value/Identifier pairs updated if values change
f    The APPEND procedure and the INSERT INTO statement in the SQL procedure update the index file after all the data is appended or inserted.
continued.,
261
Maintaining Indexes
Data Management Tasks	Index Action
	Taken
Delete a data set.	Index file deleted
proc datasets lib=work;	
delete a;	
run ;	
Rebuild a data set with a DATA step or the SQL	Index file deleted
procedure.
data a; proc sql;
set a; create table a as
run; select * from a;
quit;
Sort the data set in place with the FORCE Index file deleted option in the SORT procedure.
proc sort data=a force;
by var; run;
Guidelines for Indexing
• Suggested guidelines for creating indexes:
• Create an index when you intend to retrieve a small subset of observations from a large data file.
• Do not create an index if the data file page count is less than three pages. It is faster to access the data sequentially.
• Create indexes on variables that are discriminating. These variables precisely identify observations that satisfy WHERE expressions.
• When you create a composite index, make the first key variable the most discriminating.
• Consider the cost of maintaining an index for a data file that is frequently changed. continued...
263
Guidelines for Indexing
• To minimize I/O for indexed access, sort the data by the key variable(s) before creating the index. Maintain the data file in sorted order by the key variable to improve performance.
• Minimize the number of indexes to reduce disk storage and update costs. Create indexes only on variables that are often used in queries or BY-group processing (when the data cannot be sorted).
• Consider how often your applications use an index.
An index must be used often in order to compensate for the resources used in creating and maintaining it.
• When you create an index to process a WHERE expression, do not try to create one index that might be used to satisfy every conceivable query.
264
Index Trade-offs
Advantages	Disadvantages
fast access to a small subset  extra CPU cycles and I/O of observations                  operations to create and maintain an index	
values returned in sorted order	increased CPU to read the data
can enforce uniqueness        extra disk space to store the index file	
	extra memory to load the index pages and the compiled SAS C code to use the index
265
Chaoter 3: Accessine Observations
3.1 Creating an Index
3
TS
.2 Using an Index
i
3.3 Creating a Sample Data Set (Self-Study)
Objectives
• Create a systematic sample.
• Create a random sample with replacement.
• Create a random sample without replacement.
Business Scenario
• The Marketing Department wants to send customer satisfaction questionnaires to a sample of the customers in the orion.order_fact SAS data set.
Partial Listing of orion.order_fact
Customer _ID	Employee ID	Street_ID	Order Date	Delivery Date	Order ID	.  . .
* 63	121039	9260125492	11JAN2003	11JAN2003	1230058123	
5	99999999	9260114570	15JAN2003	19JAN2003	1230080101	
45	99999999	9260104847	20JAN2003	22JAN2003	1230106883	
41	120174	1600101527	28JAN2003	28JAN2003	1230147441	
183	120134	1600100760	27FEB2003	27FEB2003	1230315085	
	•	•	•	•	•	
268
Business Scenario
• Select a subset by reading every 50th observation from observation number 1 to the end of the SAS data set.
data subs (D do Pic	et; klt=l to TotObs by 50; <D
set	
orion.ord	er fact(keep=Customer ID
	Employee ID Street ID
Order ID)	
	point=PickIt
	nobs=TotObs; ®
output; ® Am •	
s top ;	
runl-	
269
3.09 Quiz
• Are POINT= and NOBS= individual statements or part of the SET statement?
data subset;	
do Picklt=l to TotObs by 50;	
set orion.order fact(keep=Customer	ID
Employee ID Street ID Order	ID)
point=PickIt	
nobs=TotObs;	
output;	
end;	
stop ;	
run ;	
p303d07
3.09 Quiz - Correct Answer
data subset;	
do Picklt=l to TotObs by 50;	
set orion.order fact(keep=Customer	ID
Employee ID Street ID Order	ID)
point=PickIt	
nobs=TotObs;	
output;	
end;	
stop ;	
run ;	
POINT= and NOBS= are part of the SET statement
p303d07
272
Using the POINT= Option
• To create a sample, use the POINT= option in the SET statement.
• General form of the POINT= option:_
SET data-set-name POINT=point-variable}
• The point-variable has the following attributes:
• names a temporary numeric variable that contains the number of the observation to read
• must be given a value before the execution of the SET statement
• must be a variable (for example, X) and not a constant value (for example, 12)
• must be a valid observation number
273
Using the Number of Observatio
• You can use the NOBS= option in the SET statement to determine how many observations there are in a SAS data set.
• General form of the SET statement:
SET SAS-data-set NOBS= variable,
• The NOBS= option creates a temporary variable whose value has the following characteristics:
• is the number of observations in the input data set(s)
• is assigned during compilation
• is retained
• should not be modified during execution
Using the STOP Statement
• The POINT= option has the following features:
• uses direct-access read mode
• does not detect the end-of-file marker
• To prevent the DATA step from looping continuously, use the STOP statement.
• General form of the STOP statement:
STOP;
Compilation
PDV
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Emp1oyee_ID Street_ID Order_ID) point=PickIt nobs=TotObs; output;
end; stop; run;
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
•	617	•	•	•	•	•
p303d07
276
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
PDV
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Employee_ID Street_ID Order_ID) point=PickIt nobs=TotObs; output;
end; stop ; run;
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
1	617	•	•	•	•	1
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
PDV
data subset;
do Picklt=l to TotObs by 50;
set	orion	.order fact
	(keep=	=Customer ID
		Employee ID
		Street ID
		Order ID)
	point=	=PickIt
	nobs=TotObs;	
output;
end; stop ; run;
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
1	617	63	121039	9260125492	1230058123	1
278
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
PDV
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Employee_ID Street_ID Order_ID) point=PickIt nobs=TotObs; output;
end; stop ; run;
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
1	617	63	121039	9260125492	1230058123	1
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
PDV
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Employee_ID Street_ID Order_ID) point=PickIt nobs=TotObs; output;
end; stop ; run;
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
51	617	63	121039	9260125492	1230058123	1
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
PDV
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Employee_ID Street_ID Order_ID) point=PickIt nobs=TotObs; output;
end; stop ; run;
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
51	617	63	121039	9260125492	1230058123	1
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
PDV
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Employee_ID Street_ID Order_ID) point=PickIt nobs=TotObs;
output;
end; stop ; run;
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
51	617	17023	99999999	2600100021	1230931366	1
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
PDV
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Employee_ID Street_ID Order_ID) point=PickIt nobs=TotObs; output;
end; mi u inwmiiiBa
stop ; run;
bservation.
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
51	617	17023	99999999	2600100021	1230931366	1
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
PDV
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Employee_ID Street_ID Order_ID) point=PickIt nobs=TotObs; output;
end; stop ; run;
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
101	617	17023	99999999	2600100021	1230931366	1
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
PDV
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
Picklt > TotObs
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Employee_ID Street_ID Order_ID) point=PickIt nobs=TotObs; output;
end; stop ; run;
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
651	617	215	120175	1600102721	1243963366	1
285
Execution
Partial Listing of orion.order fact
obs
1
2
50
51
Customer _ID	Employee _ID	
63	121039	
5	99999999	
•	■	
17023	99999999	
17023	99999999	
	■	
PDV
data subset;
do Picklt=l to TotObs by 50; set orion.order_fact (keep=Cus tomer_ID Employee_ID Street_ID Order_ID) point=PickIt nobs=TotObs; output; end; ■ stop ;| run;
Execution stops.
j^Picklt	LTot MDbs	Customer I D	Employee I D	Street ID	Order ID	
651	617	215	120175	1600102721	1243963366	1
286
Resulting Data Set
• Partial Listing of subset
		Systematic	Sample	
Obs	Customer ID	Employee ID	Street ID	Order ID
1	63	121039	9260125492	1230058123
2	17023	99999999	2600100021	1230931366
3	17	121037	9260123306	1231757107
4	195	120160	1600101663	1232590052
5	41	120134	1600101527	1233545775
6	11171	99999999	2600100032	1235176942
7	10	121043	9260129395	1237327705
8	53	120121	1600103258	1238674844
9	90	121040	9260111614	1239543223
10	89	121061	9260116551	1240549230
11	27	99999999	9260105670	1241930625
12	41	120195	1600101527	1242838815
13	215	120175	1600102721	1243963366
287
Creating a Random Sample
• Instead of creating a systematic sample, create a random sample where each observation has an equal chance of being selected.
• There are two types of random samples:
• with replacement, where an observation might be selected more than one time
• without replacement, where an observation cannot be selected more than once
• You can use the RANUNI function to generate random numbers from a uniform distribution.
General form of the RANUNI function:
RANUNI(seetf)
Using the RANUNI Function
• The RANUNI function returns a rational number between o and 1 (non-inclusive) generated from a uniform distribution.
o o
0 ranuni(seetf) i
Examples:
Random number
.01253689 .95196500
Using the RANUNI Function
• If you want a number between o and 5 (non-inclusive), multiply the number returned from the RANUNI function by 5.
o o
ranuni(seetf) * 5
Examples:
Random number* 5
.01253689 0.06268445 .95196500 4.75982500
290
Using the RANUNI and CEIL Functions
• If you want an integer between 1 and 5 (inclusive), use the CEIL function on the number returned by multiplying the random number by 5.
Examples:
1     2     3     4 5
ceil(ranuni(seed) * 5) Random number* 5   CEIL( )
01253689 * 0.06268445 1
95196500 4.75982500
291
Setup for the Poll
• Instead of the CEIL function, would the INT function return the same results?
ceil (ranuni (s<	eed) *
	
int(ranuni(se	sed) *
5)	
3.10 Poll
Instead of the CEIL function, would the INT function return the same results?
O Yes O No
294
3.10 Poll - Correct Answer
Instead of the CEIL function, would the INT function return the same results?
O Yes
The INT function returns the integer portion of its argument, which could possibly be 0 and
never be 5.
295
Using the SURVEYSELECT Procedure
• The SURVEYSELECT procedure has the following attributes:
• provides a variety of methods for selecting probability-based random samples
• can select a simple random sample or can sample according to a complex multistage sample design
that includes stratification, clustering, and unequal probabilities of selection
• is part of SAS/STAT
296
Using the SURVEYSELECT Procedure
• This program creates a SAS data set, ordersample, that contains 10 observations randomly selected, without replacement, from the orion.order_fact SAS data set.
proc s	urveysel<	ect data=orion.order fc	ict
		(keep=Customer ID	
Employ	ee_ID		
		Street_ID Ord*	sr_ID)
		out=ordersample	
		method=srs n=10;	
run ;			
p303dl0 297
Using the SURVEYSELECT Procedure
• General form of the SURVEYSELECT procedure:
PROC SURVEYSELECT
options;
STRATA variables',
CONTROL variables',
SIZE variabler,
ID variables, RUN;
Using the SURVEYSELECT Procedure
• The PROC SURVEYSELECT statement performs the following tasks:
• invokes the procedure
• can, if you choose, identify input and output data sets
• specifies the sample selection method, the sample size, and other sample design parameters
• The PROC SURVEYSELECT statement is the only statement required to create a simple random sample.
299
Options for the SURVEYSELECT Procedure
• The following options can be specified in the PROC SURVEYSELECT statement:
To do this:
Specify the input data set Specify the output data set Suppress displayed output Specify selection method
Use this option:
DATA=
OUT=
NOPRINT METHOD=
Specify sample size
Specify random number seed
SAMPSIZE: N=
300
Methods Used by the SURVEYSELECT Procedure
• Selected values for the METHOD= option are as follows:
SYS	This method of systematic random sampling selects units at a fixed interval throughout the sampling frame or stratum after a random start.
URS	This method of unrestricted random sampling selects units with equal probability and with replacement. Because units are selected with replacement, a unit can be selected for the sample more than once.
SRS	This method of simple random sampling selects units with equal probability and without replacement. The selection probability for each individual unit equals n/N.
Using the SURVEYSELECT Procedure
• This program creates a SAS data set, ordersample, that contains 10 observations randomly selected, without replacement, from the orion.order_fact SAS data set.
proc s	urveysel(	act data=orion.order fc	ict
		(keep=Customer ID	
Employ	ee_ID	Street_ID Ord* out=ordersample method=srs n=10;	*r_ID)
run ;			
p303dl0 302
Using the SURVEYSELECT Procedure
• In addition to creating the SAS data set, ordersample, PROC SURVEYSELECT provides the following information in the Output window:
The SURVEYSELECT Procedure
Selection Method      Simple Random Sampling
Input Data Set	ORDER FACT	
Random Number Seed	525990001	0
Sample Size	10	€
Selection Probability	0.016207	
Sampling Weight	61 .7	€
Output Data Set	ORDERSAMPLE	
303
Comparison of the DATA Step and the SURVEYSELECT Procedure
DATA Step	PROC SURVEYSELECT
full power of DATA step	less coding
processing	
can create multiple output	one output data set with
data sets	additional statistics
part of Base SAS	part of SAS/STAT
304
4. Credit scoring- historie, základní pojmy
Good customers
Bad customers
Low risk
High risk
usiness Loan
305
Úvod
• Credit Scoring je soubor prediktivních modelů a jejich základních technik, které slouží jako podpora finančním institucím při poskytování
r     v o
uveru.
• Tyto techniky rozhodují, kdo dostane úvěr, jaká má být výše úvěru a jaké další strategie zvýší ziskovost dlužníků vůči věřitelům.
• Credit Scoringové techniky kvantifikují a posuzují rizika při poskytování úvěrů konkrétnímu spotřebiteli.
Úvod
• Nerozeznají a nestanovují "dobré" nebo "špatné" (očekává se negativní cnování, tj. např. default) žádosti o úvěr na individuální bázi, nýbrž poskytují statistické šance, nebo pravděpodobnosti, že žadatel s daným skóre se stane dobrým" nebo "špatným".
• Tyto pravděpodobnosti nebo skóre, spolu s dalšími obchodními úvahami jako jsou předpokládaná míra schvalování, zisk nebo ztráty, jsou pak použity jako základ pro rozhodování o poskytnutí/neposkytnutí úvěru.
307
Why do we need score?
HISTORICAL EVOLUTION":
Money lender
• lend only to people which he knows
Operators
• they make decision based on client's information and their experience
Automatic scoring
• make decision on statistical base
PAST EXPERIENCE -> ESTIMATION FOR FUTURE
score?
ANTAGES:
• Automatization of approval proces
• Cost - effective
• Less fraud possibilities
	DISADVANTAGES	i ->	
			
• Statistical based, not take in account client like individual			
Úvod
• Zatímco historie úvěru sahá 4000 let nazpět (první zaznamenaná zmínka o úvěru pochází ze starověkého Babylonu - 2000 let před n.L), nistorie credit scoringu je pouze 50-70 let stará.
• První přístup k řešení problému identifikace skupin v populaci představil ve statistice Fisher (1936). V roce 1941, Durand jako první rozpoznal, že tyto techniky mohou být použity k rozlišování mezi dobrými a špatnými úvěry.
310
Úvod
• Významným milníkem při posuzování úvěrů byla druhá světová válka.
• Do té doby bylo standardem individuální posuzování žadatele o úvěr. Dále bylo standardem, že ve finanční sféře byli zaměstnáni (téměř) výhradně muži.
• Odchod značné části mužské populace do služeb armády měl za následek potřebu předat zkušenosti dosavadních posuzovatelů žádostí o úvěr novým pracovníkům.
• Díky tomu vznikla jakási rozhodovací pravidla a došlo k „automatizaci" posuzování žádostí o úvěr.
311
Úvod
• Příchod kreditních karet ke konci šedesátých let minulého století a růst výpočetního výkonu způsobil obrovský rozvoj a využití credit scoringových technik. Událost, která zajistila plnou akceptaci credit scoringu, bylo přijetí zákonů „Equal Credit Opportunity Acts" (o rovné příležitosti přístupu k úvěrům) a jeho pozdějších znění přijatých v USA v roce 1975 a 1976. Tyto stanovily za nezákonné diskriminace v poskytování úvěru, vyjma situace, pokud tato diskriminace „byla empiricky odvozená a statisticky validní".
312
Úvod
V osmdesátých letech minulého století začala být využívána logistická regrese, dodnes v mnoha oblastech považovaná za průmyslový standard, a lineární programování. O něco později se objevily na scéně metody umělé inteligence, např. neuronové sítě. Mezi další používané techniky lze zařadit metody nejbližšího souseda, splajny, waveletové vyhlazování, ádrové vyhlazování, Bayesovské metody, regresní a dasifikační stromy, support vector machines, asociační pravidla, klastrová analýza a genetické algoritmy.
313
Historie -detail
Date Event
2000 BC       First use of credit in Assyria, Babylon, and Egypt.
1100s First pawnshops in Europe established by charitable institutions, and by 1350
they were being run as commercial concerns. 1536 Charging of interest deemed acceptable by the Protestant church.
1730 hirst advertisement for credit placed by Christopher Thornton of Southward,
London who offered furniture that could be paid off weekly. 17S0s First use of cheques in England,
IS 03 First consumer reports by Mutual Communications Society in London.
1S 32 Fi rst pu bl ication of the A rnerican Railroad Journal.
IS41 Mercantile Agency is first American credit reporting agency.
IS49 HarrodTs established as one of the world's first department stores,
IS51 First use of credit ratings for trade creditors by John M. Bradstreet.
IS56 Singer Sewing Machines offers consumer credit.
IS 62 Poor's Publishing publishes Manual of the Railroads of the United States.
IS69 First American consumer bureau is Retailers Commercial Agency (RCA)
in Brooklyn,
1SSĚ Sears established, and launches its catalogue in 1S93. S^S^^teSe^Swažován za přijatelný
Advertisement for credit = reklama na úvěr Zdroj: Anderson Mercantile agency = obchodní agentura
314
Historie -detail
Date Event
1906 National Association of Retail Credit Agencies formed in the USA.
1909 John M, Moody publishes first credit rating grades for publicly traded bonds.
1913 Henry Ford uses production lines to produce affordable automobiles.
1927 Establishment of Schuf a Holdings AG, first credit bureau in Germany.
1934 First public credit registry (PCR) established in Germany,
1936 U.A. Fisher's use of statistical techniques to discriminate between iris species.
1941 David Durand writes report, suggesting statistics can assist credit decisions.
194? Henry Wells uses credit scoring at Spiegel Inc.
1950 Diners Club and American Express launch first charge cards.
1950s Sears uses propensity scorecards for catalogue mailings.
1956 FI consultancy established in California, USA.
1958 First use of application scoring by American Investments.
1960s Widespread adoption of credit scoring by credit card companies.
1966 Credit Data Corp, becomes first automated credit bureau.
1970 Fair Credit Reporting Act governs credit bureaus.
1974 Equal Credit Opportunity Act causes widespread adoption of credit scoring.
1975 FI implements first behavioural scoring system for Wells Fargo,
1978 Stannic implements first vehicle finance scorecards in South Africa.
1982 CCN offers Credit Account Information Sharing (CAIS), its consumer credit bureau service.
1984 FI develops first bureau scores used for pre-screening.
1987 MDS develops first bureau scores used for bankruptcy prediction.
1995 Mortgage securitisers Freddy Mac and Fannie Mae adopt credit scoring.
20QO Moody's KMV introduces RiskCalc for financial ratio scoring [FRSj.
2000s Basel II implemented by many banks.
Zdroj: Anderson
affordable = dostupný
iris species = druhy kosatců
Charge card = kreditní karta
Propensity scorecard = scoringová karta pro
modelování náchylnosti (k nákupu)
FI = splolečnost Fair, Isaac...dnes FICO
Mortgage = hypotéka
315
Historie -detail
Table 2.4. Genealogies and milestones—credit cards
Dace
Event
1914 Western Union introduces embossed metal plate first charge card in the United States,
1920s Introduction of 'shoppers plates', early version of modern store cards.
1950 Diners Club and American Express launch first charge cards.
1 -' v Diners Club launches first credit card in New York city.
I960 Bank Americard established, later to become Visa.
1966 Master Charge established, later to become MasterCard,
1966 Barclay card established in the United Kingdom,
Table 2.5. Genealogies and milestones—credit scoring consultancies
Zdroj: Anderson
Name	Year	Notes
Fair Istitic (Fii		
FI	1956	Founded San Francisco CA, by Bill Fair and Earl [saac
	19SS	First scorecard development, for American Investments
	1984	Develops first bureau score for pre-screening
	1995	First use of scoring by mortgage securitisers
Experian-Scorex		
Management Decision	1974	Founded by John Coffman and Gary Chandler
Systems (MDS)		
	1982	MDS purchased by CCN
Scorex	1984	Founded in Monaco by Jean-Michel Trousse
MDS	1987	MDS develops first monthly bureau score, for bankruptcy
Experian-Scorex	2003	Created as subsidiary of Experian, after purchase of Scores
316
Historie -detail
Table 2.7. Genealogies and milestones—credit bureaux
Name
Year
Notes
Du» & Bradsireet Mercantile Agency
John M. Bradstreet Co.
R.G. Dun Sc Co. Dun 6t Biadstreet
Expcrittn
Manchester Guardian
Society Chilton Corp. Michigan Merchants TRW
TRW
CCN
TRW Experian
Equifax
London Assn. for the Protection of Trade RCA
RCC
United Assn. for the Protection of Trade Equifax
Trans Um/on TransUnion
1841 1849 1849 1851 1859 1933
1827
1897 1932 1368
1976
1980
1884 1989 1996
1842
1869 1899 1934 1965
1975 1994
1968
1969
Founded, New York NY, by Lewis Tappan.
Benjamin Douglass takes over, and expands.
Founded, Cincinnati OH.
First use of credit rating grades.
Robert G. Dun incorporates Mercantile Agency.
Merger orchestrated by Arthur Whiteside.
Founded, Manchester, UK.
Founded, Dallas TX. Publishes "Red Book1. Founded, later to become Credit Data Corp. Purchases Credit Data Corp., and changes name to
TRW-Credit Data. Information Systems and Services (ISBfS) division
produces first business credit report. Founded, when Great Universal Stores (GUS) spins off
information services division Purchases Manchester Guardian Society Purchases Chilton Corp.
Founded, through TRW divestiture of TRW-CD & ]S6fS. Purchased by GUS, who merges it with CCN.
Founded, London, UK
Founded, Brooklyn, NY Founded, Atlanta, CA Purchase* RCA LAPT renamed
RCC renamed to Equifax
Purchases UAPT-Infolink and Canadian Bonded Credits
Founded, as holding company for Union Tank Car
Company (UTCQ Purchases the Credit Bureau of Cook County
Zdroj: Anderson
317
Historie
-detail
Table 2.8. Genealogies and milestones—credit rating agencies
Name Year     Notu s
Standard & Pant's (S&Pi
Poor's Publi shi ng Co. 18 62
S&P 1941
Moody's Investor Services (MIS)
John Moody St Co. 1900
John Moody 1909
Moody1! Investor Services 1914
1962
Moody's KMV 2002 Fitch IBCA
Fitch Publishing Co. 1913
IBCA 1973
KiKh [KCA 1997
Founded, by Henry Vamum Poor
Poors Publishing and Standard Statistics merge
Founded, by John Mood); but fails in 1907 First use of rating grades for bonds Incorporation of MIS MIS purchased by DficB
Created as MIS subsidiary after merger of Risk Management Services and KMV
Founded, by John Knowles Fitch Founded
Merger of Fitch Publishing and IBCA
Zdroj: Anderson
318
Historie -další zajímavé čtení
http://www.fundinguniversexom/company-histories/Fair-Isaac-and-Com pa ny-Com pa ny- H istory. htm I
http://www.fico.com/en/Company/News/Pages/03-10-2009.aspx http://www.directlendingsolutions.com/history_credit_scoring.htm http://www.pbs.org/wgbh/pages/frontline/shows/credit/more/scores.html http://en.wikipedia.org/wiki/Credit_score
319
Risk Management - Acquisition
• Credit Bureau
• Other External Data
Policy Rules Scorecards
• Fraud
• Delinquency
• Bankruptcy
• Claims
Strategy
Fail
Pass
Data Acquisition
Risk Management - Customer
Credit Line Management Usage Monitoring Transaction Fraud Transaction Approval Renewal/Reissue
Collections Claims
V Scorecards V  V Policy Rules
V Strategies
.. Lots of analysis
Risk Management
Risk Management
I
I
Financial
I
I
Commercial/Consumer
1
Enterprise
Delinquency, Fraud, Claim, Collections
Operational
Market, Interest, VaR (Risk Dimensions)
322
Risk Management a druhy rizik
Selhání procesů a systémů, podvody, přepadení,
pověst společnosti
Risk Management
■ Late payments - Bankruptcy _ Write-off
Commercial/Consumer
1		1		1		J_
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Applicant
Transaction
Claims
Internet
(app+trans)
	Delinquency, Fraud, Claim, Collections		
			
P&C, Life,
Health
Mortgage
insurance
Export financing
insurance
Payment Projection (recovery) Outsourcing to agency
P&C: Property & Casualty Insurance (majetkové a úrazové pojištění)
Why Manage Risk?
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Reduce exposure to high-risk accounts. Decrease bad debt and claims payouts. Ensure better pricing to reflect risk. Detect fraud early-on.
Increase approval rates (the "right kind" - potentially increasing revenue).
Handle most approvals/declines quickly (customer service).
Analysts/investigators only focus on difficult accounts.
Ensure consistent, equal and objective treatment of each applicant across the organization.
Offer more efficient marketing initiatives.
325
Users of Risk Management
• Banks
• Citibank, Royal Bank, CIBC, BankOne
• Finance Companies
• GE Capital, HFC, GMAC
• Insurance
• Life, Property and Casualty, Health
• Government
• Ministries/Departments of Health (Medicare), Ministries of Finance (IRS), Workers Compensation.
326
Users of Risk Management
Utilities
• Hydro/Power/Energy, Water
• Communications
• Bell, Sprint, AT&T (land lines and cellular)
• Retail
• JC Penneys, Sears, Hudsons Bay Company, Target
• Manufacturers/Industrials
• Those who give credit to small businesses.
327
Risk Management "Toolbox"
• Risk Data Mart/Data Warehouse
• Risk prediction models (scorecards)
• Reporting
• Analysis tools
• Operational/strategy implementation software (for example, FICO™ Blaze Advisor®, FICO@ TRIAD® Customer Manager, Experian Probe SM, Experian NBSM, Cardpac, VisionPlus, Pro-Logic Ovation).
328
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Scorecards
• Predict the probability of a negative event.
• Custom - based on clients own data
• Generic - based on pooled industry or bureau data (Beacon, Empirica)
• Application - new applicants
• Behavioral - current customers
330
Scorecard Types
Risk	
30/60/90 Delinquency	
Bankruptcy	
Write-off	
Claim	
Fraud	
Collections	
		Mktg/CRM
Combination		
		Response
Resp/approve/delq		
Response/profit		Churn
Risk/churn/profit		Revenue
Profit		Cross sell
Scoring in approval process
Policy declines - low age, unsufficient length of employment, "terorrist" etc.
What is the probability that client will pay?
Will the contract be profitable?
Is the number of client's phone valid? Etc.
Fraud Risk
• Fraud risk is one of the fastest growing areas in risk management.
• Examples include bank/retail card fraud, insurance fraud, health care fraud, welfare fraud, franchise fraud, internet fraud, mortgage fraud, investment fraud, tax fraud, merchant fraud.
• E-commerce presents opportunities.
• The F.B.I, estimates that between 10-15% of loan applications contain material misrepresentations.
333
Reporting and Analysis
• Scorecard and portfolio performance
• Approval rates, applicant profile, loss rates, high risk segments
• Behavior tracking to develop better strategies
• Capturing fraud, approval/decline, pricing,
credit line management, collections, cross sells qualification, claims.
334
Risk Applications
• Retail/banking (consumer and commercial)
• Application and behavior scorecards for all credit products.
• Strategy design for credit limit setting, authorizations and collections/reissue/suspension.
• Fraud application and transaction detection
• Pricing/down payment
• ATM limits, check holds
• Pre-qualifying direct marketing lists.
Automotive/finance
• Loans and leasing
• Application, behavioral, fraud, collection scorecards
• Pricing/down payment.
Risk Applications
• Government
• Fraud detection (for example, Welfare, health insurance)
• Entitlement/claims assessment (for example, Workers compensation)
• Communications
• Security deposit
• International call access
• Contract/"pay as you go"
• Telephone fraud
• "Shadow limit" setting
• Suspension of service
• Collections.
Risk Applications
Insurance
• Rate setting
• Fraud detection
• Claims management
• Risk control for CRM initiatives. • Utilities
• Security deposit
• Collections.
Risk Applications
• Manufacturers/pharmaceuticals/industrials
• Assessing credit risk of business clients
• Credit risk assessment of franchisees (for example, gas stations)
• Payment terms
• Collections
• Merchant fraud.
Risk Applications
• Optimizing work flow in adjudication departments
• Evaluating/pricing portfolios
• Securitization
• Setting economic/regulatory capital allocation
• Reducing turnaround time (automated scoring)
• Comparing quality of business from different channels/regions/suppliers.
Resources
www.ftc.gov/bcp/conline/pubs/credit/scoring.htm
www.creditscoring.com
www.my-credit-score.com
www.fairisaac.com, www.myfico.com
www. experian. com
www.creditinfocenter.com
www.consumersunion.org/finance/scorewc200.htm
www.phil.frb.org/files/br/brs097lm.pdf
www.nacm.org
www.rmahq.org
www.riskmail.org
www.occ.treas.gov
Resources
• Credit Scoring & Its Applications
by Lyn Thomas, Jonathan Crook, David Edelman
• Credit Risk Modeling: Design and Application
by Elizabeth Mays (Editor)
• Internal Credit Risk Models: Capital Allocation and Performance Measurement
by Michael K Ong
• Handbook of Credit Scoring
by Elizabeth Mays
• Applications of Performance Scoring to Accounts Receivables Management in Consumer Credit
by John Y. Coffman
• Introduction to Credit Scoring,
by E.M. Lewis
Scorecard Development roles-objectives
• Understand the critical resources needed to successfully complete a scorecard development and implementation project.
• Understand some of the operational considerations that go into scorecard design.
Major Roles
• Scorecard Developer
• Data miner, data issues
• Credit Scoring Manager/Risk Manager
• Strategic view, corporate policies, implementation
• Product Manager
• Client base, target market, marketing direction.
Major Roles
• Operational Managers
• Customer Service, Adjudication, Collections
• Strategy execution, impact on customers
• IT/IS Managers
• external/internal data, implementation platforms.
Minor Roles
Project Manager
• Coordination, time lines
• Corporate Risk staff
• Corporate policies, capital allocation
• Legal.
Why All of These Roles?
• Can I use this variable?
• Legal, technical (derived variables, implementation platform), future application form design
• Segmentation
• Marketing, application form design, systems
• What is the impact on this segment?
• Operational, marketing, risk manager, corporate risk.
5. Metodologie vývoje scoringových funkcí
Objectives
• Understand how scorecards to predict credit risk are developed.
• Understand the analyses and issues for implementation of scorecards.
348
Main Stages - Development
• Stage 1: Preliminaries and Planning
• Create Business Plan
• Identify organizational objectives
• Internal versus External development, and scorecard type
• Create Project Plan
• Identify project risks
• Identify project team.
349
Main Stages - Development
• Stage 2: Data Review and Project Parameters
• Data availability and quality
• Data gathering for definition of project parameters
• Definition of project parameters
• Performance window and sample window
• Performance categories definition (target)
• Exclusions
• Segmentation
• Methodology
• Review of implementation plan.
Main Stages - Development
• Stage 3: Development Database Creation
• Development sample specification
• Sampling
• Development data collection and construction
• Adjusting for prior probabilities.
Main Stages - Development
• Stage 4: Scorecard Development
• Missing values and outliers
• Initial characteristic analysis
• Preliminary scorecard
• Reject inference
• Final scorecard production
• Scaling
• Points allocation
• Misclassification
• Scorecard strength
• Validation.
352
Main Stages - Development
• Stage 5: Scorecard Management Reports
• Gains tables and charts
• Characteristic reports.
353
Main Stages - Implementation
• Stage 1: Pre-Implementation Validation
Stage 2: Strategy Development
• Scoring strategy
• Setting cutoffs
• Strategy considerations
• Policy rules
• Overrides.
Main Stages - Post Implementation
• Post-Implementation
• Scorecard and Portfolio Monitoring Reports
• Review.
Development
Stage 1: Preliminaries and Planning
Objectives
• Create a business plan to ensure a viable and smooth project.
• "All Models are wrong. Some are useful"
George Box
357
Create Business Plan
• Identify organizational objectives.
• Reasons for model development
• Profit, revenue, loss, automation, operational efficiency
• Role of scorecards in decision making
• sole arbiter or decision support tool?
Create Business Plan
• Internal/External Development and Scorecard Type
• Capability and resources
• Staff, tools, expertise, data
• Market segment
• Custom, generic, judgmental
• segment, data, time.
Create Project Plan
• Scope and timelines
• Deliverables (scorecard format and documentation,...)
• Implementation strategy
• Testing, coding
• Strategy development
• FYIlist.
• Seamless process from planning to development and implementation.
Create Project Pla
• Identify Project Risks
• Data risks
• Availability, quality, quantity
• Weak data
• Operational risks
• Organizational priority
• Implementation delays
• System interpretation of data.
Create Project Plan
• Identify Project Team
• Roles clearly defined
• Signoff, executor, advisor, FYI
• Critical path.
Development
Stage 2: Data Review and Project Parameters
363
Objectives
• Identify data requirements.
• Perform pre-modeling analysis.
• Understand the business
• Exclusions
• What is a "bad"? - target definition
• Sample Window/ Performance Window.
Data Availability and Quality
• Number of "goods" "bads" and "rejects"
• Initial idea at this stage, estimated from performance reports
• Internal data
• Reliable, accessible
• External data
• Accessible, format
• Retro pull.
Data Gathering
• To determine "bad" definition and exclusions
• All applications over the last 2-5 years (or a large sample)
• account/ID number
• Date opened/applied
• Accept/reject indicator
• Arrears/payment history
• Product/channel and other identifiers
• Account status
• Other items to understand the business.
Exclusions
• "Include those whom you would score during normal day day operations"
• VIP
• Staff
• Fraud
• Pre-approved
• Underage
• Cancelled (sometimes).
Performance
"Sample Window"
"Performance Window"
New Account
Good/Bad?
368
Parameters
Performance Window
• How far back do I go to get my sample?
• Sample Window
• Time frame from which sample will be taken.
• Definition of "bad"
• Bad and approval rates (when oversampling
Parameters
• Seasonality
• Plot approval rate/applications across time
• Establish any abnormal' zones (for example, talk to marketing).
• Sample used in development must be from a normal business period, to get as accurate a picture as possible of the target population.
370
rameters - "Bad"
• Plot "bad" rate by "month opened" (cohort)
• For different definitions of bad
• 30/60/90 days past due
• Charge off/write-off
• Bankrupt
• Claim
• Profit based
• Less than x% owed collected
«t-i        yy us~* ,yy 1 1
• Ever versus Current bad
• Ever bad should be used where possible
• Considered "bad" if you reach status anytime during performance window
Cohort Analysis - Example
Bad = 90 days					
Open Date J      1 Qtr		2 Qtr	3 Qtr	4 Qtr	5 Qtr
					
Jan-99	0.00%	0.44%	0.87%	1.40%	2.40%
Feb-99	0.00%	0.37%	0.88%	1.70%	2.30%
Mar-99	0.00%	0.42%	0.92%	1.86%	2.80%
Apr-99	0.00%	0.65%	1.20%	1.90%	
May-99	0.00%	0.10%	0.80%	1.20%	
Jun-99	0.00%	0.14%	0.79%	1.50%	
Jul-99	0.00%	0.23%	0.88%		
Aug-99	0.00%	0.16%	0.73%		
Sep-99	0.00%	0.13%	0.64%		
Oct-99	0.20%	0.54%			
Nov-99	0.00%	0.46%			
Dec-99	0.00%	0.38%			
Jan-00	0.30%				
Feb-00	0.00%				
Mar-00	0.00%				
Current versus Ever - Example
• Current bad definition: No Delinquency
• Ever bad definition: 3 months delinquent.
Month	1	2	3	4	5	6	7	8	9			12
Delq	0	0	1	1	0	0	0	1	2	(3	) 0	0
												
Month	13	14	15	16	17	18	19	20	21	22	23	
Delq	0	0	1	2	0	0	0	1	0	1	0	Co
373
Determining Parameters
Bad Rate Development
Month Opened
- mth opened from earliest to latest, and "bad rate" as of this month. For simplicity, this is straight delinquency .. No profit.
- notice at one point the bad rate levels off - this means everyone who was going to go bad has gone bad I.e. they have been given enough time. This is telling us that for this bad defn, accts from jan-march are mature enough.
-lesson 1: need sample that is mature enough, so that you wont be defining a "bad" as a good just because you haven't given them enough time.
-if you take accts from the middle (enter), some of the accts haven't matured yet so your bad rate is understated.
-Example: response scoring .. How long do you wait for the responses to come in. the period of measurement is 'perf window'.
Determining Parameters
Bad Rate Development
Sample
-Window H—4
Month Opened
So for each definition of "bad" you'll get a sample window of mature accounts, and a performance window indicating the time taken for the bad rate to mature. Also the approval rate for this sample window. Couple of notes on this "maturing" process.
- 30 day definition will mature quicker than 90 day. Cause it takes ppl less time to go 30 day than 90 day. Chargeoff even more.
- for the same bad defn, credit card quicker than mortgage (18-24 mths vs. 3-5 yrs) .
- Why are we doing all this for the different definition?
- because each one will produce different counts and based on reasons on the next slide, we'll determine the best set of parameters. 375
Determining Parameters - Bad
• Organizational objectives/purpose
• Tighter definition - more precise, low counts
• Looser definition - differentiation sub-optimal
• Interpretable and trackable
• Consistency
• Reality - the best definition under the circumstances (lack of data, history).
Lets look at the considerations.
- objectives: this may seem obvious, but it is not to a lot of ppl. If you're building a scorecard to predict profit, then use profit. Some orgs want a delinquency based defn, but also include profit. E.g. if acct is chronically 2 mths late, but still profitable.. You can't set 2 mths as a "bad" - whereas in a pure delq scorecard this may be possible.
- tighter/looser: tighter means 90 day, 120 day, writeoff.. Better differentiation, but low count. Remember 2000 bads.
- looser means more count, but sub-opt diff.
- interpretable e.g. bad is 2 times 60 days, 3 times 30 days or 1 times 90 days. Sounds good, but hell to track and interpret. Keep it simple.
- consistency across other cards, products. Also if accounting writes off acct at 7 mths, then keep it consistent with that.
- typically most delq cards are 90 days.
- Reality: you take what you got. Lack of history allows only a 30 day definition .. Take it. Can't measure real bad rate .. Use proxy, (example LOC like an account) 376
Sample Definitions - Bad
• Ever 90 days delinquent
• Bankrupt
• Claim over $1000
• 3 x 30 days, or 2 x 60 days, or 1 x 90 days
• Negative NPV
• Not profitable
• 50% recovered within 3 months
• Fraud over $500
• Closed within 6 months.
Confirming "Bad" Definition
• Analytical
• "Roll rate" analysis
• Current versus worst delinquency comparison Profitability analysis
• Consensus.
Roll Rate Analysis
Compare Worst delinquency
• for example, Previous 12 months versus Next 12 Months
Month	7	2	3	4	5	6	7	8	9	7£   7 7		12
Arrears	0	0	1	2	0	0	0	1	2	C3	0	0
												
Month	13	14	15	76	77	78	79	20	21	22	23	24
Arrears	1	2	3	3	3	-G	M	0	0	0	0	
379
Roll Rate Analysis
Roll Rate
CM
>
CD
o
90+ 60 day 30 day
^ Curr/x day
3
0%
20% 40% 60%
Worst - Next 12 Mths
80%
Curr/x day □ 30 day ■ 60 day □ 90+
5
5
5
100%
You find out which 'bad defn' is truly bad' - also known as POINT OF NO RETURN.
Lets look at 30 day: out of everyone who had worst 30 day, majority became current, only a few became worse - this is not a good bad defn. - out of those 60 days, some went over.. Most went back I.e. became better
-but those who were 90 day .. Majority did not become better. This confirms our definition.
-In general .. Once you hit 90 days, you're not coming back. That's a true bad. Rem: this is based on 'bad' objective. If other, perhaps there is a different point in time.. 380
Roll Rate Analysis
• Look for 'point of no return.
• Consider objectives.
• Consider sample counts.
• Typically for delinquency, after 90 days most accounts do not cure.
381
Current versus Worst Comparison
					Worst Delinquency						
		Current	30 days		60 days		90 days		120 days		writeoff
Current	Current	100%	68%		560/o.	34%	40°/	[15%		4%	
Delinquency	30 days			'16%		1.22%		1 8%	18%	5%	
	60 days			8%		19%		M7%		8%	
	90 days		32% m	4%		14%		32%		L11%	
	120 days			2%	—44°/cr	8%	60°/1	18%	72Q^	54%	
	writeoff			, 2%,		, 3%		10%		18%	100%
382
Parameters - Goods/lndeterminates
Good • Indeterminate
• Never delinquent • Mild delinquency, roll rate not
• Ever x- days delinquent conclusive either way
• No claims • Inactive
• Profitable, positive NPV • Offer declined
• No fraud • Voluntary cancellations*
• No bankruptcy • High balance < $50
• Recovery > 75%, $ value
• Must be good throughout performance window
383
Default - definice cílové prom. (good/bad)
• Obvykle je tato definice založena na klientově počtu dnů po splatnosti (Days Past Due, DPD) a částce po splatnosti. S částkou po splatnosti je spojena potřeba stanovení jisté míry tolerance, tedy stanovení co je považováno za významný dluh a co nikoli. Např. nemusí dávat smysl považovat za dluh částky menší než 100 Kč.
• Dále je třeba stanovit časový horizont (performance window), na kterém jsou dva zmíněné parametry sledovány.
• Za dobrého klienta lze např. označit klienta, který:
• je po splatnosti méně než 60 dnů(s tolerancí 100 Kč) v prvních 6-ti měsících od první splátky,
• je po splatnosti méně než 90 dnů (s tolerancí 30 Kč) v průběhu celé své platební historie (ever).
384
Default - definice cílové prom
□ Volba těchto parametrů závisí do značné míry na typu finančního produktu (jistě se bude lišit volba parametrů pro spotřebitelské úvěry pro malé částky se splatností kolem jednoho roku a pro hypotéky, které jsou obvykle spojeny s velmi vysokou finanční částkou a se splatností až několik desítek let) a na další využití této definice (řízení rizik, marketing, ...).
385
Default - definice cílové prom
□ Další praktickým problémem definice dobrého klienta je souběh několika smluv jednoho klienta. Například je možné, že zákazník je po lhůtě splatnosti na více smlouvách, ale s rozdílnými dny po splatnosti a s různými částkami. V tomto případě jsou většinou částky klienta dlužné v jednom konkrétním časovém okamžiku sečteny, a ze dnů po splatnosti na jednotlivých smlouvách je brána maximální hodnota. Tento přístup lze uplatnit pouze v některých případech, a to zejména v situaci, kdy jsou k dispozici kompletní účetní data. Situace je podstatně složitější v případě agregovaných údajů, např. na měsíční bázi.
386
Default - definice cílové prom
• Obecně uvažujeme následující typy klientů:
> dobrý (good),
> špatný (bad),
> nedefinovaný (indeterminate),
> s nedostatečnou úvěrovou historií (insufficient),
> vyřazený (excluded),
> zamítnutý (rejected).
Default - definice cílové prom.
První dva typy byly diskutovány. Třetí typ, tj. indeterminate, je na hranici mezi dobrým a špatným klientem a při jeho použití přímo ovlivňuje definici dobrých/špatných klientů. Uvažujeme-li pouze DPD, klienti s vysokými DPD (např. 90 +) jsou typicky označeni za špatné, nedelikventní klienti (jejich DPD je rovno nule) jsou označeni za dobré. Za indeterminate jsou pak označeni delikventní klienti, kteří nepřekročí danou hranici DPD.
• Čtvrtý typ klientů jsou typicky klienti s velmi krátkou platební historií, u kterých je nemožná korektní definice cílové proměnné.
• Vyřazení klienti jsou klienti, jejichž data jsou natolik špatná, že by vedla ke zkreslení modelu(např. fraudy). Další skupinu tvoří klienti, kteří nejsou standardně hodnoceni daným modelem (VIP klienti)
• Poslední typ klientů jsou ti klienti, jejichž žádost o úvěr byla zamítnuta.
388
Definice dobrého/špatného klienta
Customer
Accepted
Rejected
I GOOD
Default
(60 or 90 DPP)
rau
(first delayed payment, 90 DPP) j
Early default
ite defai
(5+ delayed payment, 60 DPP)
Insufficient
INDETERMINATE
389
Performance Definitions
• "Goods" and "bads" (and rejects) are used for model development.
• Indeterminates included for Gains chart and forecasting.
Segmentation
• Can one scorecard work efficiently for all the different populations within your portfolio?
• Or would more than one scorecard be better?
• Segmentation maximizes predictiveness for unique segments within your population.
Segmentation
• Experience (Heuristic)
• Knowledge/experience, operational/industry based, common sense.
• Statistical
• Let the data speak.
• "Distinct applicant/account sub-populations"
• "Better predictive power than single model".
392
Experience Based Segmentation
• Product
• Card type, loan type (auto, home, unsecured), lease, used versus new, brand
• Demographics
• Geographical (region, urban/rural, state/province, internal definition, neighborhood), age, time at bureau
• Source of business
• Channel (net, branch, store-front, 'take one', brokers)
• Applicant type
• new/existing, first time home buyer, groups (retired, students, engineers), thin/thick rile, clean/dirty file
• Product Owned
• Credit Card for existing mortgage/loan holders.
393
Experience Based Segmentation
• Consider future plans, not just historic operations
• How do we detect new segments?
• Marketing/risk analysis:
• Bad rates
• Approval rate
• Profit, and so on.
• Look for significant performance difference.
Experience Based Segmentation
• Need to confirm experience using analytics.
• Definition of segments
• What is a thin file?
• What is young' versus old'?
• What is the best demographic split?
• What break is best for 'tenure at bank'?
Confirming Experience
• Rule of thumb:
• "When the same information predicts differently across unique segments"
	Bad Rate			
		Age > 30	Age < 30	Unseg
				
c	Bent	2.1%	4.8%.	^ 2.9%
	Own	1.3%	1.8%	1.4%
	Parents	3.8%	2.0%	3.2%
				
	TrflHp«^.....,			
	D	5.0%	2.0%.	^ 4.0%
	1-3	?P%	3.4%	2.5%
	A±	1.4%	5.8%L^2.3%	
Confirming Experience
Attributes	Bad Rates	
		
Age		
Over 40 yrs	1.80%	
30-40 yrs	2.50%	
Under 30	6.90%	
		
Source of business		
Internet	20%	<^=^
Branch	3%	<^=^
Broker	8%	<^=^
Phone	14%	
		
Applicant Type		
First Time buyer	5%	
Renewal Mortgage	1%	
397
That Is the Easy Way
• You can also build full segmented models, and compare "lift" sensitivity, and so on, with a base model.
• It is best to perform this analysis for both experience and statistically based segmentation.
398
Comparing Improvement
• Use different methods to measure improvement (lift, KS, c-stat, precision, and so on.)
Segment	Total c-stat	Seg c-stat	Improvement
			
Age < 30	0.65	0.69	6.15%
Age > 30	0.68	0.71	4.41%
			
Tenure < 2	0.67	0.72	7.46%
Tenure > 2	0.66	0.75	13.64%
			
Gold card	0.68	0.69	1.47%
Platinum card	0.67	0.68	1.49%
399
Comparing Improvement
• Portfolio stats will put improvements into measurable portfolio terms.
		After Segmentation		Before Segmentation	
Segment	Size	Approve	Bad	Approve	Bad
					
Total	100%	/o	%	/o	%
					
Age < 30	65%	/o	/o	/o	/o
Age > 30	35%	/o	/o	/o	/o
					
Tenure < 2	12%	/o	/o	/o	/o
Tenure > 2	88%	/o	/o	/o	/o
					
Gold card	23%	/o	/o	/o	/o
Platinum card	77%	/o	/o	/o	/o
400
oosing Segmentation
Cost of scorecards (internal/external)
Implementation
Processing
Data storage
Monitoring/strategy development Segment size Do I have to?
Statistically Based Segmentation
• Less preconceived notions
• Clustering
• Decision Trees.
402
Clustering
Clustering
Showing 3 distinct groups and one outlier.
Clustering
Here is an insurance example of one cluster.
- What do we see here?
- lower than avg age
- more claims
- live in region A only
- likely to be single and drive a sports car.
- this is obviously a high risk segment, (confirm this group with claims analysis)
- Similar groups according to characteristics, not performance - so confirm performance for the clusters and combine those with similar risk behavior. We're not building a marketing profile, but a RISK PROFILE.
404
Clustering
• Defining characteristics for each group
• From previous example,
• Young males region A
• Young females region A, and so on.
• Performance analysis to confirm segmentation.
Decision Trees
Isolates segments based on performance (target)
Easily interpretable and differentiates between goods and bads.
All Good/Bads Bad rate = 3.8%
Existing Customer Bad rate = 1.2%
New Applicant Bad rate = 6.3%
Customer > 2 yrs Bad rate = 0.3%
Customer < 2 yrs Bad rate = 2.2%
Age < 30 Bad rate = 11.7%
Age > 30 Bad rate = 4.2%
406
So Now We Know ...
• the business
• sample and performance windows
• bad , good , indeterminate
• exclusions
• bad rate, approval rate
• number of scorecards needed, and their segments.
407
Methodology/Format
• Implementation platform and format
• Interpretability, implementation
• Legal compliance
• Data quality, sample size, target type
• Tracking and diagnosis
• Specify parameters for scorecard (range of scores, "points to double the odds").
408
Why 'Scorecarď Format?
• Easiest to interpret, justify, implement
• Reasons for decline/low scores can be explained to auditors, Mgmt, regulators, adjudicators
• No black box
• Diagnosis, tracking, monitoring
• Development process fairly simple to understand.
409
Review Implementation Plan
• Number of scorecards
• Data requirements
• Manage expectations
• Continuity.
Everyone is aware of what's going on.
This is a business process, not a mystery novel. You'd be surprised how many people in companies like to spring surprises on other departments.
Cvičení
Základní popis dat:
Jsou k dispozici následující data:
Accepts.sas7bdat (64589 řádků) Rejects.sas7bdat (35411 ř.) Applicants.sas7bdat (100.000 ř.)
...24 sloupců
ID of applicant, Date of application/opening, Accept / Reject, 30-days deliquency, 30-days deliquency date, 60-days deliquency, 60-days deliquency date, 90-days deliquency, 90-days deliquency date, Worst previous deliquency, Current deliquency, Age, Age groups, Sex, Existing client?, Phone member?, Region, Income, Income groups, Debt, Income/Debt ratio, Income/Debt ratio groups, Probability of 60-days deliquency (old), Score (old).
title 'Accepts';
proc means data=indata.accepts n nmiss min median mean max;
var age income debt idratio; run;
title 'Accepts';
proc freq data=indata.accepts;
table sex client phone region;
table (sex client phone region)*bad60;
table bad30*(bad60 bad90) bad60*bad90;
run;
title 'All applicants'; goptions ftext='arial'; proc catalog c=gseg kill; quit;
proc gchart data=indata.applicants;
vbar age / midpoints=18 to 75 name='_1data_a';
vbar income / name='_1data_b';
vbar debt / name='_1 data_c';
vbar idratio / name='_1data_d';
vbar type / name='_1data_e';
vbar scoreold / levels=10 name='_1data_f;
vbar pbad60old / levels=30 name='_1data_f;
run;
quit;
proc univariate data=indata.applicants normal;
var age income debt idratio; histogram age income debt idratio;
run; 411
Cvičení
Accepts The MEANS Procedure
Vybrané výstupy uvedeného kódu:
nie FREQ Procedure
		Sex	
Sex	Frequency	Cumulative Percent Frequency	Cumulative Percent
M	45138	69 88 45136	69.88
Z	19451	30.12 64589	100.00
		Existing client?	
Client	Frequency	Cumulative Percent Frequency	Cumulative Percent
0	60188	93.19 60188	93.19
1	4401	6.81 64589	100.00
Variable	Label	N	N Miss	Minimum	Median	Mean	Maximum
Age	Age	64589	0	18.0000000	43.0000000	43.3129945	74.0000000
Income	Income	64589	0	15000.07	19631.47	19854.56	35790.94
Debt	Debt	64589	0	100444.85	560744.83	576945.05	1611457.12
IDRatio	Income/Debt ratio	64589	0	0.0175377	0.0345483	0.0500680	0.2994807
	Phone member?			
		Cumulative	Cumulative	
Phone	Frequency	Percent Frequency	Percent	
0	8081	12.51 8081	12.51	17.5 -
1	56508	87.49 64589	■ oo.oo	150-
				
		Region		
Region	Frequency	Cumulative Percent Frequency	Cumulative Percent	
1	12537	19.41 12537	19.41	7.5 -
2	16335	25.29 28872	44.70	5 a -
3	10679	16.53 39551	61.23	
4	10797	16.72 50348	77.95	IS-
5	7199	11.15 57547	89.10	ní
6	7042	10.90 645B9	100.00	
The UNIVARIA TE Procedure
All applicants
Trie UNIVARIATE Procedure Variable: IDRatio (Income/Debt ratio)
Moments			
N	100000	Sum Weights	100000
Mean	0.04766914	Sum Observations	4756.91379
Std Deviation	0.03680037	Variance	0.00135427
Skewness	2.10159641	Kurtosis	4.8128053
Uncorrected SS	362.660032	Corrected SS	135.425362
Caeff Variation	77.1995591	Std Error Mean	0.00011637
Basic Statistical Measures Location Variability
Mean    0.047669 std Deviation o.03680
Median 0.033093 Variance 000135
Mode             - Range 0.28194
Interquartile Range 0 03334
Cvičení
/* 2a. Bad rate development, roll rate analysis */
Bad rate development - current deliquency
%let performancewindow='31dec2002'd>=datappl; %let deliq=worstdeliq;
procfreq data=indata.accepts /*noprint*/;
table datappl*&deliq / out=&deliq (keep=datappl &deliq pct_row
where=(&deliq ne '0')) outpct missing;
format datappl yyqs7.;
where &performancewindow;
run;
ods html path="&appl_root" file="2.&deliq..html";
goptions reset=all ftext='arial';
symbol 1 i=j v=dot;
axisl label=('Bad rate');
proc catalog c=gseg kill;
quit;
title 'Bad rate development - current deliquency'; proc gplot data=&deliq;
plot pct_row*datappl=&deliq / name='_2curdel' grid hreverse
vaxis=axisl hminor=0;
run;
quit;
ods html close;
2002«       2002/3      2002/2      2002/1       2001/4       2001/3      2001/2 2001/1
Date of application/opening Worst previous deliquency   *** 3 6 •«
2000/4       2000/3      2000/2 2000/1
413
Cvičení
/* analýza kohort */
%let target=bad30; %let date=dat30;
data cohorts;
set indata.accepts (keep=datappl bad: dat:);
if &target then qtr=int(yrdif(datappl,&date,'act/acť)*4)+l;
datappl=intnx('month',datappl,0);
format datappl mmyys7.;
run;
procfreq data=cohorts noprint;
table datappl / out=cohortsl (drop=percent
rename=(count=counttotal));
table datappl*qtr / out=cohorts (drop=percent);
run;
data cohorts;
merge cohorts cohortsl; by datappl;
if first.datappl then cumpct=.; if qtr ne . then do;
cumpct+(count/counttotal);
output; end; run;
ods html path="&appl_root" file='2.cohorts.html'; title "Cohort analysis for &target";
proc tabulate data=cohorts missing format=percent8.4;
class datappl qtr; var cumpct;
table datappl,qtr*cumpct="*sum="; run;
ods html close;
Cohort analysis for bad30
	1	qir 2	3
Date of applications pening			
HflM	5.0B7%	6.652%	
■HHH	8.327%	6.637%	7.055%
DffM	5.4B1%	6.441%	=..V^--:
04/2 a DO	5.456%	6.2*4%	6.387%
05,'200O	8.000%	7.648%	
002000	5.21B%	6.724%	
07,'200O	5.437%	6 130%	
06:2000	8.321%	7.401%	7.455%
osraoDO	8.345%	7010*	
i«Ma	8.023%	6.7*2%	
l-UZHD	5.613%	6 104%	6218%
12/2000	8.400%	7.346%	
01,'200l	8.064%	7.109%	
02:2001	5.BS6%	6 809%	
03720D1	8.271%	6.766%	6.078%
UiTHI	8.035%	7870%	7.025%
05,'200l	8.201%	6.844%	
00:2001	5.301%	6996%	6.051%
0 7:2 0 0 1	1.05B%	6.729%	
00:2001	8.33B%	7.377%	
09:2001	8.376%	7 iie%	
ItMl	8.446%	7200%	
11:2001	5.050%	6415%	
12:2001	5.521%	6 704%	6.781%
01:2002	5.666%	6412%	
02:2002	5.613%	6.644%	6.B12%
03:2002	5.B24%	6.404%	
04/2002	5.778%	6.446%	
05.2002	5.304%	5.974%	
06.2002	8.070%	6.900%	
07:2002	5.374%	5.417%	
06.2002	5.405%	5.622%	
03.2002	5.4B3%	5.469%	
10:2002	' 6D6%		
11:2002	2.563%		
Cvičení
/* performance window */
%let performancewindow='31dec2002'd>=datappl;
proc tabulate data=indata.accepts out=brdev (drop=_type__stable__page_);
class datappl;
var bad90 bad60 bad30;
table datappl,(bad90 bad60 bad30)*mean*format=percent8.2;
format datappl yyqs7.;
where &performancewindow;
label datappl='Month opened';
run;
ods html path="&appl_root" file='2.perf.html';
goptions reset=all ftext='arial';
symbol 1 i=j v=dot;
axisl label=('Bad rate');
proc catalog c=gseg kill;
quit;
title 'Bad rate development'; proc gplot data=brdev;
plot (bad:)*datappl / name='_2perf grid overlay legend hreverse
vaxis=axisl hminor=0;
run;
quit;
ods html close;
Bad rate development
2002«       2002«      2002/2      2002/1       2001/4      2001/3      2001/2      2001/1       2000/4       2000/3      2000/2 2000/1
Month opened
PLOT   »"Bad90 Mean   »"Bad60 Mean    »"Bad30 Mean
415
Cvičení
/* bad rate development */
%let samplewindow='30jun2001'd>=datappl>='01apr2001'd; %let samplewindow='31dec2001'd>=datappl;
procfreq data=indata.accepts noprint;
table dat60 / out=development missing; format dat60 mmyys7.; where &samplewindow; run;
data development;
set development; if _n_> 1 then do;
dat60=i ntnx(' month ',dat60,0);
cum_pct+percent;
output; end;
label datappl='Month of opening'; run;
ods html path="&appl_root" file='2.badratedev.html';
goptions reset=all ftext='arial';
symbol 1 i=j v=dot;
axisl label=('Bad rate');
proc catalog c=gseg kill;
quit;
title 'Bad rate development'; proc gplot data=development;
plot cum_pct*dat60 / name='_2brd' grid;
run;
quit;
ods html close;
cum_pct 4
Bad rate development
01/2000    04/2000 07/2000
1 0/2000    01/2001     04/2001     07/2001     10/2001     01/2002    04/2002    □7I2DD2 10/2002 60-days deliquency date
416
Cvičení
/* BRDEV macro */
%macro brdev(data,out,datevar,targetvar,samplewindow);
proc freq data=&data noprint; table &datevar / out=&out missing; format &datevar mmyys7.; where &samplewindow; run;
data &out (keep=date cum_pct); set &out;
if _n_>lthen do;
date=intnx('month',&datevar,0); cum_pct+ percent; output; end;
format date mmyys7.; run;
%mend brdev;
%let samplewindow='30jun200rd>=datappl>='01apr200rd; %brdev(indata.accepts,development,dat60,bad60,&samplewindow)
I* several bad rate development */
%let samplewindow='30jun200rd>=datappl>='01apr200rd; %brdev(indata.accepts,development30,dat30,bad30,&samplewindow) %brdev(indata.accepts,development60,dat60,bad60,&samplewindow) %brdev(indata.accepts,development90,dat90,bad90,&samplewindow)
data developmentsev;
set development30 (in=_30) development60 (in=_60) developments;
if_30 then type='30';
else if_60 then type='60';
else type='90'; Run;
data anno;
function='label';x=20;y=2;text='Sample window';output;
size=2;function='move';x=10;y=2.5;output;
function='draw';x=30;y=2.5;output;
function='move';x=20;y=3.5;output;
function='draw';x=140;y=3.5;output;
run;
ods html path="&appl_root" file='2.badratedev_several.html1;
goptions reset=all ftext='arial';
symbol 1 i=j v=dot;
axisl label=('Bad rate');
proc catalog c=gseg kill;
quit;
title 'Several bad rates development';
proc gplot data=developmentsev annotate=anno;
plot cum_pct*date=type / grid vminor=0 name='_2brds' vaxis=axisl; format date mmyys5.; label date='Performance window'; run; quit;
ods html close; Badl
Several bad rates development
Sample window
Performance window
Cvičení
/* Roll rate analysis */
ods html path="&appl_root" file='2.roll_rate.html';
proc format;
value $deliq (notsorted)
'0'=' no deliquency'
'3'='30 days'
'6'='60 days'
'9'='90+ days'; run;
proc tabulate data=indata.accepts out=rollrate missing;
class curdeliq worstdeliq;
tables worstdeliq,curdeliq*rowpctn;
format curdeliq $deliq. worstdeliq $deliq.;
title 'Roll rate analysis';
run;
proc gchart data=rollrate;
hbar3d worstdeliq / sumvar=pctn_01 subgroup=curdeliq nostats
clipref autoref raxis=axisl;
axisl label=none minor=none;
run;
quit;
Roll rate analysis
Worst previous deliquency
no deliquency
30 days
60 days
90+ days
3
1
0 10 20 30 40 50 SO 70 SO 90 100
Current deliquency   I    I no deliquency   I    130 days
] 60 days
190+ days
ods html close;
418
. Příprava dat II
Bad rates
Group of age
-6000   -40.00 -20.00    0.00    20 00   40.00   60.00    30.00   100.00 120.00
419
Development
Stage 3: Development Database Creation
Development Sample Specification
Development sample spec, means specifying what we need in the database we will use for development. We are not going to take a dump of everything from the CDW or datamart.
• Make the development process manageable and efficient:
• list of characteristics (or "variables" to be considered for devp. You don t want to have the entire DW.)
• sample sizes (for each segment and category. No point regressing on look when 3k will suffice.)
• parameters from previous section.
• Do all this bearing in mind the number of scorecards you want developed and for which segments.
421
Characteristic Selection
How do you select characteristics? Reinforce: there is a need for some thought to be put into process in selecting characteristics ..
You get together with risk, mktg, product. And get operations areas such as collections aboard (WHO knows your bad guys better than anyone else?)
• Expected predictive power
• Reliability: (is this manipulated? or prone to be manipulated?, e.g. salary. Check historical data - cannot be confirmed or too expensive to confirm. Can it be interpreted e.g. occupation/industry type is the worst cases. Do poeple usually leave this blank.)
• manipulation (non-confirmable)
• interpretation (present and future)
• missing
• Legal issues (Cant ask/get some info?.. Might get into trouble with some?)
422
Characteristic Selection
• Ease in collection
• Do you want to spend time chasing missing info for a credit card?... may be OK for a mortgage. How easy it is to get this piece of info?
• Policy rules
• Don't include anything that is unchangeable PR, e.g. bankruptcy. If you are going to decline all bankrupcy, no need to use it in scorecard.
• Derived variables - ratios
• Can do a lot of ratios .. But put some business thought into it.
• Future direction.
• Will this info be collected in the future (e.g. app form redesign)?
• Industry direction - not relevant today but will change, can include in card or collect for future e.g. higher credit lines. Talk to credit bureaus industry trend and how they affect the scorecard.
What are you doing: you re looking at objectives, company operations, business knowledge, ground realities etc. This is not just a stats exercise!!!
' 423
mpling
• Development, validation
70:30, 80:20
• If sample is small, do 100%, but validate with several 50-80%.
• Good, bad, reject
• 2000 of each (or higher)
• Oversampling (oversampling is common when modeling rare events ... it leads to better predictions)
• Proportional sample - not recommended for low bad rates.
• Take what you got for bads and sample the goods.
• Ensure that each group has sufficient numbers for meaningful analysis.
424
Data Collection and Database Construction
• Random and representative
• for each segment applicants (and accounts)
• One for unsegmented (to measure lift from segmentation)
• Data quirks, changes (preferably documented)
• e.g. code for renters changed from R to E .. Stopped collecting some data item, new data fields, started collecting data recently etc. etc.
• Objective: Data collected, as specified.
425
Adjusting for Prior Probabilities
• When oversampling
• Adjust to actual:
• Approval rate
• Bad rate
• Analysis and reports reflect reality
• Do not need if you only want to know relationships or rank ordering.
Through-the-door
10,000
_I
I--1
Rejects Accepts 2,950 7,050
I
I--1
Bads	Goods
874	6,176
426
Adjusting for Oversampling
• Separate sampling is standard practice (helps when you just did 'bad' definition)
• Prior probabilities must be known
• Can adjust before fitting the model or after.
• Two ways:
• Offset
Sampling weights (frequency variable).
427
Offset Method
• Logit (Pi)=P0+       ....+ (3kxk
• When oversampling, logits shifted by the offset:
• Logit (p*.)= In (pjijpji) + (30+ p,x1+ ....+ (3kxk
• Where
• px and p0= proportion of target classes in the sample
• tt^and ti0= proportion of target classes in the population.
Offset Method
• Adjustment post-model (after model development)
• PAi = (pA*iPcA) /   [(l " PA*i) P^o + PA*iPo^)]
• Where pA*j is the unadjusted estimate of posterior probability.
SAS Programs - Pre-model Adjustment
data develop; set develop;
In (p1n0 I p0nj
off=(offset calc) ; run;
proc logistic data=develop  ...;
model ins=......./ offset=off;
run;
proc score .... ;
p=l /   (1+exp(-ins)); proc print; var p .... ; run;
430
SAS Program - Post-model Adjustment
proc logistic data=develop...; run;
proc score run;
.  out=scored...;
data scored; set scored;
off = (offset calc) ;
p=l / (l+exp(- (Ins-off) ) ) ; run;
proc print data=scored ..;
var p  ...;
run;
431
Sampling Weights
• Adjusts data to reflect true population
• Weights:       and 7i0/p0
• Or set weight of bad=i and weight of good = p(good)/p(bad) for population.
• For example, p(bad)=4%, 2000 goods, 2000 bads. Sample will show 2000 bads and 48,000 goods.
• Normalization causes less distortion in p values and standard errors.
• Use FREQ variable in EM or calculate sample weight and use weight=sampwt in the LOGISTIC procedure.
432
SAS Program
• When using the WEIGHT statement, some output is not correct.
data develop; set develop;
saxapwt=( n0/ p0)*  (ins=0) + ( n±/ p±)*  (ins=l) ; run;
proc logistic data=develop ... ; we±ght=saxapwt ;
model ins=.......;
run;
433
What Is the Difference?
• The parameter estimates will be different.
• When linear-logistic model is correctly specified, offset is better.
• When logistic model is an approximation of some non-linear model, weights are better.
• For scorecards, weighting is better since it corrects the parameter estimates used to derive scores (prior probabilities only affect the predicted probabilities).
434
Development
Stage 4: Scorecard Development
Objective
• Understand a methodology for developing and assessing risk scorecards.
• Grouped attributes
• Logistic regression Reject inference
• Scaled points.
Process Flow-Application Scorecard
Explore Data Data Cleansing
Validate
Initial Characteristic Analysis (Known Good Bad)
Final
Scorecard (AGB)
• Scaling
• Assessment
Preliminary Scorecard (KGB)
i
Reject Inference
Initial Characteristic Analysis (All Good Bad)
437
Process Flow - Behavior Scorecard
Explore Data ^    Initial Characteristic
Data Cleansing Analysis (Known
Good Bad)
\
Final
w ,. . .       ^_, Scorecard
Validate 0 ..
• Scaling
• Assessment
438
Before you start...
Explore the data, visualize (Insight in SAS EM)
• Distributions
• mean, max/min, range, missing
• Compare with overall portfolio distributions
• Data integrity (any garbage, outliers)
• Ensure data meets the data specifications done earlier.
• Check that o's mean zero, not missing values.
• Population stability check:
• Month by month table of distribution for each predictor (e.g. 200701 men 55%, women 45%, 200702 men 57%, women 43%)
439
Missing Values and Outliers
• Missing (ALL financial data has missing and garbage values)
• Complete Case Analysis - Exclude everything with missing data .. In CS, you'll end up with nothing ©.
• Exclude characteristics or records with significant missing values
• Group 'missing' as a distinct attribute -the weight of missing will tell you what missing contains. If it is close to neutral, good since it is random. Recommended - recognize that missing data has information value and may not be randomly missing. Find the value and use it. Plus, including missing points' in scorecard will take care of ppl who leave it blank.
• Impute missing values - don't use mean/most likely, model based on decision tree may be better.
• Outliers (and mis-keys)
• Exclude/replace records.
440
Missing Values
• Missing data is not usually random
• Missing data can be related to the target
• New at job may leave yrs at empl blank
• Low income or commercial customers leave income blank
• Do bad customers leave certain fields blank?
• Including and grouping missing data can answer this question.
Initial Characteristic Analysis
• Analyze individual characteristics
• Identify strong characteristics
• Best differentiators between good' and 'bad'
• Screening
• Select characteristics for regression (variable selection).
Initial Characteristic Analysis
• Start by performing initial grouping for each characteristic and rank order Information Value (PROC DMSPLIT or SPLIT, or EM node)
• Alternate: rank order characteristics by Chi Square or other method
• Fine tune grouping for stronger characteristics
May want to perform other analysis prior to this (for example, use PC to identify collinear characteristics)
• Some people use principal components (PROC VARCLUS) to identify which characteristics they need from each cluster. And then concentrate on the best out of each.
443
Criteria for Variable Selecti
• Predictive power of attribute: Weight of Evidence
• Range and trend of WOE across attributes
• Predictive power of characteristic: Information Value, Gini index(coefficient)
• Operational/business considerations.
Weight of Evidence
		Distr		Distr		Distr		
Age	Count	Count	Goods	Good	Bads	Bad	Bad rate	Weight
								
Missing	50	3.00%	43	2.40%	8	4.10%	16%	-55.497
18-22	200	10.00%	152	8.40%	48	24.90%	24%	-108.405
23-26	300	15.00%	246	13.60%	54	(^8.00%*	) 18%	(^72.039
27-29	450	23.00%	405	"B227Fn%	45		10%	
30-35	500	25.00%	475	26.30%	25	13.00%	5%	70.771
35-44	350	18.00%	349	19.30%	11	5.70%	3%	122.044
44 +	150	8.00%	147	8.10%	_3	1.60%	2%	165.509
								
Total	2,000		1,807		193		9.65%	
								
Information Value = 0.066								
Ln     Distr Good / Distr Bad     x 100
Weight of Evidence
• Measures strength of each (grouped) attribute in separating goods and bads
• (Distr Good / Distr Bad) = odds of being good
• Negative weight: more bads than goods
• Logical trend
• Forage 23-26:
WOE = In (0.136 / 0.28) = -0.722 (xioo = -72.2)
446
Information Value (Strength)
		Distr		Distr		Distr		
Age	Count	Count	Goods	Good	Bads	Bad	Bad rate	Weight
								
Missing	50	3.00%	43	2.40%	8	4.10%	16%	-55.497
18-22	200	10.00%	152	8.40%	48	24.90%	24%	-108.405
23-26	300	15.00%	246	13.60%	54	<^2aoo^	18%	(^72.039
27-29	450	23.00%	405	22.40%	45	"""23730%	10%	
30-35	500	25.00%	475	26.30%	25	13.00%	5%	70.771
35-44	350	18.00%	349	19.30%	11	5.70%	3%	122.044
44 +	150	8.00%	147	8.10%	_3	1.60%	2%	165.509
								
Total	2,000		1,807		193		9.65%	
								
Information Value = 0.066								
SI
Distr Bad    x Weight
Kullback, S., Information Theory and Statistics (1959)
447
Information Value
•Z   [(Distr  Good  -  Distr  Bad)   x  {In  (Distr  Good  /  Distr Bad)}]
When      figures      used      in      decimals format (for example, 0.136).
• Rule of thumb:
• < 0.02: unpredictive
• 0.02 - 0.1: weak
• 0.1 - 0.3: medium
• 0.3 +: strong
• Too strong? (IV>o.5) - use it in a controlled way (add them in the end of regression to see if they add any incremental value)
448
Grouping
Groups with similar WOE are put together
• For continuous variables, groups are created so as to maximize difference from one group to next - and maintain logical trend for WOE
• Why Group?
• Easier way to deal with outliers with interval variables, and for rare classes
• Format of the scorecard
• Easy to understand relationships
• Model non-linear dependencies with linear models
• Control the process
449
Grouping
Grouping of the demographic scorecard variable "age". On the left pictures, the dependence of bad rate (smoothed using normal probability density function) on the variables is presented. On the right, the cumulative distribution function is presented. Vertical lines represent the borders between categories, horizontal red lines in the left picture represent the mean bad rate in categories, horizontal blue lines in the right picture represent the relative distribution of observations in the categories. 450
Logical Trend
gical Trend
Final weightings make sense. Enables buy-in from risk managers.
Confirms business experience
• young people are higher risk
• higher debt service means higher risk
Reduces overfitting if done right - model overall trend, not quirks. Remember how long the scorecard has to last. This is not going to be used for the next campaign and then discarded.
Linear relationship not always true, but need trend to confirm, and back up with business experience. E.g. revolving open burden shows a 'banana curve' everywhere and is now accepted as that. People don t try to make it straight.
Logical Trend
Obviously not a logical trend!!!
453
Logical Trend
Which line shows logical trend?
Both are logical. What's the difference?
Blue    line    shows good
differentiation.
Red line is flat, and this
characteristic is likely very
week and will be reflected in
the IV
Predictive Strength
200
-150 J—
Age
454
Stability check
Check the stability of grouping throughout the whole developmnet time window:
agefr  pot  risky all segment
qu nr ier 2'j U t, =■
_f r 20 29 31
3- 6
4- 1
5- 1 60
2.0 29 3-2 sa + 1 5-1 60
20 29 3-ž 54 41 51
3-2 54 41 &1 SO
Pc1H_011 SUN 1 S . OS 7 . ED
S . 25 5.25
11 12
C_-jqe_F r
PctN_011 suy I .52      I I 3
455
Business Factors
• Nominal values
• group based on similar weight (for example, postal code, occupation)
• investigate splits on urban/rural, regional
• Breaks concurrent with policy rules
• Sanity check.
456
Variable Selection
List of information values of variables (predictors)
		IV	Information
No	Character	Rank	Value
1	Max delinq L9M	1	0.176
2	Months since delinquent	2	0.176
3	Active contract (Y/N)	3	0.045
4	Average Delinquency L9M	4	0.087
5	Months since >10 dpd	5	0.144
6	Max delinq L3M	6	0.117
7	Average Delinquency L3M	7	0.108
8	Age of oldest contract	8	0.013
9	Number of months on collections as % total time on book	S3	0.132
			
10	Months since >20 dpd	10	0.091
11	Months since >30 dpd	11	0.054
12	Num rejected applications L9M	12	0.033
13	Times 30+ dpd L9M	13	0.042
14	Total Payment L3M	14	0.018
15	Months since >40 dpd	15	0.030
16	Current balance as % of highest ever balance	16	0.048
17	Times 30+ dpd L3M	17	0.024
18	Payment Method	18	0.001
457
Cvičení-profile
/* 2b. Profiles */
%let input=income; %let groups=yes; %let n_groups=4;
/* grouping 1 - kvantily */
proc rank data=indata.accepts (keep=&input) groups=&n_groups out=bins;
var &input; ranks bin; run;
proc summary data=bins nway missing;
class bin;
output out=bins (drop=_type_) min(&input)=start max(&input)=end; run;
data bins;
set bins;
label=compress(put(start,best.))| |' - '| |compress(put(end,best.));
fmtname='_bin';
type='N'; run;
proc format cntlin=bins; run;
%macro profile(input,groups);
/* Profile of &input according to BAD60 */
proc summary data=indata.accepts; class &input;
output out=_bins (drop=_type_ rename=(_freq_=_n))
sum(bad60)=_nl;
%if %upcase(&groups)=YES %then %do;
format &input_bin.;
%end; run;
data_bins;
set_bins end=_finish;
if _n_=l then do;
_all_n=_n;
_all_nl=_nl;
_all_nO=_n-_nl;
retain_all_n:;
end; else do;
_p=_n/_all_n;
_n0=_n-_nl;
_pl=_nl/_all_nl;
_pO=_nO/_all_nO;
_rl=_nl/_n;
_rO=_nO/_n;
_woe=log((_p0)/(_pl))*100; _all_iv+(_p0-_pl)*_woe/100; output; end;
if_finish then do;
call symput('groups',compress(put(_n_-l,best.)));
call symput('iv',compress(put(_all_iv,8.4)));
call symput('br',compress(put(_all_nl/_all_n,best.)));
end; attrib
_n label='N'
_p label='%' format=percent8.1
_nl label="N of Bad" _n0 label="N of Good"
_pi label="% of Bad" format=percent8.1
_pO label="% of Good" format=percent8.1
_rl label="Bad rate" format=percent8.1
_rO label="Good rate" format=percent8.1
_woe label='WOE format=8.2 &input label="Group of &input"
drop_all:;
Run;
data_chart (keep=&input_sub_n_p_r);
set_bins (keep=&input_nO_pO_rO_nl_pi_rl);
length_sub $4;
_sub="Good";
_n=_nO; _P=_pO; _r=_rO; output;
_sub="Bad";
_n=_nl;
_P=_pl;
_r=_rl;
output; attrib
_n  label='N' format=8.0
_p label='%' format=percent8.1
_r label='Rate' format=percent8.1
_sub label=Target'
run;
proc datasets nolist;
delete gseg / memtype=catalog;
quit;
ods listing close;
goptions reset=all ftext='arial' htext=1.5 ftitle='arial' htitle=2;
proc gchart data=_chart;
axisl style=0;
axis2 minor=none order=(0 to 1 by .25) label=none;
axis3 minor=none label=none; axis4 minor=(n=4) label=none;
where_sub="Bad";
hbar &input / discrete sumvar=_r noframe nostats
maxis=axisl raxis=axis3 autoref cref=grayaO clipref name="_1";
title "Bad rates";
run;
where;
hbar &input / discrete subgroup=_sub sumvar=_n noframe nostats
maxis=axisl raxis=axis3 autoref cref=grayaO clipref name="_2";
title "Bad / Good frequencies";
run;
Quit;
proc hbar
title 1 run; hbar
title run; quit;
gchart data=_bins;
&input / discrete sumvar=_woe noframe nostats
maxis=axisl raxis=axis4 autoref cref=grayaO clipref name="_3";
"Weight of evidence";
&input / discrete sumvar=_pi noframe nostats
maxis=axisl raxis=axis4 autoref cref=grayaO clipref name="_4";
"Bad distribution";
ods html path="&appl_root" file="5.profile.html" style=statdoc;
proc report data=_bins nofs style(summary)=[htmlclass="Header"];
columns ("Attributes of &input" &input) (Total'_n_p)
("Good"_nO_pO) ("Bad"_nl_pi) ('Measures'_rl_woe);
define &input / group; compute after;
_rl.sum=&br;
_woe.sum=.;
endcomp;
rbreak after / summarize; title "Bad / Good by &input";
footnote "IV=&iv (<0.02 unpredictive, <0.1 week, <0.3 medium, <0.5 strong, >0.5 over)"; run;
goptions device=gif;
proc greplay nofs;
footnote;
igout gseg;
tc sashelp.templt;
template I2r2;
treplay 1:_1 2:_2 3:_3 4:_4 name="5_profil";
run; quit; title;
footnote; ods html close; ods listing; %mend profile; °/aprofile(&input,&groups)
Bad / Good by income
	Total		Good		Bad		Measures	
Group of income	N	%	N of Good	11 of Good	N of Bad	% of Bad	Bad rate	WOE
15000,067206 - 17541.45177	16117	25.0%	15631	25.0%	516	26.1%	3.2%	4.55
17511.61083-19631.129137	16117	25.0%	15688	25.1%	459	23.2%	2.8%	7.52
19631.471069 - 21723.106242	16118	25.0%	15683	25.0%	465	23.5%	2.9%	6.19
21723.273059 - 35790.940583	16117	25.0%	15612	24.9%	535	27.1%	3.3%	-8.29
						100.«	3.1*	■
n/=0.0016 (<0.02 unpredictive, <0.1 week, <B.3 medium, <0.S strong, >0.5 over)
459
Cvičení
/^profile multiple characteristics at once*/
%model_profilevar
(
data=data.accepts,
interval=age income idratio,
binary=sex phone client,
ordinal=age_grp income_grp region,
groups=5,
target=bad30,
rep_out=&appl_root
)
Bad / Good by Sex
Attributes of	sex	Total		Good		Bad		Measures
Group of sex	Sex	X	%	N of Good	% of Good	N of Bad	% of Bad	Bad rate WOE
I M	M	45138	69.9%	42061	69.6%	3077	"4.7%	6.8% -7.16
1	Z	19451	30.1%	18410	30.4%	1041	25.3%	5.4% 18.59
		64589	100.0%	60471	100.0%	4118	100.0%	6.4%
Unpredictive [TV = 0.0133: 2 groups) Bad / Good by Phone member?
Attributes of phone		Total		Good		Bad		Measures
Group of phoue   Phone member?		N	%	N of Good	% of Good	N of Bad	% of Bad	Bad rate WOE
0	0	8081	12.5%	7431	12.3%	650	15.8%	8.0% -25.04
1	1	56508	87.5%	53040	87.7%	3468	84.2%	6.1% 4.07
		64589	100.0%	60471	100.0%	4118	100.0%	6.4%
Unpredictive (TV = 0.0102: 2 groups)
Bad / Good by Existing client?
Attributes of cLLent	Total		Good		Bad		Measures
Group of client   Existing client?	N	%	N of Good   % of Good		N of Bad	% of Bad	Bad rate WOE
0 0	60188	93.2%	56251	93.0%	3937	95.6%	6.5% -2.74
1 1	4401	6.8%	4220	7.0%	1S1	4.4%	4.1% 46.23
	64589	100.0%	60471	100.0%	4118	100.0%	6.4%
Unpredictive (TV = 0.0126, 2 groups)
Bad / Good by Age groups
Attributes of	age grp	Total		Good		Bad		Measures	
Group of age_grp	Age groups	N	%	Nof Good	% of Good	N of Bad	% of Bad	Bad rate	WOE
do 30	do 30	2957	4.6%	2662	4.4%	291	7.2%	10.0%	-48.69
30 - 60	30 - 60	58713	90.9%	55057	91.0%	3656	88.8%	6.2%	2.52
nad60	nad 60	2919	4.5%	2752	4.6%	167	4.1%	5.7%	11.53
		64589	100.0%	60471	100.0%	4113	100.0%	6.4%	
Urtpredictrve (TV = 0.0146: 3 groups)
Bad / Good by Income groups
Attributes of income_grp		Total		Go	od	Bad		Measures	
Group of iucotne_grp	Income groups	N	%	Nof Good	% of Good	N of Bad	% of Bad	Bad rate	WOE
do 17	do 17	12070	18.7%	11213	18.5%	857	20.8%	7.1%	-11.54
17-22	17-22	37859	58.6%	35567	58.8%	2292	55.7%	6.1%	5.52
22-27	22-27	13680	21.2%	12820	21.2%	860	20.9%	6.3%	1.50
	nad 27	980	1.5%	871	1.4%	109	2.6%	11.1%	-60.85
		64589	100.0%	60471	100.0%	4118	100.0%	6.4%	
Unpredicfce (TV = 0.0118: 4 groups)
Cvičení
Bad / Good by Region
Attributes of region		Total		Good		Bad		Measures	
Group of region	Region	N	%	N of Good	% of Good	N of Bad	% of Bad	Bad rate	WOE
1	1	12537	19.4%	11404	18.9%	1133	27.5%	9.0%	-37.77
2	2	16335	25.3%	15498	25.6%	837	20.3°.;	5.1%	23.18
3	3	10679	16.5%	10034	16.6%	645	15.7%	6.0%	5.77
4	4	10797	16.7%	10170	16.8%	627	15.2%	5.8%	9.95
5	5	7199	11.1%	6783	11.2%	416	10.1%	5.8%	10.47
6	6	7042	10.9%	6582	10.9%	460	11.2%	6.5%	-2.59
		64589	100.0%	60471	100.0%	4118	100.0%	6.4%	■
Weak predictivity (TV = 0.0483= 6 groups)
462
Cvičení
Bad / Good by Age
Attributes of age		Total		Good		Bad		Measures	
Group of age	Age	X	%	N of Good %	of Good	N of Bad	% of Bad	Bad rate	WOE
0	18 - 35	13688	21.2%	12420	20.5%	1268	30.8%	9.3%	-40.49
1	36-40	11385	17.6%	10485	17.3%	900	21.9%	7.9%	-23.15
2	41 -45	14645	22.7%	13918	23.0%	727	17.7%	5.0%	26.52
3	46 - 51	12383	19.2%	11806	19.5%	577	14.0%	4.7%	33.17
4	52-74	12488	19.3%	11842	19.6%	646	15.7%	5.2%	22.18
		64589	100.0%	60471	100.0%	4118	100.0%	6.4%	■
Weak predictivity (TV = 0.0931= 5 groups)
463
Cvičení
Bad / Good by Income
Attributes of income		Total		Good		Bad		Measures	
Group of m come	Income	X	%	N of Good %	of Good	>" of Bad	% of Bad	Bad rate	WOE
0	15.000 - 17.105	12917	20.0%	12011	19.9%	906	22.0%	7.0%	-10.23
1	17.105 - 18.822	12918	20.0%	12204	20.2%	714	17.3%	5.5%	15.18
2	18.822- 20.39E	12918	20.0%	12122	20.0%	796	19.3%	6.2%	3.64
3	20.398 - 22.339	12918	20.0%	12102	20.0%	816	19.8%	6.3%	0.99
4	22.340 - 35.791	12918	20.0%	12032	19.9%	886	21.5%	6.9%	-7.82
		54589	100.0%	60471	100.0%	4118	100.0%	6.4%	■
Unpredictive <IV = 0.0080=5 groups)
464
Cvičení
Bad / Good by Incom&'Debt ratio
Attributes of id ratio		Total		Good		Bad		Measures	
Group of id ratio	Iü coin e Debt ratio	N	%	X of Good %	of Good	N of Bad %	of Bad	Bad rate	WOE
0	0.0175 - 0.0225	12917	20.0%	11994	19.8%	923	22.4%	7.1%	-12.23
1	0.0225 - 0.0293	12918	20.0%	11998	19.8%	920	22.3%	7.1%	-11.87
2	0.0293 - 0.0421	12918	20.0%	12061	19.9%	857	20.8%	6.6%	-4.25
3	0.0421 - 0.0714	12918	20.0%	12216	20.2%	702	17.0%	5.4%	16.98
4	0.0714- 0.2995	12918	20.0%	12202	20.2%	716	17.4%	5.5%	14.89
		64589	100.0%	60471	100.0%	4118 100.0%		6.4%	
Unpredicth'e (TV = 0.0160. 5 groups)
465
Cvičení
Profiles for target DATA. AC CEP TS.BAD 30
Type	Type	Label	Information value	Note	Format
BINARY	BINARY	SEX - Sex	0.0133	Unpredictive (TV = 0.0133= 2 groups)	
BINARY	BINARY	CLIENT - Existing client	0.0126	Unpredictive (TV = 0.0126= 2 groups)	
BINARY	BINARY	PHONE - Phone member?	0.0102	Unpredicnve (TV = 0.0102= 2 groups)	
INTERVAL	INTERVAL	AGE - Age	0.0931	Weak predicuvity (TV = 0.0931, 5 groups)	
INTERVAL	INTERVAL	TDRATIO - Incom&Debt ratio	0.0160	Unpredicnve (TV = 0.0160= 5 groups)	8.4
INTERVAL	INTERVAL	INCOME - Income	0.0080	Unpredictive (IV = 0.0080= 5 groups)	COMMAX20.
ORDINAL	ORDINAL	REGION - Region	0.0483	Weak predicuvity (TV = 0.0483; 6 groups)	
ORDINAL	ORDINAL	AGE GRP - Age groups	0.0146	LTnpredictive (TV = 0.0146: 3 groups)	
ORDINAL	ORDINAL	INCOME GRP - Lncome groups	0.0118	Unpredictive (TV = 0.0118= 4 groups)	
466
7. Úvod do shlukové analýzy (SA). Hierarchická SA
Sil ftCCNild f Uhm S *ii OM* bs(
467
Úvod
Shluková (klastrová, z angl. Cluster) analýza je metoda, která na základě informací obsažených ve vícerozměrných pozorováních roztřídí základní množinu objektů do několika relativně stejnorodých shluků. Uvažujeme datovou matici typu n x p, kde n je počet objektů a p je počet proměnných. Uvažujeme různé rozklady množiny n objektů do g shluků a hledáme takový rozklad, který je z určitého hlediska nej výhodnější. Cílem je dosáhnout stavu, kdy objekty uvnitř shluku jsou si podobné co nejvíce a objekty z různých shluků si jsou podobné co nejméně.
468
Unsupervised Learning
• Metody shlukové analýzy patří mezi tzv. ^unsupervised learning" metody
• "Learning without a priori knowledge about the classification of samples; learning without a teacher."
Kohonen (1995), "Self-Organizing Maps"
469
Cluster Profiling
Cluster profiling can be defined as the derivation of a class label from a proposed cluster solution.
The objective is to identify the features, or combination of features, that uniquely describe each cluster.
small-investors:
1:
you n'g.ej^ Jb i g^in ve sto rs
older, big investors
4
470
Types of clustering
• Rozlišujeme tři základní shlukovací metody:
• Hiearchické shlukování (hierarchical clustering),
• Shlukování s předem neznámým počtem shluků - s možným překryvem shluků (overlapping clusters),
• Shlukování do předem daného počtu shluků (partitive/partitioning methods).
• Fuzzy shlukování - fuzzy shluky jsou definovány stupněm příslušnosti objektů do daných shluků.
471
Klasifikace shlukovacích algoritmů
• Hiearchicke shlukovaci algoritmy:
• Aglomerativni
• Divisive
• Partitioning algoritms:
• K-means
• K-medoids
• Probabilistic
• Density based
• Grid-based algoritms
• Constraint-Based Clustering
• Evolutionary Algoritms
• Scalable Clustering Algoritms
472
Hierarchical Clustering
Aqqlomerative Divisive
□□□□□
9
I
□□□□□□□
Problems with Hierarchical Clusteri
error
Partitive Clustering
The goal of partitive clustering is to minimize or maximize some specified criterion.
Initial State
reference vectors (seeds)
Final State
observations
475
Problems with Partitive Clustering
• Many partitive clustering methods
a.   make you guess the number of clusters present,
make assumptions about the shape of the clusters, usually that they are (hyper)spherical, and
are influenced by seed location, by outliers, even by the order the observations are read in.
• It is impossible to determine the optimal grouping, due to the combinatorial explosion of potential solutions.
476
Problems with Partitive Clustering
The number of possible partitions of n objects into g groups is given by:
N(»,*) = -^£(-l)~r*>1-"
m
For example, the number of partitions of 50 observations into 4 clusters, N(50,4), is equal to 5.3 x 1028. N(ioo, 4) generates 6.7 x 1058 partitions. Complete enumeration of every possible partition, therefore, is generally impossible.
477
Heuristic Search
1. Generate an initial partitioning (based on the seeds) of the observations into clusters.
2. Calculate the change in error produced by moving each observation from its own cluster to another.
3. Make the move that produces the greatest reduction.
4. Repeat steps 2 and 3 until no move reduces error.
478
Hierarchická shluková analýza
• Je třeba zvolit:
• jak měřit vzdálenost/(ne)podobnost mezi objekty (euklidovská,...)
• do úvahy je třeba vzít typ dat (intervalová, nominální,...)
značnou roli také hraje souměřitelnost dat -> standardizace (z-skóre,...)
• jak měřit vzdálenost/(ne)podobnost mezi shluky (wardova,...)
• jak určit finální rozklad objektů do shluků
479
Příklad aglomerativního hiearchického shlukování
Uvažujeme 5 objektů A,B,(ľ,D a E popsaných čtyřmi proměnnými X1-X4. Neprovádíme žádnou standardizaci.
Vzdálenost mezi objekty měříme pomocí euklidovské vzdálenosti.
Vzdálenosti mezi shluky měříme pomocí metody průměrné vzdálenosti (average linkage).
Data:
obj	XI	X2	X3	X4
A	100	80	70	60
B	80	60	50	40
C	80	70	40	50
D	40	20	20	10
E	50	10	20	10
Matice vzdáleností:
	A	B	C	D	E
A	0	0	0	0	0
B	40,00	0	0	0	0
C	38,73	17,32	0	0	0
D	110,45	70,71	78,10	0	0
E	111,36	72,11	80,62	14,14	0
480
Příklad aglomerativního hiearchického shlukování
i. krok:
V matici vzdáleností hledáme nej menší hodnotu. V našem případě je to 14,1 (vzd. mezi D a E).
Sloučíme objekty D a E do shluku D', zmenšíme a přepočteme matici vzdáleností. Používáme metodu průměrné vzdálenosti, takže:
DÄ. = — £ £ d (x,, Xj) = -±- (110,4 +111,4):
nAnD' ieA jeD' 1' ^
110,9
DBD. =^(70,7 + 72,1) =
71,4
DCD =
1-2
(78,1 + 80,6) =
79,35
	A	B	C	D	E
A	0	0	0	0	0
B	40,00	0	0	0	0
C	38,73	17,32	0	0	0
D	110,45]	f 70,711	í 78,10	0	0
E	111.36	l 72.11 J	80.62	14,14	0
	A	B	C	D'
A	0			
B	40,00	0		
C	38,73	17,3	0	
D1    | 110,90]		71,41	1 79,36 |	0
481
Příklad aglomerativního hiearchického shlukování
2. krok:
V redukované matici vzdáleností hledáme nejmenší hodnotu. V našem případě je to 17,3 (vzd. mezi B a C).
•   Sloučíme objekty B a C do shluku B', zmenšíme a přepočteme matici vzdáleností.
IV = — Z Z d (x,, Xj)=-±- (40+38,7):
nAnB' ieA jeB' 1' ^
39,35
	A	B	C	D	E
A	0	0	0	0	0
B	40,00	0	0	0	0
C	38,73	17,32	0	0	0
D	110,45	70,71	78,10	0	0
E	111,36	72.11	80.62	14,14	0
DD,B, = — ZZd(xi'xj)=^ (70'7 + 78'! + 72'! + 80'6) = \ (7 !'4 + 79'3) =ÍŤ53Ť5l
nD'nB' ieD'jeB' ^-1 1
	A	B	C	D'
A	0			
B	40,00	0		
C	38,73	17,3	0	
D'	110,90	1 71,41	79,36 1	0
	A	B1	D'
A	0		
B1	39,36	0	
D'	110,90	75,39	0
482
Příklad aglomerativního hiearchického shlukování
3. krok:
V redukované matici vzdáleností hledáme opět nejmenší hodnotu. V našem případě je to 39,3 (vzd. mezi A a LV).
Sloučíme objekty A a LV do shluku A , zmenšíme a přepočteme matici vzdáleností.
—!— £ E d   ' xj )= ~ &1 °>45 + 11136 + 70,71 + 72,11 + 78,10 + 80,62) = - (l 10,90 + 2-75,39) =[87,23
nA'nD' ieA'jeD' 3*2 3
	A	EV	D'
A	0		
EV	39,36	0	
D'	110,90	75,39	0
	A	B	C	D	E
A	0	0	0	0	0
B	40,00	0	0	0	0
C	38,73	17,32	0	0	0
D	110,45	70,71	78,10	0	0
E				14,14	0
	A'	D'
A'	0	
D'	1 87,23|	0
Pozor!!! Slučují se dva nestejně velké objekty a nelze tedy počítat obyčejný průměr průměrů!
483
Příklad aglomerativního hiearchického shlukování
proč distance data=aaa method=euclid out=dist;
var interval(X1 X2 X3 X4);
id obj;
run;
proč cluster data=dist method=ave outtree=tree nonorm;
id obj; run;
proč tree data=tree horizontál;
id obj; run;
484
Příklad aglomerativního hiearchického shlukování
obj
Dab. = 39,35
A -
Dbc =17,32
B -1
B' -
c -
DDE =14,14
D -1
D'-
E -
0 10 20 30 40 50 60 70 80 00
Average Distance Between Clusters
A'
DA,D,= 87,23
485
Příklad aglomerativního hiearchického shlukování
39,4-17,3 = 22,1
87,2-39,4 = 47,8
obj	XI	X2	X3	X4
A	100	80	70	60
B	80	60	50	40
C	80	70	40	50
D	40	20	20	10
E	50	10	20	10
	A	B	C	D	E
A	0				
B	40	0			
C	38,73	17,321	0		
D	110,45	70,71	78,10	0	
E	111,36	72,11	80,62	14,14	0
. Určili jsme tedy dva shluky A' -{A, B, C}aD' = {D, E}.
486
What Is Similarity?
To illustrate the difficulties involved in judging similarity, consider your answer to the following question:
Which is more similar to a duck, a crow or a penguin?
The answer to this question largely depends on how you choose to define similarity
Volba míry (ne)podobnosti závisí na typu proměnných (nominální, ordinální, poměrové, intervalové, binární).
487
Principles of a Good Similarity Metric
• The following principles have been suggested as the foundation of a good similarity metric:
1. symmetry: d(x,y)=d(y,x).
2. non-identical distinguishability: if d(x,y)^o then x^y.
3. identical non-distinguishability: if d(x,y)=o then x=y.
• Most good metrics are also consistent with the triangle inequality: d(x,y) < d(x,z) + d(y,z).
488
The DISTANCE Procedure
General form of the DISTANCE procedure:
PROC DISTANCE DATA=SAS-data-set METHOD=similarity-metric
<options>;
VAR level (variables < I option-list >); RUN;
• A distance method must be specified (no default), and all input variables are identified by level.
Vice na:
http://support.sas.com/documentation/cdl/en/statugdistance/61780/PDF/default/statugdistance.pdf
489
The DISTANCE Procedure
• Metody měření vzdálenosti v SASu:
Method	Range	Type	Accepting variables		Method	Range	Type	Accepting variables
GOWER	Oto 1	sim	all		HAMMING	Oto n	dis	Nominal
DGOWER	Oto 1	dis	all		MATCH	Otol	sim	Nominal
EUCLID	>0	dis	Ratio, interval, ordinal		D MATCH	Otol	dis	Nominal
SQEUCLID	>0	dis	Ratio, interval, ordinal		DSQMATCH	Otol	dis	Nominal
SIZE	>0	dis	Ratio, interval, ordinal		HAMANN	-1 tol	sim	Nominal
SHAPE	>0	dis	Ratio, interval, ordinal		RT	Otol	sim	Nominal
COV	>0	sim	Ratio, interval, ordinal		SSI	Otol	sim	Nominal
CORR	-ltol	sim	Ratio, interval, ordinal		SS3	Otol	sim	Nominal
DCORR	Oto 2	dis	Ratio, interval, ordinal		DICE	Otol	sim	Asymmetric nominal
SQCORR	Oto 1	sim	Ratio, interval, ordinal		RR	Otol	sim	Asymmetric nominal
DSQCORR	Oto 1	dis	Ratio, interval, ordinal		BLWNM	Otol	dis	Asymmetric nominal
L(P)	>0	dis	Ratio, interval, ordinal		Kl	>0	sim	Asymmetric nominal
CITYBLOCK	>0	dis	Ratio, interval, ordinal		JACCARD	Otol	sim	Asymmetric nominal, ratio
CHEBYCHEV	>0	dis	Ratio, interval, ordinal		DJACCARD	Otol	dis	Asymmetric nominal, ratio
POWER(p,r)	>0	dis	Ratio, interval, ordinal					
SIMRATIO	Oto 1	sim	Ratio					
DISRATIO	Oto 1	dis	Ratio					
NONMETRIC	Oto 1	dis	Ratio					
CANBERRA	Oto 1	dis	Ratio					
COSINE	Oto 1	sim	Ratio					
DOT	>0	sim	Ratio					
OVERLAP	>0	sim	Ratio					
DOVERLAP	>0	dis	Ratio					
CHISQ	>0	dis	Ratio					
CHI	>0	dis	Ratio					
PHISQ	>0	dis	Ratio					
PHI	>0	dis	Ratio					
Euclidean Distance
• Euclidean distance gives the linear distance between any two points in n-dimensional space.
• It is a generalization of the Pythagorean theorem.
City Block (Manhattan) Distance
d
i=l
• The distance between two points is measured along the sides of a right-angled the triangle.
• It is the distance that you would travel if you had to walk along the streets of a right-angled city.
		(*i,x2)
		
	•	
Hamming Distance
d
i=l
12345..._17
Gene A 01 1 001 001 001 1 1 001 Gene B 01110000111111011
DH =      00010100011000010 = 5
Gene expression levels under 17 conditions
(low=o, high=i)
Power Distance
• Minkowského metrika (r=q)
• Hemmingova vzdálenost (r=q=i)
• Euklidovská vzdálenost (r=q=2)
• Čebyšovova vzdálenost (r=q->oc)
Correlation
Similar (+1)
bis^imiiar (-1)
No Similarity (0)
Density-Based Similarity
1...................
similarity
density estimate 1 density estimate 2
(cluster 1) (cluster 2)
Density-based methods define similarity as the distance between derived density "bubbles" (hyper-spheres).
496
Gower's Metric i^ww
j=l
^Gower v
j=i
Wj .. .váha pro j -tou proměnnou
• For nominal, ordinal, interval, or ratio variable:      (x' y) = 1
• For asymmetric nominal variable: $. (x, y) = 1,  if either Xj or y. is present
S- (x, y) = 0,  if both Xj and yj are absent
• For nominal or asymmetric nominal variable:    d j (x, y) = 1,   if Xj = yj
dj(x,y) = 0,  if Xj *Vj
• For ordinal, interval, or ratio variable: d j (x, y) = 1 - Xj - yj
• Gower's is the only similarity metric that accepts any measurement level.
Gower, J. C. (1971) A general coefficient of similarity and some of its properties, Biometrics 27, 623-637.
497
Další míry podobnosti
v
Jaccardův koeficient w+W-ýxy
j=l        H j=i
V
2Zxjyj
Diceův koeficient
j=i
D
j=i j=i
v
2^min(xj,yj)
Czekanowského koeficient   D = _h_
C v
Míry podobnosti pro binární data
Koeficient souhlasu -
a+b+c+d
• Jaccardův koeficient ___
a+b + c
_2a
Diceův (Czekanowského) koef. 2a+b
	Kategorie objektu w	
Kat. objektu x	1	0
1	a	b
0	c	d
v   i    o     !        n-   .       . Väď-VbČ
Yuleuv koeficient —ř=—1=
Vad + vbc
499
Míry (ne)podobnosti pro binární data
• Goodman-Kruskalovo lambda
max( a,b) + max( c, d) + max( a, c) + max(b, d) - max( a + c,b + d) - max( a +b, c + d)
2(a+b + c + d) - max( a + c,b + d) - max( a+b, c + d)
• Binární Lanceova-Williamsova míra nepodobnosti b + c
2a+b + c
» Euklidovská vzdálenost
• Bin. čtvercová euklid. vzdálenost (=Hammingova vzd.)       b + c
500
Standardizace/normalizace
Před vlastním výpočtem vzdáleností je nanejvýš vhodné standardizovat (normalizovat) proměnné.
Důvodem je snaha o unifikaci měřítka a tím vyvážení vlivu jednotlivých proměnných.
Typicky: _ x-location
^standard.
scale
^u v , 11 . . . original - location O becne: result = add + multiply----
scale
result = final output value
add = constant to add (ADD= option)
multiply = constant to multiply by (MULT= option)
original = original input value
location = location measure
scale = scale measure
The STDIZE Procedure
General form of the STDIZE procedure:
PROC STDIZE DATA=SAS-data-set METHOD=A77e#70c/ <options>; VAR variables; RUN;
Standardization Methods
METHOD	LOCATION	SCALE
MEAN	mean	1
MEDIAN	median	1
SUM	0	sum
EUCLEN	0	Euclidean Length
USTD	0	standard deviation about origin
STD O	mean	standard deviation
RANGE	minimum	range
MIDRANGE	mid range	range/2
MAXABS	0	maximum absolute value
IQR	median	interquartile range
MAD	median	median absolute deviation from median
ABW(c)	biweight 1-step M-estimate	biweight A-estimate
AHUBER(c)	Huber 1-step M-estimate	Huber A-estimate
AWAVE(c)	Wave 1 -step M-estimate	Wave A-estimate
AGK(p)	mean	AGK estimate (ACECLUS)
SPACING(p)	mid minimum-spacing	minimum spacing
L(p)	L(p)	L(p) (Minkowski distances)
IN(ds)	read from data set	read settings from data set "ds"
O „Z-sköre" 503
The Problem with Z-Score Standardizati
Before
After
Standardization using the reciprocal of the variance can actually dilute the differences between groups!
Source: Everitt et al. (2001)
Cluster Preprocessing
• Řešením tohoto problému může být procedura ACECLUS (approximate covariance estimation for clustering)
o oo oo $
o 9)
:o™v°<8š
° <S> o r.   O O
'o e
o
o Od
" ^gco° ca    1110°°°
o
0 °™ o
cP
O o
o# o
o     * o o °
* % °        ^ CJ       o o o  eo^oo o
o °c?   ° o
o
o o
o
o ^ o o o o „
OOo '
o o
oo
8^ ^
°  ° 8 % % °°     o    o o o   ° oo
o Oj
o
o
Before ACECLUS After ACECLUS
Více na: http://support.sasxom/documentation/cdV
505
The ACECLUS Procedure
General form of the ACECLUS procedure:
PROC ACECLUS DATA=SAS-data-set <options>;
VAR variables;
RUN;
506
Vzdálenost mezi shluky
• Mimo určení jak měřit vzdálenosti mezi objekty uvnitř shluků je třeba definovat jak měřit vzdálenosti shluků mezi sebou.
• Mezi základní metody patří metoda:
• metoda nejbližšího souseda (single linkage),
• metoda nej vzdálenějšího souseda (complete linkage),
• metoda průměrné vazby (average linkage),
• centroidní metoda,
• Wardova metoda.
507
The CLUSTER Procedure
The general form of the CLUSTER procedure:
PROC CLUSTER DATA=SAS-data-set METHOD=method <options>;
VAR variables;
FREQ variable;
RMSSTD variable; RUN;
• The required METHOD= option specifies the hierarchical technique to be used to cluster the observations.
The CLUSTER Procedure, method=...
The METHOD= specification determines the clustering method used by the procedure. Any one of the following 11 methods can be specified for name:
• AVERAGE | AVE requests average linkage (group average, unweighted pair-group method using arithmetic averages, UPGMA). Distance data are squared unless you specify the NOSQUARE option.
• CENTROID | CEN requests the centroid method (unweighted pair-group method using centroids, UPGMC, centroid sorting, weighted-group method). Distance data are squared unless you specify the NOSQUARE option.
• COMPLETE | COM requests complete linkage (furthest neighbor, maximum method, diameter method, rank order typal analysis). To reduce distortion of clusters by outliers, the TRIM= option is recommended.
• DENSITY | DEN requests density linkage, which is a class of clustering methods using nonparametric probability density estimation. You must also specify either the K=, R=, or HYBRID option to indicate the type of density estimation to be used. See also the MODE= and DIM= options in this section.
• EML requests maximum-likelihood hierarchical clustering for mixtures of spherical multivariate normal distributions with equal variances but possibly unequal mixing proportions. Use METHOD=EML only with coordinate data. See the PENALTY= option for details. The NONORM option does not affect the reported likelihood values but does affect other unrelated criteria. The EML method is much slower than the other methods in the CLUSTER procedure.
• FLEXIBLE | FLE requests the Lance-Williams flexible-beta method. See the BETA= option in this section.
• MCQUITTY | MCQ requests McQuitty's similarity analysis (weighted average linkage, weighted pair-group method using arithmetic averages, WPGMA).
• MEDIAN | MED requests Gower's median method (weighted pair-group method using centroids, WPGMC). Distance data are squared unless you specify the NOSQUARE option.
• SINGLE | SIN requests single linkage (nearest neighbor, minimum method, connectedness method, elementary linkage analysis, or dendritic method). To reduce chaining, you can use the TRIM= option with METHOD=SINGLE.
• TWOSTAGE | TWO requests two-stage density linkage. You must also specify the K=, R=, or HYBRID option to indicate the type of density estimation to be used. See also the MODE= and DIM= options in this section.
• WARD | WAR requests Ward's minimum-variance method (error sum of squares, trace W). Distance data are squared unless you specify the NOSQUARE option. To reduce distortion by outliers, the TRIM= option is recommended. See the NONORM option.
509
Supported Data Types
Hierarchical Method	Coordinate Data	Distance Data
Average Linkage	Yes	Yes
Centroid Linkage	Yes	Yes
Complete Linkage	No	Yes
Density Linkage	No	Some Options
EML	Yes	No
Flexible-Beta Method	No	Yes
McQuitty's Similarity	No	Yes
Median Linkage	No	Yes
Single Linkage	No	Yes
Two-Stage Linkage	No	Some Options
Ward's Method	Yes	Yes
Average Linkage
• The distance between clusters is the average distance between pairs of observations.
Centroid Linkage
• The distance between clusters is the squared Euclidean distance between cluster centroidsxK and xL.
Complete Linkage
The distance between clusters is the maximum distance between two observations, one in each cluster.
'K
^ DKL=ieCKj GCLinaxdC^,^)
Density Linkage
1. Calculate a new distance metric, c/*, using /c-nearest neighbor, uniform kernel, or Wongs hybrid method.
2. Perform single linkage clustering with d*.
d*(*i>xj) = x
+
f(Xl) f(Xj)
J
Equal Variance Maximum Likelihood
• The distance between clusters CK and CL is given by a penalized maximum-likelihood variant.
VKL = nyfa
f				
1+	wm	"wk	"wl	
		p.		
V				)
- P (nM ta («m )" nk111 (nJ- nl111 (nL))
Flexible-Beta
516
McQuitty's
• The average distance between an external cluster, J, and each of the component clusters (CK and CL)
Median Linkage
• The average distance between an external cluster and each of the component clusters, minus the distance between the component clusters.
Single Linkage
• The distance between clusters is the distance between the two nearest observations, one in each cluster.
DKL=ieCK J eCLinindCxpXj)
519
Two-Stage Density Linkage
• The same as density linkage except that a cluster must have at least "n" members before it can be fused.
1. Form 'modal' clusters 2. Apply single linkage
520
Ward's
• Ward s method uses AN OVA at each fusion point to determine if the proposed fusion is warranted.
□□□□□□□□
The TREE Procedure
General form of the TREE procedure:
PROC TREE DATA=<dendrogram> <options>;
RUN;
• The TREE procedure either
• displays the dendrogram (LEVEL= option) or
• assigns the observations to a specified number of clusters (NCLUSTERS= option).
Interpreting Dendrograms
change in fusion level
Mane of Observation or Cluster
523
Určení finálních shluků
Finální shluky získáme vhodným „řezem" dendrogramu.
Neexistuje univerzální postup, vždy záleží na konkrétních datech a interpretovatelnosti výsledku.
Lze ale použít např. tento postup:
• Označíme   \x{   vzdálenosti   shluků,   které   vznikli   v průběhu shlukovacího algoritmu v okamžicích spojování objektů/shluků.
• Spočteme rz= \x[+1 - \x{.
• Spočteme max(rz) a určíme tím místo, kde „říznout".
3
14
4-11
0        2 4 6 8 10
							
				] ■ 10 J	/		
					/ -ts	+8	
					\	•	5 _
	7— — \   + •	* 12 ♦ 1 t 1					
							
0        2 4 6 & 10
Zdroj obrázků : L.Žák, Shluková analýza (II), http://www.volny.cz/elzet/Libor/Aut cl 2.pdf
Cvičení
Generování dat: c data.sas
• COMPACT : Three well-separated, compact clusters.
Source   : SAS/STAT User's Guide (Introduction to Clustering Procedures).
• DERMATOLOGY: Differential diagnosis of erythemato-squamous disease.
Source    : Nilselliter, N. and Altay Guvenir, H. (1998)
• ELONGATED : Two parallel elongated clusters in which the variation in one dimension is 6 times the variation of the other dimension. There are 150 members in each of the clusters, for a total of 300 observations.
Source   : SAS/STAT User's Guide (Introduction to Clustering Procedures).
• FISH : Seven species of fish caught off the coast of Finland.
Source : Data Archive of the Journal of Statistics Education
• INVESTORS : ...(training data)
• OUTLIERS: Create two clusters with severe outliers.
• PIZZA : Nutrient levels of various brands of frozen pizza.
Source: D.E. Johnson (1998), Applied Multivariate Methods for Data Analysis, Duxbury Press, Cole Publishing Company, Pacific Grove, CA. (Example 9.2)
• RING : A normal cluster surrounded by a ring cluster.
Source : SAS/STAT User's Guide (The MODECLUS Procedure - Examples).
• STOCK : Dividend yields for 15 utility stocks in the U.S. for 1986-1990.
Source : SAS/STAT User's Guide (The DISTANCE Procedure - Examples).
• TINVESTORS : Investors data set (test data)
• UNEQUAL : Generate three unequal variance and unqual size clusters.
Source : SAS/STAT User's Guide. 525
Cvičení
/*
clusOldOl: Generating distances.
The sasuser.stock data set contains the dividend yields for 15 utility stocks in the U.S.
The observations are names of the companies, and the variables correspond to the annual
dividend yields over the period 1986-1990.
*/
Stock Dividends The STOCK Data Set
[lbs	company	div.1386	div.1387	div-1988	div.1389	div.1330
1	Cincinnati G&E	8.4	8.2	8.4	8.1	8.0
j	Texas Utilities	7,3	8.3	10.4	8.9	š i
3	Detroit Edison	3.7	10.7	11.4	7.3	6,5
4	Orange 8 Eockland Iftilitie	6,5	7.2	7.3	7.7	7,9
5	Kentucky Utilities	6.5	6.3	7.0	7.2	7.5
6	Kansas Power 8 Light	5,3	6.4	6.9	7.4	8,0
7	Union Electric	7,1	7.5	8.4	7.3	7,7
í	Dominion Eesources	6,7	6.9	7.0	7.0	7,4
3	Allegheny Power	6.7	7.3	7.8	7.9	8.3
10	Minnesota Power 8 Light	5,6	6.1	7.2	7.0	7 5
11	Iowa-Ill Gas 8 Electric	7,1	7.5	8.5	7.:j	8,0
12	Pennsylvania Power 8 Light	7,2	7.6	7.7	7.4	7,1
13	Oklahoma Gas 8 Electric	6.1	6.7	7.4	6.7	6.8
14	Wisconsin Energy	5,1	5.7	6.0	5.7	5,3
15	Green Mountain Power	7,1	7.4	7. í	7.3	8,3
options nodate nonumber; goptions reset=all;
%let inputs = div_1986 div_1987 div_1988 div_1989 div_1990;
/* display the input data set */ title 'Stock Dividends'; title2 'The STOCK Data Set'; proc print data=sasuser.stock;
var company &inputs;
run;
/* calculate the range standardized Euclidean distance */
proc distance data=sasuser.stock method=euclid out=dist;
var interval(&inputs/std=range);
id company; run;
/* display the distance matrix generated */ title2 'Euclidean Distance Matrix'; proc print data=dist;
id company;
run;
Stock Dividends Euclidean Distance Matrix
Orange_
	Cincinnati-	Texas.	Detroit-	dockland-		Kentucky.	Power___	Union-	Dominion-
company	G_E	Utilities	Edison	Utilitie		Utilities	Light	Electric	Eesources
Cincinnati G8E	0.00000								
TexasUtilities	0.49670	0.00800							
Detroit Edison	1,01879	0,98884	0\00080						
Orange & Eockland ITtilitie	(i m-Hlu	d U0:c'	1.37598	0	00000				
Kentucky Utilities	0.65416	1.02098	1.99076	0	J4Jŕ.5	0'. 08000			
Kansas Power & Light	0.74161	1.04618	1 Wíŕl	0	24213	o :7:cc.	O!00800		
UnionElectric	0.95197	0.65906	1.19477	0	26463	0.37514	8.47420	0'.00008	
Dominion Eesources	(i (.72 iS	1,05719	1,96747	0	31586	0,08678	0,34455	0,40883	0.00800
Allegheny Power	0.44817	0.70706	1.97689	0	20627	0.43497	0.36120	0.29152	0.43807
Minnesota Power S Light	0.87055	1.17406	1.57540	0	40338		0.26451	0.55036	0.28307
Iowa-Ill Gas & Electric	0.92854	0.60517	1.18664	0	26965	0.43259	0.46830	0.12636	0.47342
Pennsylvania Fower & Light	0.59641	0.38827	1.10787	0	33363	0.90207	0.54776		0.28180
Oklahoma Gas & Electric	j 'Ulli	1,23233	1,39103		57i>:.4	0,35232	O.'SM'i		
Wisconsin Energy	l m::;*	1.85581	1.86380	1	15137	0.32124	1.06088	1.22855	(i :;:7f.f.f,
Green Mountain Power	0.97719	0.68574	1.32741	0	23652	0.44185	0.40876	0.27431	0.48258
		Minnesota-	Iowa_Ill_				Oklahoma-		Green-
	Allegheny-	Power___	Gas___		Pennsylvania-		Gas___	Wisconsin-	Mountain-
company	Power	Light	Electric		Power.	„Light	Electric	Energy	Power
Cincinnati G&E Texas Utilities Detroit Edison Orange & Eockland ITtilitie Kentucky Utilities Kansas Power & Light Union Electric Dominion Resources Allegheny Power Minnesota Power & Light Iowa-Ill Sas & Electric Pennsylvania Power & Light Oklahoma Sas $ Electric Wisconsin Energy Green Mountain Power
0.00800										
0,56339	0	08000								
0.20632	0	53042	0	08000						
0.59868	0	51288	0	42317	0	00000				
0.75376	0	34848	0	68464	8	38515	0	08000		
1.94490	0	82285	1	31501	0	88284	0	62670	0	00000
0,03454	0	58881	0	18118	8	51773	0	76232	1	ŕc.ííŕ
526
Cvičení
Stock Dividends
/* generate hierarchical clustering solution (Ward's method)*/ proc cluster data=dist method = ward outtree=tree noprint;
id company;
run;
/* display the EUCLID dendrogram horizontally */
title2 "Cluster Solution";
proc tree data=tree horizontal;
id company;
run;
/* calculate the range standardized city block distance */
proc distance data=sasuser.stock method=cityblock out=dist;
var interval(&inputs/std=range);
id company; run;
/* display the distance matrix generated */ title2 'City Block Distance Matrix'; proc print data=dist;
id company;
run;
/* generate hierarchical clustering solution (Ward's method)*/
proc cluster data=dist method = ward outtree=tree noprint; —
id company;
run; ™
/* display the CUYBLOCK dendrogram horizontally */ title2 "Cluster Solution";
proc tree data=tree horizontal; _
id company;
run; ~-
			
			
v—			
			
Cincinnati GSE Texas Utilities Detroit Edison Orange 8 Eockland lit i 1 Kentucky Utilities Kansas Power S Light
Electr:
i, ,■
Domin______________
Allegheny Power Minnesota Power S Light Iowa-Ill Gas S Electric Pennsylvania Power & Light Üxlahcia Gas S Electric Wisconsin Energy Green Mountain Power
company
Cincinnati GSE Texas Utilities Detroit Edison Orange & Portland TIti] Kentucky utilities Kansas Power S Light
G_E
D DDDDD 0 99407
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Kansas. Light"
Stock Dividends
Electr:
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l Eesources Allegheny Power Minnesota Power S Light Iowa-Ill Gas S Electric Pennsylvania Power & Light Oklahoma Gas S Electric Wisconsin Energy Green Mountain Power
0 00000
1 20482 0 41284
0 84346
1 82451
2 68866 0 18821
...........
. " ".J 1.76009 . 1 < 2.17668 1 ,1 "i
1.37485 2.57968 1.27451 1
Minnesota. °Li|ht"
00000 30516
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2 76949 2 87463
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].00000
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].48557 3.73333 ]. 97681 •1.30942 3.46034
Oklahoma.
Pennsylvania. Gas___
Power___Light Electric
: :.........
0 51979 0 7S053
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] 80188
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].51932 L ľ-ľ-, 3.14352 ;, -L.28133 í.64548 J.38111
0 00000 0 88440
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h 1
527
Cvičení
/* clus02d4: Impact of input standardization on clustering.
This demonstration evaluates the impact on cluster performance of changing the method of input standardization. Several methods are ranked according to their Cramer's V value and their misclassification rate. PROC FASTCLUS is used to cluster the observations. The input data set is the pizza data set. The input variables are the three inputs recommended using by the PROC VARCLUS 1-R**2 criterion. */
options nodate nonumber;
%let group = brand;
%let inputs = carb mois sodium;
data results;
length method$ 12; length misclassified 8; length chisq 8; length pchisq 8; length cramersv 8; stop;
run;
%macro standardize(dsn=, nc=, method=); %mend standardize;
%standardize(dsn=sasuser.pizza,nc=10,method=ABW(ll)); %standardize(dsn=sasuser.pizza,nc=10,method=AGK(l));
Method: iEfl(U) The FF.EQ Procedure Table of brand by C1USIEE
brand CUTSTEB(Clister)
Frequency	11	2	3	4	51	61	7	3	31	ID	Iota]
1 1	0 1	14	0	0 1	15 1	0 1	0 1	0 1	0 1	0	23
B 1	15 1	0	0	0 1	0 1	0 1	16 1	0 1	0 1	0	31
C 1	Q 1	Q	Q	Q 1	D 1	D 1	0 1	16 1	0 1	11	27
D 1	5 1	0	0	0 1	0 1	0 1	0 1	1 1	0 1	26	32
E 1	0 1	0	0	0 1	0 1	28 1	0 1	0 1	0 1	0	28
F 1	0 1	0	0	30 1	0 1	0 1	0 1	0 1	0 1	0	30
E 1	0 1	0	0	23 1	0 1	0 1	0 1	0 1	0 1	0	23
9 1	0 1	0	0	0 1	0 1	33 1	0 1	0 1	0 1	0	33
I 1	0 1	0	0	0 1	0 1	0 1	0 1	0 1	23 1	0	23
J 1	0 1	0	32	0 1	0 1	0 1	0 1	0 1	0 1	0	32
Total	20	14	32	53	15	61	16	17	23	37	300
Statistics for Table of brand by CLUSTEF
Statistic DF Value Prob
Chi-Square 81    1850.8203      <,0001
Livelihood Patio Chi-Square 81    1138.3575 <,0001
ttantel-Haenssel Chi-Square 1        0.0318 0,8584
Phi Coefficient    _  _ 2.4838
Cordingency Coefficient 0,8276
Cramer's V 0.8280
MRBIBG: 30% of the cells have expected counts less than 5, Chi-Square my not be a valid test,
Sample Size = 300
Method: AGK(l) The FPEQ Procedure Table of brand by CLUSTEE
brand CLUSTER(Cluster)
Frequency	11	21	31	41	51	61	71	81	31	101	Total
A	0 1	23 1	0 1	0 1	0 1	0 1	0 1	0 1	0 1	0 1	23
E	3 1	0 1	0 1	0 1	0 1	23 1	0 1	0 1	0 1	0 1	31
C	1 1	0 1	0 1	0 1	0 1	0 1	0 1	5 1	0 1	21 1	27
1	2 1	0 1	0 1	0 1	0 1	3 1	0 1	26 1	0 1	1 1	32
E	0 1	0 1	3 1	0 1	13 1	0 1	0 1	0 1	0 1	0 1	28
F	0 1	0 1	0 1	0 1	0 1	0 1	30 1	0 1	0 1	0 1	30
G	0 1	0 1	0 1	0 1	1 1	0 1	28 1	0 1	0 1	0 1	23
H	0 1	0 1	4 1	0 1	23 1	0 1	0 1	0 1	0 1	0 1	33
I	0 1	0 1	0 1	23 1	0 1	0 1	0 1	0 1	0 1	0 1	23
J	0 1	0 1	0 1	0 1	0 1	0 1	0 1	0 1	32 1	0 1	32
Total	11	23	13	23	43	26	58	31	32	22	300
		Statist Stat istic		ics for	Table o	brand by CLUSTEE DF Value		Frob			
Ch i-Square 81    1905.5468      <,D0D1
Likelihood Ratio Chi-Square 31    1133.8333 «,0001
ttantel-Haenszel Chi-Square 1       21.5331 <,0001
Phi Coefficient 2.5203
Contingency Coefficient 0,3285
Cramer's V 0,3401
MESIBG: 36% of the_eel Is have expected counts less than 5. Chi-Square May not be a valid test,
Cvičení
%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-%standardize(dsn-
■sasuser.pizza,nc-■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc ■sasuser.pizza,nc sasuser.pizza,nc
■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method-■10,method--10,method-
AHUBER(.l)); AWAVE(.2)); EUCLEN); IQR);
MD);
L(1.5));
L(2));
MAD);
MAXABS);
MEAN);
MEDIAN);
MIDRANGE);
NONE);
RANGE);
SPACING(.9));
STD);
SUM);
USTD);
I* sort by number of misclassifications within Cramer's V */ proc sort data=results;
by descending cramersv misclassified;
run;
/* display Cramer's V and misclassifications for each method */
titlel 'Results';
proc print data=results;
var method cramersv misclassified ;
run; quit;
Results
Obs	method	cramersv	misclass
1	SPACIHG^g)	0.85070	30
j	AMVEC.2)	0.84716	45
3	L(l)	0.84484	:::
4	AGE 1	0.84009	34
5	L(2)	0.84009	34
6	STD	0.84009	34
7	MIDEAHGE	0.84003	48
8	EASGE	0.84003	48
9	MAXABS	0.83122	50
10	U1.5)	0.82816	43
11	ABWfll)	0.82796	46
12	EUCLE11	0.81871	60
13	USTD	0.81871	60
14	SUM	0.81076	6i:
15	MEAS	0.78492	72
16	MEDIAM	0.78492	72
17	BOBE	0.78492	72
18	IQE	0.77553	50
13	AHUBEE(.l)	0.76885	58
20	MAD	0.70940	79
529
8. Vývoj CS modelu
530
Process Flow
Preliminary Scorecard (KGB)
531
Preliminary Scorecard (Known Good/Bad)
• Group of characteristics, that together, offer the most predictive power
• Logistic Regression (forward, backward, stepwise)
• 8-20 characteristics
• stability.
Logistic Regression
Logit (Pi)=ß0+ ßA+ ....+ ßkxk
p - posterior probability of event' given inputs x - input variables ß - parameters
• Logit transformation is log of the odds, and is used to linearize posterior probability and limit outcome to between o and 1.
• Maximum Likelihood used to estimate parameters.
Parameters estimates measure rate of change of logit for one unit change in input variable (adjusted for other inputs)
Depends on the unit of the input, therefore need to standardise (e.g. WOE)
533
Logistic Regression
• Binary target (good/bad)
• Variables
• Raw data
• Grouped data (for example, mid value of each group)
• Weight of evidence Z1 I
Logistic Regression
• Forward Stepwise
• Select best variable, add it to the model, and then add/subtract variables until no improvement in indicator.
• Efficient, but weak when too many variables or high correlation
• Backward Elimination
• Start with all variables in the model, then eliminate least important variables.
• Correlation is better taken care of
• Better than stepwise, but can be computationally intensive.
535
Preliminary Scorecard
• Choose the best - and build the most comprehensive risk profile
• With as many independent data items as possible
• independent data items representing different data types e.g. demog, financials, inquiries, trades info
• 10 characteristics with 100' each preferred to 4 with '250' each.
• Correlation, co linearity etc. considered
• Scorecard coherent with decision support structure
• Sole arbiter or decision support tool: model needs to be coherent with overall decision support structure
• Interpretability, implementability, and other business considerations.
536
Example of a Good Scorecard
Age
Residential status Time at address
• Number of products
at bank
• Delinquency at bank
• Total Debt Service
• Inquiries 12 months ^ • lotal Uebt service
t     • • +u Ratio
• Inquiries 3 months
• Trades 90 days+ as % of total
• Revolving balance/Total Utilization
> contains some demographics, some inquiries, some trade, some utilization, internal bank perforamnce and capacity to pay.
^ Počet žádostí o úvěr za posledních 12 měsíců
537
How Do We Get There?
• Try statistically optimal approach (let the data speak)
• "Design" a scorecard using stepwise/backward
• Force characteristics in, or fix at each loop and adjust the hurdle rate Consider:
■ "must have" Weaker/ stronger
■ Similar
538
Weaker, Similar
• Weaker - consider first
• Can 2 characteristics worth 40 points
each model behavior better than one worth 70?
• Same strength, broader base Similar - put together
• Time related, inquiries, trades, debt capacity, demographic
• Takes care of correlation
Putting It Together
• Try different  combinations  of characteristics in regression
• Instead of putting all characts in, separate into categories, and try combinations.
• Leave very strong characteristics out, or use at the end (for example, bureau scores)
• Example "levels"
• Weaker application info
• Stronger application info
• Weaker bureau
• Stronger bureau
• Mix and adjust with experience.
540
Putting It Together
• Age, time at address, time at employment, time at bank
• Region, postal code, province
• TDSR, GDSR, capacity, Loan To Value
• Time at bureau, current customer (Y/N)
• Inq 3 months, inq 6 months, inq 12 months, inq 3/12 months
• Trades delq, trades 3 mth/total, current trades
• Utilization, public records
• Bureau score, bankruptcy
GDSR( Gross Debt Service Ratio) = (Annual Mortgage Payments + Property Taxes + Other Shelter Costs)/(Gross Family Income)
TDSR (Total Debt Service Ratio) = (Annual Mortgage Payments + Property Taxes + Other Shelter Costs + Other Debt Payments)/(Gross Family Income)
541
Logistic Regression
• Use stepwise or backward
• stepwise means dominating variable will stay in.
• Backward: set of weak variables may end up staying.. That together add value (sometimes better than stepwise).. Also backward takes care of correlation better than others.
• Modify to consider only selected characteristics at each "level"
• series of regression runs, each as one "level", force selected characteristics from previous "levels" in.
• EM nodes in series.
542
Logistic Regression
• It is strongly recommended that all coefficients are logical. If some of them are not, include comments with explanation why it is good to keep them in scorecard. Include column, where it is easy to see the contribution of each category (either scaled scorepoints for linearization, either simply bi*xi*iooo). Order categories in each predictor according to badrate (WOE) so that the worst are the first.
543
LR - scorecard example
Own / Rent		Rent	Other	NI				
		15	10	17				
Years at	<5	.5-2.49	2.5-6.49	6.5-10.49	>10.49	NI		
address	12	10	15	19	23	14		
Occupation	Prof	SemiPrf	Mgr	Offc.	Bl.Col	Retired	Other	NI
	50	44	31	28	25	31	22	27
Years on job	<5	.5-1.49	1.5-2.49	2.5-5.49	5.5-12.49	12.5	Retired	NI
	2	8	19	25	30	39	43	20
Dept St / Major CC	None	Dept-St	Maj-CC	Both	No answr	NI		
	0	11	16	27	10	12		
Bank	Check	Sav	Ck&Sav	Other	NI			
reference	5	10	20	11	9			
Debt ratio	<15 22 _	15-25 15	26-35 12	36-49 5^.	50+	NI 13 _		
No. of recent	0	—T*				5-9	No Rcrd	
inquiries	3	11	3	-7	-7	-20	0	
Years in file	<5	1-2	3-4	5-7	8+			
	0	5	15	30	40			
# Rev trades outstanding	0	1-2	3-5	6+				
	5	12	8	-4				
% Credit line	0-15%	16-30%	31-40%	41-50%	>50%			
utilization	15	5	-3	-10	-18			
Worst	1             1             1 1							
reference	1             1             1 1							
scorecard example
Obs	colnamew	colvalue	Bi_x_Xi_x_1000	bad_rate	freq_rate		Xi
1	Intercept		3129			3.129451	
3	age_fr w	20	-359	10.3	3.5	0.377612	-0.950967
4	age_fr w	29	-154	6.3	28	0.377612	-0.408556
5	age_fr w	32	-47	4.8	8.4	0.377612	-0.123244
6	age_fr w	36	20	4.1	10	0.377612	0.05253
7	age_frw	41	48	3.8	11	0.377612	0.12723
8	age_frw	51	173	2.7	23	0.377612	0.458154
9	age_frw	60	327	1.8	16	0.377612	0.865979
10	car owner frw	0	-60	4.5	76	1.179055	-0.051044
11	car owner frw	1	211	3.6	24	1.179055	0.179078
12	child_num fr w	99	-59	4.9	1.9	0.424104	-0.138759
13	child_num fr w	0	-33	4.6	60	0.424104	-0.078474
14	child_num fr w	1	34	4	27	0.424104	0.080184
15	child_num fr w	2	134	3.2	11	0.424104	0.315117
16	education frw	5	-174	6.1	4.3	0.453663	-0.384073
17	education frw	4	-79	5	3.3	0.453663	-0.174838
18	education frw	2	-10	4.4	73	0.453663	-0.021929
19	education frw	36	112	3.4	19	0.453663	0.247396
545
Logistic Regression
• For all predictors in scorecard estimated coefficient, wald chi-square, p-value (e.g. in SAS output Analysis of maximum likelihood estimate), summary of predictor selections (order of predictors entering the model, e.g. in SAS output summary of stepwise selection)
Parameter	Analysis of Maximum Likelihood Estimates DF                     Estimate Standard Error		Wald Chi-Square	Pr > ChiSq
Intercept	1 3.1295	0.0106	86436.032	<.0001
age_fr_w	1 0.3776	0.0254	221.2018	<.0001
carownerfrw	1 1.1791	0.1093	116.2664	<.0001
educationfrw	1 0.4537	0.066	47.2419	<.0001
fam_state_fr_w	1 0.4167	0.0297	196.864	<.0001
goods_group_fr_w	1 0.2716	0.0311	76.3139	<.0001
child_num_fr_w	1 0.4241	0.0867	23.9081	<.0001
ident_card_age_fr_w	1 0.5677	0.0269	446.5471	<.0001
Summary of predictor selection
Step	Summary of Stepwise Selection Effect DF Entered Removed	Number In	Score Chi-Square	Wald Chi-Square	Pr > ChiSq
1	price1_fr_w 1	1	3858.056		<.0001
2	agefrw 1	2	3007.7932		<.0001
3	init_pay_by_price1_f 1	3	1434.1863		<.0001
4	ident_card_age_fr_w 1	4	868.4661		<.0001
5	type_suite_fr_w 1	5	800.2294		<.0001
6	time_on_job_fr_w 1	6	554.571		<.0001
7	mobile_phone_fr_w 1	7	342.7936		<.0001
8	sexfrw 1	8	357.5026		<.0001
9	famstatefrw 1	9	331.6358		<.0001
10	ident_type2_fr_w 1	10	358.4905		<.0001
11	weekendfrw 1	11	323.0631		<.0001
12	regionfrw 1	12	299.3854		<.0001
547
Good Scorecard?
• Eye Ball Test
• Point allocation logical, no flips (after scaling)
• "Flips" occur for several reasons: low count, correlation.
• Scorecard characteristics make sense
what went in, what did't., does it cover all the major categories of information?
• Misclassification
• Strength
• Validation.
548
Scorecard Development
• Build more complex models and compare predictiveness -difference not significant, then scorecard is OK
• Examine findings - is there a valid business reason?
• Build several 'different' scorecards
What Have I Just Done?
• "Designed" a scorecard
• Used regression, with business considerations
• Stable, represents strong major/independent information categories
• Measurable strength and impact
• Something a risk manager can buy and use.
• Used only known goods and bads (that is, approves)
• But need to apply scorecard on all applicants.
550
Reject Inference
• Everything to this point has been for known performance - e.g. approval rate is 60%, building a model for 100% of the population based on 60% sample is not accurate.
Total Applicants
Declined
551
Reject Inference
• This is where you need to get to: so need to create a sample representative of the "through the door" or entire applicant pop performance -100% approval rate.
Bad	
	
• Inferring the behavior of declined applicants
552
The Known Good Bad Picture
Through-the-door
10,000
_I
I--1
Rejects Accepts 2,950 7,050
I
I--1
9 Bads Goods
874 6,176
553
Reject Inference
Make the scorecard relevant
• ignoring rejects distorts model
• Influence of past decision making
For decision making Get population odds
• Expected performance
• Swap set.
		Old scorecard	
		Approve	Decline
New	Approve	A	B
Scorecard	Decline	C	D
A - is approved goods B - is rejected goods C - is approved bads D - is rejected bads
554
Where?
• Medium/low approval rates
• a 95% approval rate is close to "through the door"
• Manual adjudication environment
• Incorporates experience/intuition based overriding
• "cherry picking" distorts performance.
Reject Inference Techniques
• "True" Performance
• "Nearly True" Performance
• Statistical Inference
• Or ignore the problem
• Assume accepts = total population
• not recommended unless previous credit granting was random scorecard was perfect ( assume all rejects = bad).
"True" Performance
Approve every applicant Or random sample Expensive
... but the only true way to determine performance of below cutoff applicants.
0)
> o
q. q. <
eu
toffi
q.
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if)
q. q. <
2 3
557
"Nearly True" Performance 1
• Bureau data
• performance of declined apps on similar products with other companies
• difficult to implement in practice - timings, definitions, programming
Need consent to get bureau at any time
data - if u rejected them, they probably were rejected elsewhere timings - performance window, sample window must be consistent bad definition must be closely replicated
product must be similar - credit cards, unsecured line of credit with similar limit and conditions as you would have given
Experience - Programming effort is tremendous, depending on how detailed credit bureau reports are
Jan 99
Dec 00
Declined - got credit elsewhere
Analyze performance
558
Nearly True" Performance 2
• In-house data
• performance of declined apps on similar products, for example, credit cards/line of credit
• timings, definitions my cause problems.
data - if u rejected them for a lower level product, they probably were rejected for higher one .. HOWEVER, in multiple product environments, scorecards are not always aligned and there is "ARBITRAGE".
timings - performance window, sample window must be consistent bad definition must be closely replicated
product must be similar - credit cards, unsecured line of credit with similar limit and conditions as you would have given
Jan 99
Dec 00
Declined - got similar products
Analyze performance
559
Bureau Score Migration
• Analyze bureau score migration of existing accounts with below cutoff scores
• Identify accounts whose scores migrate to above cutoff within specified time frame
560
Reclassification
• Build an accept/reject model
• Score all rejects and designate worst as accepted 'bad'
• Can use score or "serious derogatory" information to select accounts
• Analyze Accept/Reject vs. Good/Bad cross tabs
• Add to accepts and Re-model
561
Simple Augmentation
• Simple Augmentation
• Build good/bad model
• Score rejects - establish a p(bad) to assign class
• Add to Accepts and re-model
Simple
• Arbitrary cutoff to assign goods and bads
• Good/Bad model needs to be very good
• No adjustment for p(approve).
562
Augmentation 2
• Augmentation 2 (Coffman, Chandler i977)
• Build accept/reject model, obtain p(accept)
• Build good/bad model
• Adjust case weights of good/bad model to reflect probability of acceptance
• Recognizes need to adjust for p(approve).
563
Parceling
• Parceling (also called re-weighting)
• score rejects with G/B model
• split (randomly) rejects into proportional G and B groups.
continued..
564
reeling
But..
• Reject bad proportion cannot be the same as approved? Allocate higher proportion of bads from reject
• Rule of thumb: bad rate for rejects should be 2-4 times that of approves.
Quick and simple
Good/Bad model better be good
May understate rejected bad rate.
Iterative Reclassification
• Iterative Reclassification (McLachlan, 1975)
• Build good/bad model using accepts
• Score rejects and assign class based on chosen p(bad) cutoff
• Rebuild model with combined dataset
• Score rejects and re-assign class
• Repeat until parameter estimates (and p(bad)) converge.
• Can be modified for p(good) and p(bad) target assignment.
Iterative Reclassification
• can be done as a plot of In (odds) versus score.
Fuzzy Augmentation
• Step 1: Classification
• Build good/bad model
• Score rejects with G/B model
• Do not assign a reject to a class
• Create 2 weighted cases for each reject, using p(good) and p(bad).
568
Fuzzy Augmentation
• Step 2: Augmentation
• Combine rejects with accepts, adjusting for approval rate
• For this, weigh rejects again: weight determines how much more frequent an actual case is compared to an inferred case in the augmented dataset
• Freq of a 'Good' from rejects = p(good) x weight
• Step 3: Remodel.
EM users: This is in the EM RI node.
Freq= p(good) x (reject rate/approval rate) x (#accepts/#rejects)
# rejects/accepts are proportional to actual population I.e. weighted, not raw counts
569
uzzy Augmentation
• No need for arbitrary classification cut-off
• Augmentation step: better approach for choosing importance of rejects.
Nearest Neighbor (Clustering)
• Clustering
• Create 2 sets of clusters: goods and bads
Run rejects through both clusters
• Compare Euclidean distances to assign most likely performance
• Combine accepts and rejects and re-model
• Measures are relative
• Adjustment for p(approve) can be added at augmentation step.
• Can also use Memory-based Reasoning.
571
Other Techniques
• Heckman s Correction
• http://ewe3.sasxom/techsup/download/stat/heckman.html
• Heckman, James. "Sample Selection Bias as a Specification Error", Econometrica, Vol 47, No i., January 1979, pp. 153-161.
• Greene, William. "Sample Selection Bias as a Specification Error: Comment", {\sl Econometrica}, Vol. 49, No. 3, May 1981, PP- 795-798.
Mixture Decomposition
• B.S Everitt and D.J. Hand, Finite Mixture Distributions (London:Chapman & Hall, 1981)
572
Verification
• Compare bad rates/odds for known versus inferred, and use rule of thumb.
• Review bad rates/weight of evidence of pre- versus post inference groupings.
• Create "fake rejects" and test.
• assign some accepted accounts as rejects with an artificial cutoff and test methods.
573
Factoring - Post Inference
Through-the-door
10,000 _I_
1		1
Rejects 2,950		Accepts 7,050
I_ _I
I       I       I I
Bads	Goods	Bads	Goods
914	2,036	874	6,176
Bad rate = 30.98% Bad rate = 12.4%
• After rejects have been inferred, we build the post-inference data sets for the final scorecard production.
• So the sample bias is solved and you can apply the scorecard on the entire population.
574
Process Flow
1
Final Initial Characteristic
Scorecard (AGB)   I        Analysis (AGB)
575
Final Scorecard
Repeat Exploration, Initial Characteristics Analysis and Regression for "All Good Bad" data set
• Scaling
• Assessment
• Misclassification
• Strength.
576
Scorecard Scaling (conversion into points)
• Why scale?
• Implementation software - batch versus on-line
• Marketing uses (off line selection, build retention model, score and isolate account numbers) vs. online decision support and app processing software
• Ease of understanding and interpretation
• End user can deal with points easier than weights
• Continuity
• previous scorecards were grouped/scaled . .and you want to have the same format and scaling.
• Legal requirements
• legal requirements to identify characteristics and reasons for decline
• Components
• Odds at a score
• Points to double the odds
• Example: Odds of 20:1 at 200, and odds double every 20 points.
Scorecard Scaling
This is the transformation from parameter estimates to scores.
Result: get a score card with discrete points, related to each other and the final score related to odds.
odds doubling every 20 points
	
Age	
18-24	10
25-29	15
30-37	25
38-45	28
46+	35
	
Time at Res	
0-6	12
7-18	25
19-36	28
37+	40
	
Region	
Major Urban	20
Minor Urban	25
Rural	15
	
Inq 6 mth	
0"	40
1-3	30
4-5	15
6+	10
Score	Odds
	
200	20
201	23
202	25
203	26
	
	
220	40
	
240	80
578
Scorecard Scaling
In general:
Score = A + B log (odds)
Score +PDO = A + B log (2*odds)
• Offset A and Factor B are to be calculated
• Odds = odds at which to fix a score
• Score = score at point x
• PDO = points to double the odds
Scorecard Scaling
• Solving for PDO:
PDO = B Log (2), therefore_
B = PDO/log(2) ; A = Score - {B log (Odds)}
Example, Odds of 50:1 at 600 and 20
B = 20/log(2) = 28.8539
A = 600 - {28.8539 l°g (5°)} = 487.123 Score = 487.123 + 28.8539 l°g (odds) Or log (odds) = (-16.88239) + o.o3465*Score
Scorecard Scaling
• The points for each attribute are calculated by multiplying the Weight of Evidence of the attribute with the regression coefficient of the characteristic, then adding a fraction of the regression intercept, then multiplying this by -1 and by the factor and finally adding a fraction of the offset.
• The negative sign is there because we switch from bad/good in modeling (regression) to good/bad in scaling (high scores being better than low scores).
factor +
offset
n
n
Scorecard Scaling
score = log(odds) * factor + offset =
n
-     (woei */X) + a)* factor + offset =
i=l n
-     (woei * J& h—)) * factor + offset =
i=l
a n
a
offset.
(-(woei * yfi h—) * factor h--)
i=i n n
P = is the regression coefficient
WOE = weight of evidence for the attribute
n = number of characteristics
a = intercept
582
Check Points Allocation
Age	Weight	Scorecard 1	Scorecard 2
			
Missing	-55.50	16	16
18-22	-108.41	12	12
23-26	-72.04	18	18
27-29	-3.95	26	<J4
30-35	70.77	35	38
35-44	122.04	43	44
44 +	165.51	51	52
• Scorecard i looks OK - logical distribution - as age increases, points increase according to weight
• But Scorecard 2 doesn't. •Why?
• Correlation? Quirk in the data? Grouping? Maybe weights were too close together and not enough differentiation - repeat grouping with more distinct groups, and repeat regression.
583
FICO score
FICO is a unified score, which you can get from your score by linear transformation. The aim is to compute these transformation coefficients for every scorecard, because then you can compare quality of portfolios. If your development data are old enough, so that you can observe 90DPD @12MOB, take random sample (30 000 observations) from them, if not, take older data and score them by your new scorecard. Make a table according to example below, compute FICO score for each category as linear transformation ln(G/B)->Fico, defined
Apply linear regression on median score and FICO.
(-0.5319 + 7.58)/0.0157 = 449 497-943)/943 = 0.5874
FICO=(x+7.58)/0.0157.
Median of the	Lower bound of	Upper bound of	Numb @12 J	'Ever 90@12 J			
category	the score	the score	Mob /	MOB 1	Good/Bad /	ln(G/B) \	Fico
0.716	0	0.752399981	1497 '	943	0.5874867 '	-0.5319	449
0.778	0.7524	0.7968	1504	733	1.0518418	0.050543	486
0.8132	0.7968	0.8268	1496	630	1.3746032	0.318165	503
0.8371	0.8268	0.8457	1508	564	1.6737589	0.515072	516
0.8532	0.8457	0.8596	1495	510	1.9313726	0.658231	525
0.8654	0.8596	0.8703	1500	474	2.164557	0.772216	532
0.875	0.8703	0.8792	1513	447	2.3847875	0.86911	538
0.8833	0.8792	0.8869	1489	414	2.5966184	0.95421	544
0.8901	0.8869	0.8934	1496	393	2.8066158	1.031979	549
0.8968	0.8934	0.8996	1521	378	3.0238095	1.106517	553
0.9024	0.8996	0.9051	1491	351	3.2478633	1.177997	558
584
FICO score
FICO transformation graph
	700
	600
	500
0)	
o u	400
(0 1	
1 o	300
o	
LL	200
	100
0
y = 678.99x-49.314
R =0.9613
0.65        0.7        0.75        0.8 0.85
sc1
0.9
Radal —Lineärni (Radal)
0.95
9. Introduction to Survival Analysis
What Is Survival Analysis?
• Survival analysis is a class of statistical methods for which the outcome variable of interest is time until an event occurs.
• Time is measured from the beginning of follow-up until the event occurs or a reason occurs for the observation of time to end.
Examples of Survival Analysis
• Follow-up of patients undergoing surgery to measure how long they survived after the surgery
• Follow-up of leukemia patients in remission to measure how long they remain in remission
• Follow-up of clients to measure how long they stay non-defaulted
What Is Survival Analysis?
Subjects
B C D E F
Event
►  End of Study
Withdrew -► Event
Lost to follow-up Event
Event
1
1
2
I
3
Time
I
4
I
5
589
Data Structure
Subject        Survival Time Status
A 4.0 1 (event)
B 6.0 0 (censored)
C 3.0 0
D 5.0 1
E 3.0 0
F 3.0 1
G 2.0 1
Problems with Conventional Methods
•Logistic regression
• ignores information on the timing of events
• cannot handle time-dependent covariates. •Linear regression
• cannot handle censored observations
• cannot handle time-dependent covariates
• is not appropriate because time to event can have unusual distribution.
591
Right-Censoring
Subjects
►  End of Study
Withdrew
Lost to follow-up
Time
An observation is right-censored if the observation is terminated before the event occurs.
592
Left-Censoring
Event-► A
Event-► B
Time before Start of End of
Study Study Study
An observation is left-censored when the observation experiences the event before the start of the follow-up period.
593
Interval-Censoring
^ Event
B
Event
Time
An observation is interval-censored if the only information you know about the survival time is that it is between the values a and b.
594
Types of Right-Censoring
• Type I subjects survived until end of the study. Censoring time is fixed.
• Type II subjects survived until end of the study. Censoring time occurs when a pre-specified number of events have occurred.
• Random observations are terminated for reasons that are not under the control of the investigator.
595
Uninformative Censoring
•Censoring is uninformative if it
• occurs when the reasons for termination are unrelated to the risk of the event
• assumes that subjects who are censored at time X should be representative of all those subjects with the same values of the predictor variables who survive to time X
• does not bias the parameter estimates and statistical inference.
596
Informative Censoring
•Censoring is informative if it
• occurs when the reasons for termination of the observation are related to the risk of the event
• results in biased parameter estimates and inaccurate statistical inference about the survival experience.
597
Recommendations Regarding Informative Censoring
• When designing and conducting studies, reduce the amount of random censoring.
• Always analyze the pattern of censoring to see whether it is related to a subset of subjects.
• Include in your study any explanatory variables that may affect the rate of censoring.
598
Time Origin Recommendations
• Choose a time origin that marks the onset of continuous exposure to the risk of the event.
• Choose the time of randomization to treatment as the time origin in experimental studies.
• If there are several time origins available, consider controlling for the other time origins by including them as covariates.
599
Survival Analysis
•The goals of survival analysis might be to
• estimate and interpret survival and hazard functions from survival data
• compare survival and hazard functions among different groups
• assess the relationship of time-independent and time-dependent explanatory variables to survival time
• predict the remaining time until the event.
600
Survival Function (funkce přežití)
•T ... náhodná veličina označující délku přežití (čas do sledované události nebo cenzorování).
•S... indikátor události (S=i pokud událost nastala, S=o pokud je pozorování cenzorované)
• S(t)... funkce přežití (survival function) S(t) = P (T >t) vyjadřuje pravděpodobnost, že jedinec v čase t ještě žije.
• Platí:
S(0) = 1 limS(t) = 0
601
Kaplan-Meier estimation
^ /y j -J-* _
S (t. ) = S (t •   )(1 — d /n ) = I I —i_{-      nr~ P°čet objektu pozorovaných do doby ŕ;-
J J_1 J/   J     11    n počet objektu s udalostí v dobé ŕ;-
Time
Number Number Events Censored
Number At Risk
0	0	0
1	0	0
2	1	0
3		
4	1	0
5	1	1
6	0	0
Cumulative Survival
1.00
LOO )/7=.86
.86*5/6=.71 .71*2/3=.48 .48*1/2^.24
602
an-Meier Curve
1.00
0.86 0.75
Survival
Distribution 0.50 Function
0.25
0.00 4,_,__,_,__,_J
0 2    3    4    5 6
Další metody odhadu
The Breslow estimate of the survivor function is
\ J=lnJS
Note that the Breslow estimate is the exponentiation of the negative Nelson-Aalen estimate of the cumulative hazard function. The Fleming-Harrington estimate (Fleming and Harrington; 1984) of the survivor function is
If the frequency values are not integers, the Fleming-Harrington estimate cannot be computed.
604
Life Table Method
The life table method
• is useful when there are a large number of observations
• groups the event times into intervals
• can produce estimates and plots of the hazard function.
Life Table Method
The life-table estimates are computed by counting the numbers of censored and uncensored observations that fall into each of the time intervals [f r-i,/,},
i= 1,2.....k+ ], where io = 0 and       = ™. Let rti be the number of units entering the interval [f,_!,/,), and let J; be the number of events occurring in the interval. Let
bi = tj — A-1, and let nj = n, — Wj/2, where Wj is the number of units censored in the interval. The effective sample size of the interval [f is denoted by nj. Let /mj-denote the midpoint of ffj_|,/j}.
The conditional probability of an event in is estimated by
d;
and its estimated standard error is
The estimate of the survival function at is
m=
i=0
where £j = ] — fy.
and its estimated standard error is
j—I
606
Differences between KM and Life Table Methods
•In the Kaplan-Meier method,
• time interval boundaries are determined by the event times themselves
• censored observations are assumed to be at risk for the whole event time period.
•In the life table method,
• time interval boundaries are determined by the user
• censored observations are censored at the midpoint of the time interval.
Standard error of KM estimate
• The corresponding estimate of the standard error is computed using Greenwood s formula (Kalbfleisch and Prentice; 1980) as
Pointwise Confidence Limits
Pointwise confidence limits are computed for the survivor function, and for the density function and hazard function when the life-table method is used. Let a be specified by the ALPHA= option. Let Zafi be tne critical value for the standard normal distribution. That is,      Za/2} = a /2, where    is the cumulative distribution function of the standard normal random variable.
Survivor Function
When the computation of confidence limits for the survivor function S(t) is based on the asymptotic normality of the survival estimator S(t), the approximate confidence interval might include impossible values outside the range [0,1] at extreme values of /. This problem can be avoided by applying the asymptotic normality to a transformation of S(/} for which the range is unrestricted. In addition, certain transformed confidence intervals for S(/} perform better than the usual linear confidence intervals [Borgan and Liestsl; 1990). The CONFTYPE= option enables you to pick one of the following transformations: the log-log function [Kalbfleisch and Prentice; 1980). the arcsine-square root function [Nair; 1984). the logit function (Meeker and Escobar; 1998). the log function, and the linear function.
Let g be the transformation that is being applied to the survivor function S(t). By the delta method, the standard error of g(S(t}) is estimated by
r<0 - a WWW (SO W)l
where g* is the first derivative of the function g. The 100[1-a)% confidence interval fbr5(/} is given by where g_l is the inverse function of g.
609
Pointwise Confidence Limits
Arcsi n e - S q u a re Root Transformation
The estimated variance of sin 1 ^yjS(t )^ is Tr(t) = 4j^|f      ■      100(1-«)% confidence interval for S(t) is given by
sin-jmax 0,sin-1 (yß(t))-z&f(t)
Linear Transformation
<S(t}< sin- i min
This is the same as having no transformation in which g is the identity. The 100(1-«)% confidence interval for      is given by
5(0-«©[5(r)]<J(f)<Hr)+atf[i(/)]
Log Transformation
The estimated variance of Iob(J(/)) is r(t) = ^p-The 100(1-«}% confidence interval for S{t) is given by 5(*)exp < S(t) < S(/)exp
610
Pointwise Confidence Limits
Log-Log Transformation
The estimated variance of log(-log(S(/)) is f2^) = ^^^j^p.The 100[1-a)% confidence interval for S(f) is given by
[$(t)]<S(t)< [i(r)]Hip(-ffSfW)
Logit Transformation
The estimated variance of log ^ ,f jg^ J is       = jl^^^jl-100[1—«)% confidence limits for 5(f) are given by
< s(t) <
S(f)+ [1 - m «P (lf ffr)) AM + [l - 5(f)] »p (-1, *(/))
611
Simultaneous Confidence Intervals
• Confidence bands show with a given confidence level that the survival function falls within the interval for all time points.
• There are two approaches in SAS for constructing simultaneous confidence intervals.
• Equal precision (CONFBAND=EP) confidence intervals are proportional to the pointwise confidence intervals.
• Hall-Wellner (CONFBAND=HW) confidence intervals are not proportional to the pointwise confidence intervals.
• Transformations that are used to improve the pointwise confidence bands can be used to improve the simultaneous confidence bands.
612
Simultaneous Confidence Intervals
Let    aL =--^77^- and aa =
Let {!V°(u),a < u < 1} be a Brownian bridge. Hall-Wellner Band
The 100[1-ff}% HW band of Hall and Wellner (1980) is
for all 1l<1< fa, where Aa(fl£,fli/} is given by a = Pr{   sup |W°(n)|>AB(fl£lflff)}
The critical values are computed from the results in Chung (1986).
613
Simultaneous Confidence Intervals
Note that the given confidence band has a formula similar to that of the [linear) pointwise confidence interval, where ha(aL<Qu) and n * [] -\-na^(t)]S(t) in the former correspond to z« and in the latter, respectively. You can obtain the other transformations [arcsine-square root, log-log, log, and logit) for the confidence bands by
replacing z« and z(l) in the corresponding pointwise confidence interval formula by /ia(fl£,fl<y} and the following z(i), respectively.
• Arcsine-Square Root Transformation
2 ]jn[]-S(!}] Log Transformation
Log-Log Transformation
1 + «<*#(0
f(/) =
v«Mty)]| Logit Transformation
f(0=
v«[l-^)]
614
Simultaneous Confidence Intervals
Equal-Precision Band
The 100[1-a)% EP band of Nair [1984) is
for all 1l < 1 < tu, where *"a(flt,fl(/) is given by
a=Pr{   sup     lW ^j, ><?a(fl^flc/))
PROC LIFETEST uses the approximation of Miller and Siegmund [1982. Equation 8} to approximate the tail probability in which fa(fl/,, au) is obtained by solving x in
au{\ —aL)'
= a
where $(x) is the standard normal density function evaluated at jr. Note that the confidence bounds given are proportional to the pointwise confidence intervals. As a matter of fact, this confidence band and the (linear) pointwise confidence interval have the same formula except for the critical values [z« for the pointwise confidence interval and fa(fli,fli/} for the band). You can obtain the other transformations (arcsine-square root, log-log, log, and logit) for the confidence bands by replacing z% by eaipL-au) in the formula of the pointwise confidence intervals.
615
Comparing Survival Functions
Survival
Distribution o.so Function
	Female
Male	
n—,-<-,-,-,-,-,—1
0 10 20 30 40 50 60
Time
Let k be the number of groups. Let       be the underlying survivor function /th group, i= ].....k. The null and alternative hypotheses to be tested are
H0 : Si (t) =       = ■ ■ ■ = St(t) for all t < r versus
Hi : at least one of the £j(/}'s is different for some t < z respectively, where r is the largest observed time.
616
Likelihood-Ratio Test
•The likelihood-ratio test
• is a parametric test that assumes that the distribution of event times follows an exponential distribution
• can be verified if the plot of the negative log of the survival function by time follows a linear trend with an origin of o.
The likelihood ratio test statistic [Lawless; 1982) for test Ho versus Hi assumes that the data in the various samples are exponentially distributed and tests that the scale parameters are equal. The test statistic is computed as
where Nj is the total number of events in the jtU stratum, IV = Y?j=i ^Y>> 's me total t'me on test 'n the /th stratum, and T = Y,j=i Tj- The approximate probability value is computed by treating X1 as having a chi-square distribution with k-A degrees of freedom.
617
Nonparametric Tests
Let t\ < fa < ... < to be the distinct event times in the pooled sample. At time U, let W(tj) be a positive weight function, and let n,j and djj be the size of the risk set and the number of events in the yth sample, respectively. Let rij = Y?j= \ nij> £ = TJj=| djj, and Sj = rij — dj.
The choices of the weight function W(tj) are given in Table 49.3.
Table 49.3 Weight Functions for Various Tests	
Test	W(tt)
Log-rank	1.0
Wilcoxon	»;
Ta rone-Ware	
Peto-Peto	
Modified Peto-Peto	
Harrington-Fleming [p,q)         [] -S{li}]q,p> 0,q> 0	
where S(t) is the product-limit estimate at / for the pooled sample, and      is a survivor function estimate close to S(t) given by
^-SO-STt)
618
Log-Rank Test
•The log-rank test
• tests   whether   the   survival   functions   are statistically equivalent
• is a large-sample chi-square test that uses the observed and expected cell counts across the event times
• has maximum power when the ratio of hazards is constant over time
• loses power in the presence of interactions.
619
Log-Rank Test for Two Groups
r r \2
J
r
var
X(du-eij)
V j=i
J
where cL is the number of events that occur in group 1 at time   and e is the expected number of events in group 1 at time ;.
Wilcoxon Test
•The Wilcoxon test
• is also known as the Gehan test or the Breslow test
• can be biased if the pattern of censoring is different between the groups
• loses power in the presence of interactions.
621
Wilcoxon Test for Two Groups
'   r V
ZVdij -eij)
J
'   r A
Znj(dij -eij)
var
where rij is the total number at risk at each time point,
622
Log-Rank versus Wilcoxon Test
•Log-rank test
• is more sensitive than the Wilcoxon test to differences between groups in later points in time.
•Wilcoxon test
• is more sensitive than the log-rank test to differences between groups that occur in early points in time.
623
New Tests in SAS®9
• Tarone-Ware test uses a weight equal to the square root of the number at risk. This gives more weight to differences between the observed and expected number of events at time points where there is the most data.
• Peto-Peto and Modified Peto-Peto tests use weights that depend of the observed survival experience of the combined sample. The principle advantage of these tests is that they do not depend on the censoring experience of the groups.
• Harrington-Fleming test incorporates features of both the log-rank and Peto-Peto tests.
624
Stratified Tests
• Stratified tests are used when you want to compare survival functions across k populations while controlling for other covariates.
• They are different than the /c-sample tests which only compare survival functions across k populations.
• Stratified tests are available in SAS@9 with the use of the GROUP= option in the STRATA statement.
625
Syntax for Stratified Tests
STRATA variablel / GROUP variable2 TEST=(list);
Distinct values Distinct values
represent the m represent the k
strata populations
626
Multiple Comparison Methods
• Bonferroni correction to the raw p-values
• Dunnett s two-tailed comparisons of the control group with all other groups
• Scheffe s multiple-comparison adjustment
• Sidak correction to the raw p-values
• Paired comparisons based on the studentized maximum modulus test
• Tukey's studentized range test
• Adjusted p-values from the simulated distribution
627
Specification of Comparisons
• DIFF=ALL requests all paired comparisons.
• DIFF=CONTROL <( string' <...string>)> requests comparisons of the control curve with all other curves.
• To specify the control curve, you specify the quoted strings of formatted values that represent the curve
in parentheses.
628
Unstratified Tests
The rank statistics [Klein and Moeschberger; 1997. Section 7.3} for testing Hq versus //| have the form of a ^-vector v — (vi, .....v^'with
and the estimated covariance matrix, V = (V^), is given by
where Sj/ is 1 if j = I and 0 otherwise. The term vj can be interpreted as a weighted sum of observed minus expected numbers of failure under the null hypothesis of identical survival curves. The overall test statistic for homogeneity is v'V_vI where V-denotes a generalized inverse ofV. This statistic is treated as having a chi-square distribution with degrees of freedom equal to the rank of V for the purposes of computing an approximate probability level.
Stratified Tests
Suppose the test is to be stratified on M levels of a set of STRATA variables. Based only on the data of the ith stratum [s = ] ...M), let vs be the test statistic (Klein and Moeschberger; 1397. Section 7.5) for the sth stratum, and let \s be its covariance matrix. Let
v = Y,y*
s ■■■■ L
v = £v,
A global test statistic is constructed as
Under the null hypothesis, the test statistic has a X2 distribution with the same degrees of freedom as the individual test for each stratum.
629
Multiple-Comparison Adjustments
Let denote a chi-squared random variable with r degrees of freedom. Denote $ and <I» as the density function and the cumulative distribution function of a standard normal distribution, respectively. Letm be the number of comparisons; that is,
DIFF = ALL
1     DIFF = CONTROL
For a two-sided test comparing the survival of the y'th group with that of /th group. \ < j^l < r. the test statistic is
_2 (vj-vt)2 Jl Vjj+V,,-2Vj,
and the raw p-value is
630
Adjusted p-values for various multiple-comparison adjustments are computed as follows: Bonferroni Adjustment
p = min{], mPr(x^ > S^)}
Dunnett-Hsu Adjustment
With the first group being the control, let C = (cjj) be the (r — 1) xr matrix of contrasts; that is,
f 1      >"=].....r-],j = 2.....r
cij = \  -1   j = i+hi=2.....r
[ 0 otherwise
Let £ = (dfj) and R = (r,j) be covariance and correlation matrices of Cv, respectively; that is.
E=CVC'
and
r'J =
The factor-analytic covariance approximation of Hsu [1992) is to find X\.....Xr-\ such that
R=D + iU'
where D is a diagonal matrix with the jih diagonal element being ] — Xj and X = (X\.....Ar_i)'. The adjusted p-value
which can be obtained in a DATA step as
p = PROBMC("DUNNETT2",Zij.....r- .....X,_,).
Schaffe Adjustment
Sidäk Adjustment
p=]-{]-Pr(^>4)r
SMM Adjustment
p=]-p*(^)-ir
which can also be evaluated in a DATA step as
p= 1 -PROBMCC'MAXMOD*',^,.,.,™). Tukey Adjustment
r^(y)[<%)-<%-v^)]r-^V which can also be evaluated in a DATA step as
p = ] -FROBMCC'RANGE", .....r).
LI FETEST Procedure
•General form of the LIFETEST procedure:
PROC LIFETEST DATA=SAS-data-set <options>;
TIME variable <*censor(list)>;
STRATA variable <(list)> <...variable <(list)» </options>\
TEST variables; RUN;
• The simplest use of PROC LIFETEST is to request the nonparametric estimates of the survivor function for a sample of survival times. In such a case, only the PROC LIFETEST statement and the TIME statement are required. You can use the STRATA statement to divide the data into various strata. A separate survivor function is then estimated for each stratum, and tests of the homogeneity of strata are performed. 633
Hazard Function (riziková funkce)
•The hazard function
• is the instantaneous risk or potential that an event will occur at time t, given that the individual has survived up to time t
• takes the form number of events per interval of time
• is a rate, not a probability, that ranges from zero to infinity.
634
Hazard Function ^ conditional
Probability
P(t<T<t + AtlT>t) h(t) = lim —----
At^O At
Interval of time
Instantaneous risk or potential (okamžité riziko/potenciál)
Platí:
\\(A\ =        — __^_ln(S(t)) kde f (t) je hustota náhodné veličiny T.
S(t) ôt
t
S(t) = exp(-H(t)) kde  H(t) = Jh(x)dx   je tzv. kumulativní riziková funkce.
0 635
Hazard Function
Hazard
Function 0.03
0.01
10. Cox model
Survival Models
•Models in survival analysis
are written in terms of the hazard function
• assess the relationship of predictor variables to survival time
• can be parametric or nonparametric models.
638
Parametric versus Nonparametric Models
•Parametric models require that
• the distribution of survival time is known
• the   hazard   function   is   completely   specified except for the values of the unknown parameters.
•Examples include the Weibull model, the exponential model, and the log-normal model.
639
Parametric versus Nonparametric Models
Properties of nonparametric models are
• the distribution of survival time is unknown
• the hazard function is unspecified.
•An example is the Cox proportional hazards model.
Cox Proportional Hazards Model
^(t) = ho(t)e
{AXii+...+/?kXik}
Baseline Hazard function -involves time but not predictor variables
Linear function of a set of predictor variables - does not involve time
641
Popularity of the Cox Model
The Cox proportional hazards model
• provides the primary information desired from a survival analysis, hazard ratios and adjusted survival curves, with a minimum number of assumptions
• is a robust model where the regression coefficients closely approximate the results from the correct parametric model.
642
Measure of Effect
Hazard ratio =-hazard in qroup A
hazard in group B
— ^A(XiA_XiB)
roperties of the Hazard Rati
		No Association		
	Group B		Group A	
	Higher		Higher	
	Hazard		Hazard	
0 1
oo —>
Proportional Hazards Assumptio
Log h(t)
Time
Nonproportional Hazards
Log h(t)
Time
Cox model in credit scoring
Credit-scoring systems were built to answer the question, "How likely is a credit applicant to default by a given time in the future?" The methodology is to take a sample of previous customers and classify them into good or bad depending on their repayment performance over a given fixed period. Poor performance just before the end of this fixed period means that customer is classified as bad; poor performance just after the end of the period does not matter and the customer is classified as good. This arbitrary division can lead to less-thanrobust scoring systems. Also, if one wants to move from credit scoring to profit scoring, then it matters when a customer defaults. One asks not if an applicant will default but when will they default. This is a more difficult question to answer because there are lots of answers, not just the yes or no of the "if question, but it is the question that survival analysis tools address when modeling the lifetime of equipment, constructions, and humans.
Zdroj: Thomas, Edelman, Crook - Credit scoring and its application.
647
Cox model in credit scoring
Using survival analysis to answer the "when" question has several advantages over standard credit scoring. For example,
• it deals easily with censored data, where customers cease to be borrowers (either by paying back the loan, death, changing lender) before they default;
• it avoids the instability caused by having to choose a fixed period to measure satisfactory performance;
• estimating when there is a default is a major step toward calculating the profitability of an applicant;
• these estimates will give a forecast of the default levels as a function of time, which is useful in debt provisioning;
• this approach may make it easier to incorporate estimates of changes in the economic climate into the scoring system.
Zdroj: Thomas, Edelman, Crook - Credit scoring and its application.
648
Cox model in credit scoring
Let T be the time until a loan defaults. Then there are three standard ways to describe the randomness of Tin survival analysis (Collett 1994): S(t), f(t) and h(t).
Two of the commonest lifetime distributions are the negative exponential, which with parameters X has S(t) = e~xtt f(t) — \e~kt> and h(t) — k, and the Weibull distribution, which with scale X and shape k has S{t) = e~()J)\ f(t) = kXtk~le~{Xt)\mdh(t) — kkktk~l. The former has no aging effect in that the default rate stays the same over time; the latter is more likely to default early on if k < 1, is more likely to default late on if A: > 1, and becomes the negative exponential distribution if k = 1.
Zdroj: Thomas, Edelman, Crook - Credit scoring and its application.
649
Cox model in credit scoring
In standard credit scoring, one assumes that the application characteristics affect the probability of default. Similarly, in this survival analysis approach, we want models that allow these characteristics to affect the probability of when a customer defaults. Two models have found favor in connecting explanatory variables to failure times in survival analysis:
• proportional hazard models
• accelerated life models.
If x = (xlf...f Xp) are the application (explanatory) characteristics, then an accelerated life model assumes that
S(t) = Sq(*wxO   or  h(t) = e™h0{e™t)
where hQ and SQ are baseline functions, so the x can speed up or slow down the aging of the account. The proportional hazard assumes that
hit) = e^hoit)
so the application variables x have a multiplier effect on the baseline hazard.
Zdroj: Thomas, Edelman, Crook - Credit scoring and its application.
650
Cox model in credit scoring
Cox (1972) pointed out that in proportional hazards one can estimate the weights w without knowing hgftj using the ordering of the failure times and the censored times. If £7and xs are the failure (or censored) times and the application variables for each of the items under test, then the conditional probability that customer / defaults at time £7given that R(i) are the customers still operating just before tr is given by
exp{w • Xi }h0(t)      _      exp{w • xt} which is independent of h0.
Zdroj: Thomas, Edelman, Crook - Credit scoring and its application.
651
PHREG Procedure
PROC PHREG DATA=SAS-data-set <options>)
CLASS variable <(options)x... variable <{options)»<l options>)
MODEL response<*censor(list)>=variables </options>)
STRATA variable<(list)x...variable<(list)>> </options>) CONTRAST < 'label>effect values<,.., effect values> </options>}
ASSESS keyword <Ioptions>)
HAZARDRATIO <'label> variable <Ioptions>)
<label:> TEST equationl <,..., equationlo < /options>}
WEIGHT variable</optiorrr
BASELINE <0UT=5>15-^-5e^><C0VARIATES=
SAS-data-set> < keyword=name.. > </options>)
OUTPUT <0UT=SAS-data-set> <key word=name... keyword=name> </options>)
programming statements', RUN;
_
652
11. Měření kvality (síly) modelu, validace modelu.
How Good Is the Scorecard?
• And which one is the best?
• Combination of statistical measures and business objectives
Misclassification (Confusion) matrix
• Scorecard strength measures
Misclassification
Confusion matrix
• Accuracy
• (TP+TN)/total
• Error rate
• (FP+FN)/total
• Sensitivity; Specificity
		Predicted		
		Good	Bad	
3	Good	True Positive	False Negative	
Act	Bad	False Positive	True Negative	
"GoodTBad" is above/below chosen cutoff.
• (TP)/Actual Positives ; (TN)/Actual Negatives Positive ; Negative predicted value
• TP/predicted positives ; TN/predicted negatives
Want to max accuracy and min error rate.
655
Misclassification
Confusion matrix
• Acceptance of bads (FP)
• Acceptance of goods (TP)
• Decline Goods (FN)
• Decline Bads (TN)
		Predicted		
		Good	Bad	
re	Good	True Positive	False Negative	
Act	Bad	False Positive	True Negative	
Want to min rejection of goods and max rejection of bads.
656
Misclassification
• Approval rate: bad rate relationship
• Objective:
• Minimize the rejection of goods or acceptance of bads
• Best option for desired bad rate, approval rate
• Compare scorecards and cutoff choices.
"Yd rather approve some bads than reject good customers" vs "the cost of approving bads is too high, we can deal with PR".
Generate these stats for different cutoff rate choices and compare with base I.e. current approval and bad rates.
If several models are being compared, generate these for same bad rate or approval rate. I.e. choose different cutoffs to get same bad rate.
657
Misclassification: Oversampling
• Need to adjust for oversampling if have not done so before this step
• Sensitivity/specificity unaffected by oversampling
• Multiply cell counts by sample weights (tt0 and ttJ
		Predicted	
		Good	Bad
Actual	Good	n*(True Ps/Actual Ps)* tt-|	n*(1-Sens)* jt^
	Bad	n*(1 - Spec)* ttq	n*(Spec)* tt0
			
Scorecard Strength
• Akaike s Information Criterion (AIC)
• Schwartz Bayesian Criterion (SBC) • -(score test statistic) + penalty term
Penalty term = (k + 1). Ln(n) k = number of variables n = sample size
Penalise for adding parameters to the model ... Smaller values are better.
659
KS Statistic
Max difference between cumulative distributions of goods and bads across score ranges
Kolmogorov-Smirnov
100% 80% 60%
*o n   n.  "v5 n° n  n° v5 <i? v v nJ3 <v> <i?      <v <ir
45%
40%
35%
30%
25% (o
20% *
15%
10%
5%
0%
Score
Good - A
Bad - A — n— Good - B -      - Bad - B
KS - B — - - KS- A
660
Scorecard Strength
• C - Statistic
• Area under the ROC curve, Wilcoxon-Mann-Whitney test.
ROC Curve
0 0.2 0.4 0.6 0.8 1
(1 - Specificity)
Scorecard - A----Random - - - -Scorecard - B
You may be wondering where the name "Receiver Operating Characteristic" came from. ROC analysis is part of a field called "Signal Detection Theory" developed during World War II for the analysis of radar images. Radar operators had to decide whether a blip on the screen represented an enemy target, a friendly ship, or just noise. Signal detection theory measures the ability of radar receiver operators to make these important distinctions. Their ability to do so was called the Receiver Operating Characteristics. It was not until the 1970's that signal detection theory was recognized as useful for interpreting medical test results.
Scorecard Strength
• Gains Chart: Cumulative Positive Predicted Value versus Distribution of Predicted Positives (depth)
• Lift/concentration curve: Sensitivity versus Depth
Lift = Positive predicted value / % positives in the sample
• Misclassification costs (losses assigned to false +positive and -positive)
• Bayes Rule (minimizes expected cost)
• Cost ratio (at what cutoff do I break even based on prior bad rate I.e. if bad odds are 9:1, you need a cutoff where 1 bad and 9 goods)
• Somers' D, Gamma, Tau-a
Information value
□ The special case of Kullback-Leibler divergence given by:
Ivai = J fiv[■'■)<!■'■   where fivi?) = (/iG*0 - fo(x))la \J^nx
— :x:.
/o ? fi    are densities of scores of bad and good clients.
The example of fIV{x) for 10% of bad clients with f0 ~ JV(0, 1) and 90% of good clients with fi ~ Ar(4, 2)
663
score rejection scale
Information value
- Informační hodnota (lva.) - spojitý případ (Divergence):
CO
Jval = j (/GOOD i*)'/BAD O))111
í
—co
f GOOD (X) L f BAD iX) J
dx
fdiff (X) — f GOOD (X) f RAD (X)
GOOD
BAD
í
fLR(x) = ln
GOOD
(x)
I   fBAD(X) J
-1 0 1
Information value
- Informační hodnota (lva,) - diskretizovaný spojitý případ:
• Nahradíme hustotu jejím jádrovým odhadem a spočteme integrál numericky (např. pomocí složeného lichoběžníkového pravidla).
• S použitím Epanečnikova jádra, K(x) = -(1_x2)"I(XG t-1'1]), a optimální šířky vyhlazovacího okna     k dostaneme
(x) = (i
GOOD
(x, hoS2) f]
BAD
(x'hos,2))
í r-
ln
GOOD
(x,hoS 2)
V
f BAD (X' ^OS,2)
J
Pro daných M+l bodů Xq,...,xm dostáváme
I-val ~~
2M
M-l
V
frv(xo) + 2Z fiv(xi)+ frv(xM)
i=l
J
665
Information value
- Informační statistika/hodnota (lva,) - diskrétní případ:
• Vytvoříme intervaly skóre - typicky decily. Počet dobrých (špatných) klientů v i-tém intervalu označíme   gi fe)
• Musí platit   ^ >0,bi >0 Vi
• Potom dostáváme
score int.	# bad clients	#good clients	% bad [1]	% good [2]	[3] = [2]-[1]	[4] = [2] ŕ [1 ]	[5] = ln[4]	|B]= [3]" [5]
1	1	10	2,0%	1,1%	-0,01	0,53	-0,64	0,01
2	2	15	4,0%	1,6%	-0,02	0,39	-0,93	0,02
3	8	52	16,0%	5,5%	-0,11	0,34	-1,07	0,11
4	14	93	28,0%	9,8%	-0,18	0,35	-1,05	0,19
5	10	146	20,0%	15,4%	-0,05	0,77	-0,26	0,01
6	6	247	12,0%	26,0%	0,14	2,17	0,77	0,11
7	4	137	8,0%	14,4%	0,06	1,80	0,59	0,04
8	3	105	6,0%	11,1%	0,05	1,84	0,61	0,03
9	1	97	2,0%	10,2%	0,08	5,11	1,63	0,13
10	1	48	2,0%	5,1%	0,03	2,53	0,93	0,03
All	50	950					Info. Value	0,68
666
Information value
I Informacni hodnota pro 2 pnklady scoringovych modelö: SC 1:
SC
decile	# cleints	# bad clients	#good	% bad [1]	% good [2]	[3] = [2]-[1]	[4] = [2]/[1]	[5] =ln[4]	[6] = [3] * [5]	cum. [6]
1	100	35	65	35,0%	7,2%	-0,28	0,21	-1,58	0,44	0,44
2	100	16	84	16,0%	9,3%	-0,07	0,58	-0,54	0,04	0,47
3	100	8	92	8,0%	10,2%	0,02	1,28	0,25	0,01	0,48
4	100	8	92	8,0%	10,2%	0,02	1,28	0,25	0,01	0,49
5	100	7	93	7,0%	10,3%	0,03	1,48	0,39	0,01	0,50
6	100	6	94	6,0%	10,4%	0,04	1,74	0,55	0,02	0,52
7	100	6	94	6,0%	10,4%	0,04	1,74	0,55	0,02	0,55
8	100	5	95	5,0%	10,6%	0,06	2,11	0,75	0,04	0,59
9	100	5	95	5,0%	10,6%	0,06	2,11	0,75	0,04	0,63
10	100	4	96	4,0%	10,7%	0,07	2,67	0,98	0,07	0,70
All	1000	100	900					Info. Value	0,70	
I:										
decile	# cleints	# bad clients	#good	% bad [1]	% good [2]	[3] = [2]-[1]	[4] = [2]/[1]	[5] =ln[4]	[6] = [3] * [5]	cum. [6]
1	100	20	80	20,0%	8,9%	-0,11	0,44	-0,81	0,09	0,09
2	100	18	82	18,0%	9,1%	-0,09	0,51	-0,68	0,06	0,15
3	100	17	83	17,0%	9,2%	-0,08	0,54	-0,61	0,05	0,20
4	100	15	85	15,0%	9,4%	-0,06	0,63	-0,46	0,03	0,22
5	100	12	88	12,0%	9,8%	-0,02	0,81	-0,20	0,00	0,23
6	100	6	94	6,0%	10,4%	0,04	1,74	0,55	0,02	0,25
7	100	4	96	4,0%	10,7%	0,07	2,67	0,98	0,07	0,32
8	100	3	97	3,0%	10,8%	0,08	3,59	1,28	0,10	0,42
9	100	3	97	3,0%	10,8%	0,08	3,59	1,28	0,10	0,52
10	100	2	98	2,0%	10,9%	0,09	5,44	1,69	0,15	0,67
All	1000	100	900					Info. Value	0,67	
Information value
668
1«. for normally distributed scores
> Assume that the scores of good and bad clients are normally distributed, i.e. we can write their densities as
1
1 2a\
e g
(x-jub )
<ygy[27T
/oW =
2ai
> Assume that standard deviations are equal to a common value cr
where   D =
Mg-Mb a
> Generally (i.e. without assumption of equality of standard deviations):
Ival=(A + l)D*2+A-l,   A = ^
r
.2\
&b +<Tg
^2 '
where   D* =
2 2
cr. + at
1«. for normally distributed scores
> We can see a quadratic dependence on difference of means.
> Ival takes quite high values when both variances are approximately equal and smaller or equal to 1, and it grows to infinity if ratio of the variances tends to infinity or is nearby zero. 67(
Ivai for normally distributed scores
□ Velmi silná závislost na ju . Navíc hodnota Iva| míří velmi rychle k nekonečnu pokud   se <j2 blíží nule.
671
Empirical estimate of I
The main idea of this approach is to replace unknown densities by their empirical estimates. Let's have n score values, of which tiq score values Sq^, i = for bad clients and      score values Siji j = 1,... ,ni for
good clients and denote L (resp. H) as the minimum (resp. maximum) of all values. Let's divide the interval [L, H] up to r equal sub intervals [<?o, 72], - - -, (9r-1, Qt] j where q0 = L, ^r = iJ. Set
"Oj = 22 ^Oo; € (qj-uqj]) i=l
observed counts of bad or good clients in each interval. Then the empirical Information value is calculated by
672
Empirical estimate of I
□ However in practice, there could occur computational problems. The Information value index becomes infinite in cases when some of n0j or nr are equal to o. When this arises there are numerous practical procedures for preserving finite results. For example one can replace the zero entry of numbers of goods or bads by a minimum constant of say o.oooi. Choosing of the number of bins is also very important. In the literature and also in many applications in credit scoring, the value r=io is preferred.
673
Empirical estimate with supervised interval selection
> We want to avoid zero values of nn. or nv .
> We propose to require to have at least k, where k is a positive integer, observations of scores of both good and bad client in each interval.
> Set qv = L-l
where Fp^() is the empirical quantile function appropriate to the empirical cumulative distribution function of scores of bad clients.
Empirical estimate with supervised interval selection
> Usage of quantile function of scores of bad clients is motivated by the assumption, that number of bad clients is less than number of good clients.
> If nQ is not divisible by k, it is necessary to adjust our intervals, because we obtain number of scores of bad clients in the last interval, which is less than k. In this case, we have to merge the last two intervals.
> Furthermore we need to ensure, that the number of scores of good clients is as required in each interval
> To do so, we compute nx. for all actual intervals. If we obtain nx. < k for jth interval, we merge this interval with its neighbor on the right side.
> This can be done for all intervals except the last one. If we have nx. < k for the last interval, than we have to merge it with its neighbor on the left side, i.e. we merge the last two intervals.
675
Empirical estimate with supervised interval selection
> Very important is the choice of k. If we choose too small value, we get overestimted value of the Information value, and vice versa. As a reasonable compromise seems to be adjusted square root of number of bad clients given by
k = IVräö]
> The estimate of the Information value is given by
where nQ. and nr correspond to observed counts of good and bad clients in intervals created according to the described procedure.
676
Simulation results
> Consider n clients, 100pB% of bad clients with 100(l-pB)% of good clients with f:: nc^,^)
f0 :N(//0,cr0) and
> Because of normality we know ival =
Mi Mo
V
& J
> Consider following values of parameters:
■ n = 100 000 , n = 1000 -Mo = 0
- o0 = o1 = 1
■ pt = 0.5, 1, 1.5
■ pB = 0.02, 0.05, 0.1, 0.2
677
Simulation results
1) Scores of bad and good clients were generated according to given parameters.
2) Estimates lval,DEC,  Wern*  Cese were computed.
3) Square errors were computed.
4) Steps l)-3) were repeated one thousand times.
5) MSE was computed.
678
Simulation results
n=100000,   Mi-Mo = 05				
MSE	Ps			
	0.02	0.05	0.1	0.2
IV decil	0,000546	0,000310	0,000224	0,000168
IV_kern		0,000232	0,000131	0,000076
IV esis	0,000910	0,000384	0,000218	0,000127
				
n=100000,   Mi ~Mo = 10				
MSE	Ps			
	0.02	0.05	0.1	0.2
IV decil	0,006286	0,004909	0,004096	0,002832
IV kern	0,003396	0,001697	0,001064	0,000646
				
				
n=100000,   Mi ~Mo = 15				
MSE	Ps			
	0.02	0.05	0.1	0.2
IV decil	0,056577	0,048415	0,034814	0,020166
IV_kern	0,019561	0,010789		
1 0,013045		0,008134	0,007565	0,027943
• worst
• average
• best performance
n=	1000,	Mi -Mo= 10			
MSE		Ps			
		0.02	0.05	0.1	0.2
IV	decil	0,186663	0,084572	0,043097	0,029788
IV	kern		0,072381	0,045344	0,032131
IV	esis	0,150881 ■iMiMli?:«			IÜSBSI
					
n=	1000,	Mi-Mo =	1.5		
MSE		Ps			
		0.02	0.05	0.1	0.2
IV	decil	1,663859	1,037778	0,535180	0,200792
IV	kern			0,266912	0,196856
IV	esis	0,609193	0,352151		
679
Adjusted empirical estimate with supervised interval selection (AESIS)
> Je zřejmé, že volba parametru k je zcela zásadní. Otázkou tedy je:
Je volba k = fv^l optimální (vzhledem k MSE)?
■ Jaký vliv na optimální k má n0l
■ A jaký vliv, pokud vůbec, má rozdíl středních hodnot Mi~Mo?
680
Simulation results
□ Consider 10000 clients, 100pB% of bad clients with f0:N(//0,i)and 100(l-pB)% of good clients with f,: ^(^,1). Set n0 = Oand consider^ = 0.5,1 and 1.5,
pB = 0.02,0.05,0.1 and 0.2
MSE = E((Ival - I^)2) I S fcm. = argruin MSE.
MSE		Pb[			
		0.02	0.05	0.1	02
Mi Mo	0.5	29	42	62	84
	1	12	18	23	32
	1.5	6	9	8	9
k = [\M)1		15	23	32	45
■=>
avg.#ofbins		Pb			
		0.02	0.05	0.1	0.2
	0.5	8,00	13,00	18,00	24,90
	1	18,00	28,80	42,76	51,88
	1.5	33,62	50,20	95,96	127,67
681
Simulation results
□ Dependence of MSE on k, a ~Mo = 1.
> The highlighted circles correspond to values of /c, where minimal value of the MSE is obtained. The diamonds correspond to values of kgiven by k = \^/r^^^ •
k =
| y/PB ■ n + 2
1.4
0
		Pb			
I 1ST-(SI |		0.02	0.05	0.1	0.2
	0.5	31	45	61	84
	1	12	17	24	32
	1.5	7	10	14	19
mse		Pb			
		0.02	0.05	0.1	0.2
	0.5	29	42	62	84
	1	12	18	23	32
	1.5	6	9	8	9
where /ii and [1q are suitable estimates of means of scores of good and bad clients, pb = ?r is the proportion of bad clients.
val,AESIS
ESIS.l
> Algorithm for the modified ESIS:
1) q = []
2) qji=Fi
vniy
qj0
vnoy
3) =max(qjl,qj0)
4) Add smax to the sequence, i.e. q = [q, simx ]
5) Erase all scores^ s
max
6) While n0 and nx are greater than 2*k, repeat step 2) - 5)
where/,- = \^fr^^^
7) q = [min( score) — 1, q, max( score)]
683
ESIS.2
> U původního E SI S často dochází ke slučování vypočtených intervalů ve druhé fázi algoritmu.
> Pro výpočet se používá jen Fo 0.
> Aby byla splněna podmínka n2>k, je zřejmě nutné, aby hranice prvního intervalu byla větší než
vniy
> To vede k myšlence použít ke konstrukci intervalů nejprve F^Q a následně, od nějaké hodnoty skóre F0 1Q.
> Jako vhodná hodnota skóre pro tento účel se jeví hodnota soJ ve které se protínají hustoty skóre, rozdíl distribučních funkcí skóre nabývá své maximální hodnoty a také platí, že funkce fIV nabývá nulové hodnoty.
Point of intersection of densities
Point of maximal difference of CDFs
Point of zero value of fIV
684
ESIS.2
> Algorithm for the modified ESIS:
i)    s() = arg max F, - F()
2) % = Fi
^ q0 = Fo_1
V ni J
V no J
^■•F.(So) k
n,
^•Fo(s0) k
-1
4) q = [min( score) — 1, qx, q0, max( score) +1]
5) Merge intervals given by qx where number of bads is less than k.
6) Merge intervals given by qQ where number of goods is less than k.
Ival,
ESIS 2
where k = \t/uq ]
685
AESIS.2 - Simulation results
□ Consider 1000, 10000 and 100000 clients, ioopB% of bad clients with f0 : N(//0,l)and ioo(i-pB)% of good clients with fx: N(/^,l) . Set ju0 = 0 ,jux = 0.5,1 and 1.5 and consider pB = 0.02,0.05,0.1 and 0.2.
MSE = E((Ival-Ivair)|
n = 1000
1
MSE		PR			
		0.02	0.05	0.1	0.2
Mi Mo	0.5	15	19	22	45
	1	3	8	11	16
	1.5	2	3	6	7
		5	8	10	15
n = 10000
n = 100000
MSE		PR			
		0.02	0.05	0.1	0.2
	0.5	29	51	77	112
	1	15	24	28	45
	1.5	6	11	11	14
& = [\/«0 1		15	23	32	45
MSE		PR			
		0.02	0.05	0.1	0.2
Mi Mo	0.5	118	198	298	371
	1	50	61	106	141
	1.5	17	28	32	48
k = \s/no]		5	8	10	15
686
Simulation results
□ Dependence of MSE on k.
n = 1000, pB = 0.2
Mi-Mo =0-5
n = 10000, pB = 0.2
Mi-Mo =0-5
k =
V Ph • n
n = 10000
val,AESIS2
Mi-Mo
0.5
1.5
n = 100000, pB =0.05
m "^o =°-5
Pb
0.02
38
15
0.05
60
23
13
0.1
85
32
18
0.2
120
45
26
mse		Pb			
		0.02	0.05	0.1	0.2
Mi Mo	0.5	29	51	77	112
	1	15	24	28	45
	1.5	6	11	11	14
687
J-divergence
> Bude nás zajímat vyjádření J-divergence (neboli informační hodnoty) pro normální, Beta a Gamma rozložení.
Consider logistic regression model: ^"j^—J = ^   Sf-i^"" xi* w^ere
p is the modeled outcome (probability of default), bj are coefficients and are regressors. Then we use following markings:
• score =bQ + Y^=\bi
A 1 1
* pgood - p -
l+ -*-Y*=1**   1 + .-™'
. odds = = e**+5£i V* = e*cor*
l-p
Consider score to be iiormally distxibuted random variable, which is quite common consideration. Then it can be shown that pgood is beta distributed and odds follows log-normal distribution.
688
J-divergence
Definition 1.1. Jeffreys divergence (called J-divergence) of random variables X and Y with probability density functions f{x) and g(x) is a
symmetrized KuUback-Leibler divergence given by
Dj{X, Y) = DKL(X:¥) + Djs(7 : X)
where the Kullback-Leibler divergence Dg^ (X : Y) is given by
Dkl(x : r) = f" (/(*)) ln(^j)'fc 0 2)
The connection to more general class of divergences, like general Alpliadivergences, Alpha-Renyi or Jens en-Shannon divergence, can be found in the literature, e.g., Cichocki and Aman [2]. Important properties like convexity or strict positivity of Dj are direct consequences of Alpha-divergence properties, witch could be found there as well.
[2]  A. Cichocki and S. A mari Families of alpha-beta-and gamuia-divergences: flexible and robust measures of similarities. Entropy 12 (2010), 1532-1568.
689
2. Normally Distributed Scores
Let X and Y be normally distributed random variables with density' functions fo(x) and f\{x) given by
2*4
x e (
—QO, oo
)-
(2.1)
(2.2)
where \Xq , [l^, CJq > 0 and     > 0 are real constants.
Lemma 2.1. Consider X, Y to be random variables. Let fa{x) arcef /lOO 5e density functions given by (2.1) arcef (2.2), respectively. Then it holds
M , (mi - no)2 +(qp -g?)
2af
(2.3)
Proof.
9
'-At')*
4
Z
Using this lemma, we can get a formula for the J-divergence. It is provided in the following Theorem 2.1.
Theorem 2.1. Consider X, Y to be random variables. Let fa(x) and f\{x) be density functions given by (2.1) and (2.2), respectively. Then it holds
Proof. Following Definition 1.1 and the previous Lemma 2.1. we have
T) = -PfcxpT : T) + DKL{Y : X)
= \JSl[+ (^i - Mo)2 +(Qq -q?)
2q?
2of 2rjg
- iiQ)2 - (of + qg) + (of - q2,)2 2qgq2
Z
For parametric estimation of Dj, one can use (2.4) with MLE estimates of the parameters. Consider      ,     X^  ~ / = 0, 1 is a random
sample of scores. MLE estimates (see [6]) are given by
1 "J
J i=l
[d]  N. L. Johnson, S. Kotz and N. Balakrishnaa Continuous Univariate Distributions, Volume 1, 2nd ed., Wiley, New York, 1994.
692
3. Bern Distributed Scores
Let X and Y be beta distributed random variables with density functions fQ(x) and frfx) given by
*Ha0* Po) (3.1) AGO = 0, re (-^d. 0] U [1. °°),
where EXq > 0„ ot^ > 0,      > Q and     > 0 are real constants. Lemma 3.1. For real constants cXq > 0, and     > 0 frofrfc
Jo J^pp)^"1 (1" x)^~l Hx)dx = v(0£t))" v{a° + Po)' (3"3)
wAere is the digamma function given by \|/(x) =-
r(*>
Proof. Using the formula which holds for all real constants |.i > 0, v > 0 and r > 0 (see [3, p. 570.
equation 4.253.1]). the statement of the leimna follows considering = ct^, r = 1 and v = J30. □
More details about the digamina function can be found for instance in Gradslitein and Ryzhik [3] or Medina and Moll [10]. Using the previous lemma, we can get a formula for Dg£.
Lemma 3.2. ConsiderX, Y to be random variables. Let /q(x) and f\(x) be density Junctions given by (3.1) and (3.2), respectively. Then it holds
Dn(X : Y) = h^lgifiJJ + («(,- ai)V(a0) + (ft, - ^MM
+ (a, - o0 + ft, - P0)v(a0 + ft,). (3.4)
[3]   I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Sums, Series and Products, Academic Press, New York and London, 1965.
[10]   L. A. Medina and V. H. Moll The integrals in Gradshteyn and Ryzhik. Part 10: the diganinia function Scientia: Series A: Matkeinaieal Sciences 17 :'2G0!?i. 45-66.
694
Proof. Using the previous Lemma 3.1 and the fact that        — x) =
x^-1 we have
dx
J * iMx) - la
1
5(a0, P0)
I. Pi)
+     - a0 + ft - P0)v(a<j +■ P0)
Z
The formula for J-divergence is the direct consequence of the previous lemma.
695
Theorem 3.1. Consider X, Y to be raiidom variables. Let /o(jc) and fl(x) be density fiiflctions given by (3.1) and (3.2), respectively. Then it holds
Dj(X, Y) = (et! - a0) (ii/faO - y(a0)) + (px - p0) (^(fr) -
+ (cq - a0 +■ pt - p0) (V(a0 + p0) - yfa + ft)). (3.5) Proof. Follows from Definition 1.1 and the previous Lernrna 3.2: Dj(X, Y) = DnlX : Y) + D^(Y : X)
= (ot! - a0) - - V(a0)) -f (pt -ß0) - (\|/(ß,) - V(p0))
+ («! - a0 + p! - p0) - (M/(a0 + ßo)-v(a! +■ Pi)).
If we do not like to use the digatnina function, we can use its approximation. Then the fomiula for the J-divergence can be expressed in the following way.
696
Corolla jy 3.1.1. Following assumptions of the Theorem 3.1 and approximation of digamma function * ln(jr - 0.5) (can be found in [7] p. 223), if holds
Dj(X> Y) h In
i
a0
otj + p! - 0.5
(3.6)
When the beta distributioii is considered, one can use (3.5) or (3.6) for parametric estimation of Dj   with moment or MLE estimates of the
parameters. Consider XJ,     X^  ~ Beta(tl,., pA  j = 0, 1 is a random
sample of scores. MLE estimates of OLj and p^ (see [7]) can be computed iteratively by
697
J		-afy
B: k-w		
- g(a<k>, p£>f - Ko« pf >)r1, (3.7)
where
*(a>P) =
Mot, p) =
A,- ■ (v(a + p) - \|/(a)) + X"=iln^" n/ - (V(a + p) - V(a)) + X"=i Ml " */)
»/ " (¥1 (a + P) -   (a))    w;-i|/i(a + p)
n; - Vl(a + p) W; ■ (V](a + p) - it/!(p))
and is the tngamma function defined as Ufi (x) = ^^x) — ^ ^n^ix)
dx -
c x
an initial approximation one can take the moment estimates (see [7] for more details).
[7]  N. L. Johnson. S. Kotz andN. Balakrishnan Continuous Univariate Distributions Volume 2. 2nd ed.r Wiley, New Y«t, 1995.
698
4. Gamma Distributed Scores
Let X and Y be gamma distributed random variables with density functions f${x) and f\(x) given by
70 {}   r(ot0) 5 l'   J' (4.1)
/oW = 03 t e (-oo, 0],
^W=rfo^"V^-  *E<0^ (42)
/iW = 0. * e 0],
where rig > 0, otj > 0, Xq > 0 and     > 0 are real constants. Lemma 4.1. For real constants ot^ > 0r and     > 0 fro/dfs
Proof. Follows from formula
f ^ ^T  b(x)cfr = -^r(v)[¥Cv) - ln(u)], JO
which holds for all real constants u. > 0 and v > 0 (can be found in [3, p. 604, equation 4.352.1]), if we choose \i =     and v = gcq. □
Provided the previous lemma we can get a formula for for the case of gamma distributed random variables, such as odds.
Lemma 4.2. Consider Xr Y to be random variables. Let /q(r) and fl(x) be density junctions given by (4.1) and (4.2), respectively. Then it holds
DaXX : Y) = (a0 - a,) - v(ao) +tfj^)
+ a, lnf      + ao . f *L - A (4.4)
Proof. One can find this result in Gupta and Kundu [4]. However, it is easy to showT that using the relation T(jc +1) = xT(x) and Lemma 4.1, we
obtain (4.4). □
700
Theorem 4.1. Consider X, Y to be random variables. Let /q(x) and fl(x) be density fiinctioris given by (4.1) and (4.2), respectively. Then it holds
Dj(X, Y) = (O! -o0)-fvK)- V(oo) +■ 4£rT
+«° ßH+a'"GH (45)
Proaf. Following Definition 1.1 and the previous Lemtua 4.2V we have Dj(JT, 7) = D^X : Y) + Da(F X)
+ (oo - «i) (v(cto) - hi(X0)) + txo       - lj
+ a1ln^1)-«t)M^) + ^^y)
+ (a, - tx&) ■ Met!) - ln(^)) +    ■ ^ - lj
+- (H+a'-GH
z
When the gamma distribution is considered, one can use (4.5) for parametric estimation of Dj  with moment or MLE estimates of the
parameters. Consider XJ,     XJ  ~ Gamma(o. j, X.-)a j = 0,1 is a random
sample of scores. MLE estimates of CLj and Xj (see [6. pp. 360-367]) can be computed by
"j Hj wj1 Z tog *f = M&j) ~ log Xj,   "J1^^ = ~f*~' <4 6>
i=i i=i h
which leads to solving
S^J=J^) = hi*J-Vfrjl (4-7)
\ jJ
where Xj is the arithmetic mean and Xj is the geometric mean of appropriate realizations of X{, ..., X]n , j = 0, 1. If we use the approximation ty(x) & ln(jr - 0.5), then we can get
Further approximation can be found in [6]:
Scorecard Strength
Discriminating power comparison (target variable 6-90)
0,45
0,4
0,35
0,3
on
0,25
0,2
0,15
~c>>      -äP ^5? ^      «sP ^P ^cP
month of the first installment prescription
3000
2500
2000
1500
1000
500
I number of loans
current scorecard
■proposed scorecard
703
Scorecard Strength
Discriminating power comparisonftarget variable 4-90)
0,45
0,4 0,35
0,3 0,25
0,2 0,15
0.1
KO     KD i£>
J =1
b
rvi    r^j    r^j r*i
month of the first installment prescription
i numberof loans
current scorecard
-proposed scorec
Discriminating power comparison (target variable 1-90)
ID LO i£>    ID t£>
r-- r--
oooooooooooo oooooooooooo
r-.r--r--oooooooooooo
cj  ^  cq oc
—
I-  > u
y O ""
month of the first installment prescription
i number of loans
current scorecard
-proposed scorecard
Process Flow
Validate
Validation
• Why?
• Confirm that the model is robust and applicable on the subject population
• Holdout sample
• 70/30, 80/20 or random samples of 50-80%
• 2 Methods
• Compare statistics for development versus validation
• Compare distributions of goods and bads for development versus validation.
706
Validation - Comparing Statistics
Fit Statistic	Label	Training	Validation	Test
_AIC_	Akaike's Information Criterion	6214.0279153		
_ASE_	Average Squared Error	0.0301553132	0.0309774947	
_AVERR_	Average Error Function	0.1312675287	0.1355474611	
_DFE_	Degrees of Freedom for Error	23609		
_DFM_	Model Degrees of Freedom	7		
_DFT_	Total Degrees of Freedom	23616		
_DIV_	Divisor for ASE	47232	45768	
_ERR_	Error Function	6200.0279153	6203.7361993	
_FPE_	Final Prediction Error	0.0301731951		
_MAX_	Maximum Absolute Error	0.9962871546	0.9959395534	
_MSE_	Mean Square Error	0.0301642541	0.0309774947	
_NOBS_	Sum of Frequencies	23616	22884	
_NW_	Number of Estimate Weights	7		
_RASE_	Root Average Sum of Squares	0.1736528525	0.1760042464	
_RFPE_	Root Final Prediction Error	0.1737043324		
_RMSE_	Root Mean Squared Error	0.1736785944	0.1760042464	
_SBC_	Schwarz's Bayesian Criterion	6270.5156734		
_SSE_	Sum of Squared Errors	1424.295752	1417.777979	
_SUMW_	Sum of Case Weights Times Freq	47232	45768	
_MISC_	Misclassification Rate	0.0320121951	0.0325117986	
_PROF_	Total Profit forGB	3430000	2730000	
_APROF_	Average Profit for GB	145.24051491	119.29732564	
If stats are similar, then scorecard is validated
707
Validation - Compare Distributions
Validation Chart
o-^-^-^-^-^-^-^-^rororororororororoco ^oo-P^cna5~vioocDO-^roco-P^cna5~viooo ooaiaiaiaiaiaiaiaiaiaiaiaiaicncno
Score
Good-Dev -■— Good-Val —±— Bad-Dev Bad-Val
Valid if no significant difference
708
Validation
• Common reasons for not validating
• Characteristics with large score ranges,
• Concentration of a certain type of attribute in one sample (for example, not random sampling),
• small sample sizes
709
Validation
Comparison with the old scorecard
Month by month comparison of performance of the old and the new scorecard, both for development and hold-out sample - on given segment
Comparison of performance month by month
Mobiles: Model performance
a> |o
"a3 o o
CD
a> "S3
.7
.6
.5
to a> O
— O
.4
.3
0.2
11 12 2005
01   02  03   04   05  06   07   08   09  10   11 12
2006
Month of first date due
01   02   03   04 05   06 07 2007
Actual SC, fraud part New SC, fraud part
Actual SC, defaulter part New SC, defaulter part
710
Validation
Power on fresh data
Use fresh data and compute "softer" good bad definitions (e.g. 1_30, 1_60 instead of 1_90). Measure power of the scorecard on development sample according these definitions and compare it with performance on the fresh data.
Comparison with real default
Month by month comparison of average predicted pd by the new scorecard and real default, for both development and hold-out samples. Diagonal test - score on x-axis and real default on y-axis - graph of average default should be ideally monotonous (the higher the score, the lower the default)
0.45 0.4
0.35 0.3
0.25
Graph of diagonal test
hi
0.2 ■ 0.15 ■
0.1 ■ 0.05 -I 0
^^^^^^^^^^
I-1 Nb contracts ^—AVG default       AVG score
1000000
100000
10000
1000
100
10
711
^09613961398
Validation
Comparison with real default
Graph of predicted pd versus the real default
1 - audio-video
60000 50000 40000 30000 20000 10000 0
												
^ n												
							i					
												—
0.07 0.06 0.05 0.04 0.03 0.02 0.01 0
,^      _§§>     _cg>      ,^      _^ ^ sSS>     ^ A#
i       i Počet srriuv Default Score
712
. Cutoff, RAROA, Monitoring
cutoff
713
Možné zamítací škály - cutoff
> cutoff hodnota určuje mez, při které je žádost o úvěr schválena/zamítnuta
> Je možné použít tyto zamítací škály:
> PD    -    Pravděpodobnost   Defaultu    (Probability of
Default)
> KRN - Kreditní Rizikové Náklady (CRE - Credit Risk Expenses)
> Marže (Margin) >RAROA
>...
Cutoff na škále PD
cutoff = o.i (tj. zamítám všechny s pravděpodobností defaultu větší než 10 %)
Cut off
• Pro SCi je reject rate 22 %.
• Pro SC2 je reject rate 33 %.
30 40 50 60 70
Score (relative) - the higher the better
715
Strategická křivka (Strategy curve)
Bad acceptance rate = pB (l - f(s\b))
Acceptance rate = 1 - F(s)
Pb{\-F{s\b))
i
Actual bad rate
1-F(s)
perfect information
Při zavádění nové scoringové funkce typicky dochází k tomu, že stávající nastavení schvalovacího procesu (nastavení eutoff) je reprezentováno bodem O , který leží nad novou strategickou křivkou. Otázkou pak je směr, kterým se chceme vydat při stanovení nového eutoff. Pokud se posuneme do bodu A, potom zachováme poměr schválených špatných klientů, ale současně zvýšíme celkový poměr schválených klientů. Při posunu do bodu B schválíme stejný poměr klientů, ale snížíme poměr schválených špatných klientů a tedy i poměr špatných klientů (bad rate). Posunem do bodu C zachováme bad rate při současném zvýšení poměru schválených klientů.
716
Nastavení cutoff maximalizující zisk (profit)
Profit - náhodná veličina definovaná jako:
0, je-li úvěr zamítnut
R = < L, je-li úvěr schválen a stane se dobrým - D, je - li úvěr schválen a stane se špatným
Označme pG a pB proporci dobrých a špatných klientů v populaci. q(G\s) (q(B\s)) označuje podmíněnou pravděpodobnost, že klient mající skóre s bude dobrý (špatný), přičemž q(G\s) + q(B\s) = i. Nechťp(s) je proporce populace se skóre s.
Střední hodnota profitu při schválení klientů se skóre s:
E{R\s] = Lq{G\s) - D(i - q{G\s)) = (L + D)q(G\s) - D
Tedy k maximalizaci profitu je třeba schválit ty klienty, jejichž skóre splňuje podmínku:
q{C\s) > ^
717
Nastavení cutoff maximalizující profit
Nechť A označuje množinu skóre, kde je splněna předchozí podmínka. Pak je střední hodnota zisku (profitu) na jednoho klienta dána vztahem:
Pokud L a D navíc závisí na skóre s, je situace ještě o něco složitější. Více viz Thomas et al. (2002).
718
Nastavení cutoff maximalizující profit
0.9 08 0.7 06 0.3 0.4 0.3
0.1
-o-o-o-
o O o
o o
0
OJ
0.2
0.3
E i profits)
(14
11.5
0.6
Body na spodní části křivky odpovídají vyšším cutoff hodnotám, a tedy i menšímu počtu přijatých špatných klientů, zatímco body na horní části křivky odpovídají menším hodnotám cutoff, tj. vyššímu počtu přijatých špatných klientů. Efektivní hranicí je tedy spodní část křivky od bodu C do bodu D.
Jestliže aktuální nastavení schvalovacího procesu odpovídá bodu O, opět máme možnost posunu na křivku odpovídající nové scoringové funkci. První možností je zachování poměru schválených špatných klientů, tj. posun do bodu A. Druhou možností je zachování celkového poměru schválených klientů, tj. posun do bodu B. Je zřejmé, že posun do bodu A není vhodná volba, protože tento bod neleží na efektivní hranici a lze snadno dosáhnout stejného očekávaného zisku při nižší očekávané ztrátě.
719
Definice KRN (CRE)
1 (.06)
N
1
OJ-r+ OJ
O C/5 C/5
Číslo defaultní splátky (pravděpodobnost (PD))
2 (.02)
3 (.02)       4 (.02)_
5 (.02)       6 (.02)        7 (.02)       8 (.02)       9 (.02)
N
1
OJ-
r+
OJ
N
1
OJ-r+ OJ
N
1
OJ-r+ OJ
Pravděpodobnost defaultu silně závisí na scoringové funkci
CRE = ((l-Recovery) * SUM(PD * Loss))/(Expected Average Volume) Profit = (Interest rate — CRE)*Expected Average Volume
1
J
Úroková míra
Očekávaný průměrný objem úvěru
10 (.03)
N
-a*
OJ
720
Recovery (=Late collection(LC))
Číslo defaultní splátky	score			
	bandl	band2	band3	band4
1.	20%	25%	30%	35%
2.-4.	50%	55%	60%	65%
5. +	75%	80%	85%	90%
odhad
-1 sp1 -1 sp2 1 sp3 -1 sp4 -4 sp1 -4 sp2 -4 sp3 -4 sp4 -5 sp1 -5 sp2 -5 sp3 -5 sp4
Cutoff na skale KRN
722
Cutoff na skale KRN
723
(Očekávaná) Marže
(Očekávaná) Marže = Úroková míra (vč. poplatků) - KRN -OPEX
Úroková míra
Efektivní míra ideálního finančního toku (-výše úvěru-poplatky; anuita; anuita;. anuita).
□ KRN
Viz výše.
□ OPEX
Cena peněz.
Režijní náklady, variabilní náklady, podpora prodejní sítě.
Náklady na administrátory - vlastní zaměstnance zajišťující zpracování úvěru.
Marže (Margin)
> Optimální cutoff: marže=0
RAROA
(Risk Adjusted Return On Assets)
Prob. oluVJ'aull .0(5 (basudL on S^rin^!
.0:
.0:
.0:
.0:
.0:
.0:
.0:
.0:
recoveries.
.50
.50
.50
O
Q-
<
r—*
3
EXPECTED INCOME - EXPECTED LOSS
No. of payment
TOTAL
RAROA=(EXPECTED INCOME - EXPECTED LOSS)/BORROWED VOLUME
726
RAROA
* t... pořadí splátky úvěru, 0 je okamžik poskytnutí úvěru
* T... počet splátek
* x(t) ... nesplacená část úvěru podle splátkového plánu v čase ŕ, .. .ŕ = 0,... tT. x(0) je výše úvěru, z(T) = 0.
* u(ť) .. . úroková část anuity t, t = 1,.. ., T.
* j (t)... část anuity odpovídající splátce jistiny ťř í = 1____,T.
* k(t) ... komise od klienta v čase t, t = 0,. .. ,T.
* A ... výše anuity (absolutné). A = u(ť) + j (t),t = 1,... ,T.
* pit)... pravděpodobnost 90 denního defaultu úvěru na splátce t,t = 1,...,T
* E Z ... očekávaná ztráta z úvěru
* E P ... očekávaný úrokový příjem z úvěru
* RC. .. absolutní výše z dlužné částky klienta 90 dní po splatnosti, která je klientem splacena v budoucnu, přepočtena přes NPV k okamžiku deva-desáticlenního defaultu klienta
* r(t, f).. . procento výtěžnosti z dlužné částky klienta, který je poprvé 00 dní po splatnosti na splátce t a klient má hodnotu podvodníckeho skóre f nesplacení první splátky) /. Procento zohledňuje NPV všech budoucích splátek klienta po okamžiku defaultu.
727
RAROA
• GM ... hrubý očekávaný zisk z klienta
• s je sazba úvěru p.a.
• i. .. cena zdroju vyjádřená v procentu p.a.
• c.. . komise z obchodu poskytnutá obchodnímu partnerovi vyjádřená jako procento z jistiny
• NMj . .. čistý očekávaný zisk typu I z klienta po odečtení ceny zdrojů
• NMjj . .. čistý očekávaný zisk z klienta typu II po odečtení ceny zdrojů, a komisí z obchodu.""'
• ROA .. . ukazatel Re tur n on Asset počítaného z hrubého zisku
• ROAj ... ukazatel Return on Asset typu I počítaný z čistého zisku typu
I
• ROAii . .. ukazatel Return on Asset tvpu II počítán v z čistého zisku tvpu
II
• KRN je úroková míra p.a. vyjadřující rizikovost úvěru.
728
RAROA
t=i
ep = ho)+J2 (1 - J2p{sn (<*)+*(*))■
f=l V     a=l / GM = ep-ez +RC.
t
iíC = ^p(í)-r(ť,/)-a;(ŕ-l) ATM; = CM -       ( 1 - X>^> ) ^ ■ *(* - !)■
t=l   V s=l /
N M ji = N Mi - cx(Q).
ROA =	GM x(oy
ROAj =	NM! x(ö) ■
ROAii =	NMji x(0) ■
KRN
12
^ ( 1 - ) »Cr -l) = EZ-RC.
t=i
3=1
í=l   \ s=l / '
u(t)
KRN = - ■ s.
EP
729
Výhody RAROA
	Case A		Case B	
	Ideal flow	Expected flow	Ideal flow	Expected flow
	-1000	-1000	-1000	-1000
1	400	200	150	110
2	400	180	150	100
3	400	170	150	90
4	400	160	150	80
5			150	70
6			150	60
7			150	50
8			150	40
9			150	30
10			150	16
11			150	10
12			150	0
A - krátkodobý úvěr s vysokým rizikem fraudu B - dlouhodobý úvěr s vysokým rizikem defaultu
Úroková míra (A) = 22% Úroková míra (B) = 10%
KRN(A) = 44% KRN(B) = 20%
cutoff na škále KRN preferuje B
Marže (A) = -22% Marže (B) = -10% cutoff na škále marže preferuje B
RAROA (A) = -0.29 RAROA (B) = -0.36 cutoff na škále RAROA preferuje A
Úvěr A je lepší, protože z něj plyne vyšší zisk (7io>656), navíc je ho dosaženo mnohem dříve.
730
Cutoff segmentace
□ Možná segmentace podle:
> Prodejní síť (skupina obchodních míst)
> Profitabilita produktu
> Kvalita prodejního místa
> Typ zboží (pro spotřebitelské úvěry)
> Výše úvěru
> ...
Cutoff scénáře
all						
	All credits		Approved credits			
scenario	Reject rate		Avg. margin		Avg. KRN	
	Credits	Volume	Credits	Volume		
EBB	0.0%	0.00%	-7.83%	-21.34%	30.70%	
tk	22.4%	24.74%	^3.97%	-15.72%	26.33%	
current	36.8%	46.79%	2.32%	-4.58%	19.11%	
	29.5%	37.07%	3.18%	-3.36%	19.78%	
						
	30.3%	38.55%	4.11%	-1.29%	19.26%	
	31.5%	39.99%	4.63%	-0.77%	18.96%	
	35.8%	46.01%	7.32%	3.22%	16.07%	
	38.9%	48.97%	8.17%	3.41%	15.19%	
	59.3%	70.03%	19.39%	17.14%	13.47%	
ekonom	50.9%	63.64%	19.24%	17.03%	14.23%	
new
	All credits		Approved credits		
	Reject rate		Avg. margin		Avg. KRN
	Credits	Volume	Credits	Volume	
	0.0%	0.00%	-4.19%	-16.40%	26.19%
	9.0%	10.25%	-2.39%	-13.71%	24.50%
	24.5%	34.89%	3.26%	-3.42%	17.99%
	16.5%	23.87%	4.07%	-2.34%	18.60%
	17.3%	25.42%	4.85%	-0.59%	18.19%
	18.6%	27.16%	5.36%	-0.03%	17.87%
	23.2%	33.80%	7.74%	3.52%	15.34%
	26.7%	37.35%	8.61%	3.88%	14.45%
	50.7%	62.90%	19.53%	17.26%	13.05%
	47.5%	60.46%	19.48%	17.23%	13.26%
732
Cutoff impact evaluation
Evaluation of Reject rate, Profitability, Default and Loss rates before and after cutoff change according to Distribution channel or Segment of scorecard.
Cutoff impact evaluation table
								
		Before Christmas (approved credits)				\fter Christmas (approved credits)		
			Loss rate	Profit (per year)	Reject rate	RAROA	Loss rate	Profit (per year)
Segment 1	24.7%	3.65%	11.33%	414363 110	24.3%	3.75%	11.19%	428 757 430
Segment 2	12.1%	4.01%	8.22%	160 364 072	12.9%	3.95%	8.29%	159 917 943
Segment 3	45.1%	9.64%	9.69%	747 636 468	45.1%	9.8%	9.5%	758 966 512
Segment 4	22.2%	5.80%	4.89%	52 213 720	20.1%	5.62%	5.05%	51 715 263
Segment 5	20.9%	6.77%	5.41%	54312 614	19.7%	6.61%	5.48%	53 975 903
Segment 6	33.4%	7.04%	7.22%	212 090 365	32.6%	7.04%	7.16%	211 684 371
Segment 7	49.3%	9.30%	8.93%	36 840 287	49.2%	9.4%	8.8%	37 140 165
Segment 8	19.3%	4.68%	2.96%	15 668 962	14.9%	4.54%	3.16%	15 636 910
Segment 9	32.0%	8.41%	5.06%	3 679 430	27.2%	7.97%	5.26%	3 535 809
Segment 10	33.4%	7.14%	6.69%	1 823 050 341	33.4%	7.2%	6.6%	1 832 986 599
Segment 11	28.5%	6.34%	7.36%	2 633 609 071	28.6%	6.47%	7.24%	2 651 352 740
ALL	32.6%	6.64%	8.37%	6153 828 440	32.6%	6.96%	8.17%	6 205 669 645
733
Cutoff sensitivity analysis
Profitability, Default and Loss rates according to reject rate into one graph
Characteristics of approved credits according to reject rate
.o\o
<o3 <bx «6"' <cP /V"-Reject rate
000 000 000 000 000 000 000 000 000 000 000 000 000 000 '+ 1 000 000 000 0
Profit (per year)
RAROI
Loss rate
Decision
Reasoning, why the final cutoffs were chosen
734
onitoring
	výv. vzorek [1]	týdenl [2]	[3]=[2] -[1]	[4]=[2]/[1]	[5]=ln[4]	[6]=[3]*[5]
skórel	10,00%	5,63%	-0,044	0,563	-0,574	0,025
skóre_2	10,00%	11,21 %	0,012	1,121	0,114	0,001
skóre_3	10,00%	11,00%	0,010	1,100	0,095	0,001
skóre_4	10,00%	10,97%	0,010	1,097	0,092	0,001
skóre_5	10,00%	10,31%	0,003	1,031	0,031	0,000
skóre_6	10,00%	10,12%	0,001	1,012	0,012	0,000
skóre_7	10,01%	9,62%	-0,004	0,961	-0,039	0,000
skóre_8	10,00%	9,89%	-0,001	0,989	-0,011	0,000
skóre_9	10,00%	10,31%	0,003	1,031	0,030	0,000
skóre 10	10,00%	10,94%	0,009	1,095	0,091	0,001
					PSI	0,030
Stabilita SF -týdny
0,4 ■ 0,3 ■ 0,2 ■
Vzorek 2006-   2006-   2006-   2006-   2006-   2006-   2006-   2006-   2006- 2006-13        14       15       16        17       18        19       20       21 22
Monitoring scoringových modelů
□ Není překvapivé, že prediktivní modely se ve statistickém slova smyslu chovají nejlépe na vývojovém vzorku dat. Výstupy těchto modelů, např. skóre nebo rating klienta, jsou počítány pomocí jistých vzorců, jejichž koeficienty příslušející nezávislým proměnným (prediktorům) jsou odvozeny na datech vývojového vzorku. Posun distribuce výstupu daného modelu je pak zapříčiněn právě změnou vstupních hodnot modelu, tj. prediktorů, v průběhu času. V podstatě ihned (alespoň většinou) po nasazení prediktivního modelu do praxe dochází k jistému poklesu jeho prediktivní síly, který je způsoben určitou změnou vstupních hodnot modelu. Zásadní je v praxi nastavení takových procesů, které odhalí, že se tak děje, proč se tak děje a jak vážný problém to ve svých důsledcích znamená.
736
Monitoring scoringových modelů
□ Faktorů způsobujících posun v distribuci prediktorů, a následně posun v distribuci výstupu prediktivního modelu, je několik:
> Přirozený posun v datech/změna demografické struktury dat
> Databázové chyby
> Změna datového zdroje
>Změna definice/formátu vstupních dat
> Změna datového univerza Ostatní
737
Monitoring scoringových modelů
□ Typickým příkladem prvního uvedeného důvodu je příjem klienta (všeobecným trendem je růst příjmu populace). Změnou definice/formátu vstupních dat je myšlena například situace, kdy je rozšířen číselník hodnot, kterých může vstupní proměnná nabývat. Změnou datového univerza je myšlen případ kdy je vyvinutý prediktivní model použit např. pro odlišný/nový segment portfolia nebo odlišný/nový produkt.
738
Monitoring scoringových modelů
□ K-S, Gini:
Stabilita SF -týdny
Vzorek 2006-   2006-   2006-   2006-   2006-   2006-   2006-   2006-   2006- 2006-13        14       15        16        17        18        19       20        21 22 V_J
739
Monitoring scoringových modelů
Závislost defaultu na Skóre
.vN .sQ, ,<b ,\U .Á .sfo ,<\ .sffj ,s°>
1 vzorek -2006-13 2006-14 2006-15 -2006-16 -2006-17 -2006-18 -2006-19 2006-20 2006-21 -2006-22
> Čím strmější křivka tím lépe.
> V průběhu času se zplošťuje - jde o to, jak moc.
740
Monitoring scoringových modelů
□ c-statistika:
100.00% 90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00%
Rating (pst Defaultu naeODPS do 12 měs.)
		B		B		B				
										
										
vývojirzorek
Xr04
XK54
»04
I-05
1-05
lľlB07 (6%)
I     lhB10 (13.5%)
I-ihC01 (21.25%)
i-iľlC04 (34%)
IľiBOS (9%) lhB11 (16.25%) lhC02 (25%)
■odhad průměr, pst. defaultu
□ hB09 (11%)
■ hB12 (18.75%)
■ hC03 (30%)
18.00%
17.50%
16.50%
16.00%
15.00%
KRN
vývoj.vzorek        X-04 Xl-04 XII-04
I-05
0.55
0.54
0.53
0.52
0.51
II-05
1KRN1 (1%) 1 KRN5 (16.5%)
1 KRN2 (4%) 1 KRN6 (20%)
] KRN3 (9%) 1 KRN7 (24%)
] KRN4 (13.5%) -C-statistika
741
Monitoring scoringových modelů
□ Chceme posoudit zda se distribuce skóre na vývojovém vzorku liší od distribuce skóre v daném časovém intervalu:
1=1
PSI = ^{0, -E,)\n
i=l
742
onitoring scoringových modelů
	výv. vzorek [1]	týden 1 [2]	[3]=[2] -[1]	[4]=[2]/[1]	[5]=ln[4]	[6]=[3]*[5]
skóre_1	10,00%	5,63%	-0,044	0,563	-0,574	0,025
skóre_2	10,00%	11,21%	0,012	1,121	0,114	0,001
skóre_3	10,00%	11,00%	0,010	1,100	0,095	0,001
skóre_4	10,00%	10,97%	0,010	1,097	0,092	0,001
skóre_5	10,00%	10,31%	0,003	1,031	0,031	0,000
skóre_6	10,00%	10,12%	0,001	1,012	0,012	0,000
skóre_7	10,01%	9,62%	-0,004	0,961	-0,039	0,000
skóre_8	10,00%	9,89%	-0,001	0,989	-0,011	0,000
skóre_9	10,00%	10,31%	0,003	1,031	0,030	0,000
skóre_10	10,00%	10,94%	0,009	1,095	0,091	0,001
					PSI	0,030
743
Monitoring scoringových modelů
8
PSI < 091 značí žádný nebo jen velmi malý rozdíl daných distribucí skóre.
091 < PSI < 0925    znamená, že došlo k nějakému posunu distribuce, nicméně
nikterak významnému.
signalizuje významný posun v distribuci skóre, tj. zamítáme
OCT     (\ signalizuje významný posun v dist
> U9Zľ> hypotézu o shodě daných distribucí.
744
Monitoring scoringových modelů
745
Monitoring scoringových modelů
PSIDR=É(DR2i-DRli)ln
i=l
	def_rate	Gini	PSI_DR	PSI	chi-kvardat
vzorek	7,69%	0,643			
200613	9,38%	0,564	0,120	0,030	0,024
200614	9,35%	0,542	0,131	0,034	0,027
200615	8,70%	0,537	0,093	0,032	0,025
200616	8,57%	0,523	0,089	0,033	0,026
200617	8,59%	0,540	0,071	0,030	0,025
200618	9,19%	0,544	0,111	0,030	0,024
200619	8,03%	0,558	0,063	0,034	0,026
200620	8,52%	0,552	0,055	0,023	0,019
200621	8,05%	0,555	0,043	0,027	0,022
200622	7,76%	0,539	0,039	0,045	0,034
746
onitoring scoringových modelů
747
Champion-challenger (mistr-vyzýva tel)
□ K rozšíření využití strategie champion-challenger došlo v devadesátých letech minulého století. Princip je velmi jednoduchý. Předpokládejme, že existuje nějaký způsob dělání něčeho (např. aktuálně používaný scoringový model pro schvalování/zamítání žádostí o úvěr). Tento způsob nazveme mistrem (champion). Nicméně existují další, jeden nebo více, alternativní způsoby jak dosáhnout téhož (nebo velmi podobného) cíle. Tyto nazveme vyzyvateli (challengers). Na náhodném vzorku otestujeme vyzyvatele a porovnáme s mistrem. To nám umožní nejen porovnat efektivnost vyzyvatelů a mistra, ale získáme možnost identifikovat existenci a rozsah vedlejších efektů. Výsledkem pak může být zjištění, že některý z vyzyvatelů je lepší než mistr a tento vyzyvatel se stane novým mistrem.
748
13. Reference
Literatura - knihy
> Anderson, R. (2007). 777c? Credit Scoring Toolkit: Theory and Practice for Retail Credit Risk Management and Decision Automation, Oxford: Oxford University Press.
> Giudici, P. (2003). Applied Data Mining: statistical methods for business and industry, Chichester: Wiley.
>Han, 1, Kamber, M. (2006). Data mining: Concepts and Techniques, 2nd ed. San Francisco: Morgan Kaufmann.
>Hastie, T., Tibshirani, R., Friedman, J. (2009). 777c? Elements of Statistical Learning: Data Mining, Inference, and Prediction, New York: Springer-Verlag.
> Hosmer, D. W., Lemeshow S. (2000). Applied Logistic Regression, Textbook and Solutions Manual, 2nd ed., New York: John Wiley and Sons.
750
Literatura - knihy
> Siddiqi, N. (2006). Credit Risk Scorecards: developing and implementing intelligent credit scoring, New Jersey: Wiley.
> Thomas, L.C. (2009). Consumer Credit Models: Pricing, Profit, and Portfolio, Oxford: Oxford University Press.
> Thomas, L.C, Edelman, D.B., Crook, J.N. (2002). Credit Scoring and Its Applications, Philadelphia: SIAM Monographs on Mathematical Modeling and Computation.
>Wilkie, A.D. (2004). Measures for comparing scoring systems, In: Thomas, L.C, Edelman, D.B., Crook, J.N. (Eds.), Readings in Credit Scoring. Oxford: Oxford University Press, pp. 51-62.
> Witten, LH., Frank, E. (2005). Data Mining: Practical Machine Learning Tools and Techniques, San Francisco: Morgen Kaufmann.
751
Literatura - časopisy
> Crook, J.N., Edelman, D.B., Thomas, L.C. (2007). Recent developments in consumer credit risk assessment. European Journal of Operational Research, 183 (3), 1447-1465
> Hand, DJ. and Henley, W.E. (1997). Statistical Classification Methods in Consumer Credit Scoring: a review. Journal, of the Royal Statistical Society, Series A., 160,No.3, 523-541.
> Harreil, F.E., Lee, K.L. and Mark, D.B. (1996). Multivariate prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statistics in Medicine, 15, 361-387.
> Lilliefors, H.W. (1967). On the Komogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 62, 399-402.
752
Literatura - časopisy
> Nelsen, R. B. (1998). Concordance and Gini's measure of association. Journal of Nonparametric Statistics, 9, Isssue 3, 227-238.
> Newson R. (2006). Confidence intervals for rank statistics: Somers' D and extensions. The Stata Journal, 6(3), 309-334.
> Somers R. H. (1962). A new asymmetric measure of association for ordinal variables. American Sociological Review, 27, 799-811.
> Thomas, L.C. (2000). A survey of credit and behavioural scoring: forecasting financial risk of lending to consumers. International Journal of Forecasting, 16(2), 149-172 .
753
Literatura - web
> Coppock, D.S. (2002). Why Lift?, DM Review Online, www.d mreview.com/news/53291. html
> Xu, K. (2003). How has the literature on Gini's index evolved in past 80 years?, www.economics.dal.ca/RePEc/dal/wparch/howgini.pdf
> Xin Ming Tu, Wan Tang (2006). Categorical Data Analysis.
http://www.urmc.rochester.edu/smd/biostat/people/faculty/TuSite/bst466/handouts.htm
Jiawei Han and Micheline Kamber (2006). Data Mining: Concepts and Techniques. http://www.cs.illinois.edu/~hanj/bk2/
> Jens Peter Dittrich (2007). Data warehousing.
http://www.dbis.ethz.ch/education/ss2007/07_dbs_datawh/Data_Mining.pdf
> Joe Carthy (2006). Data Warehousing.
http://www.csi.ucd.ie/staff/jcarthy/home/DataMining/DM-Lecture02-01.ppt
> Jan Spousta (?). Prednasky kdata miningu. [cit. 19.03.2009] http://samba.fsv.cuni.ez/~
Další zajímavé zdroje informací
> http://www.es. uiuc.edu/homes/hanj/
> http://www-users.es. umn.edu/~kumar/
> http://www.kdnuggets.com/
> http://www.kdnuggets.com/datasets/competitions.htmI
> http://www.crc.man.ed.ac.uk/conference/
> http://www.crc.man.ed.ac.uk/conference/archive/
> http://www.kmining.com/info_conferences.html
> http://en.wikipedia.org/wiki/Data_mining
> http://cs.wikipedia.org/wiki/Data_mining
> http://en.wikipedia.org/wiki/Credit_scorecards
Užitečné zdroje dat
>http://archive.ics.uci.edu/ml/ >http://kdd.ics.uci.edu/
	mi	
Machine Learning Repository		
>http://sede.neurotech.com.br:443/PAKDD2009/
> http: / / www. dataminingbook. com/
>http://www.stat.uni-muenchen.de/service/datenarchiv/welcome_e.html
> www. kaggle.com
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