Logistic-SPSS.docx
Binary Logistic Regression with SPSS
Logistic regression is used to predict a categorical (usually dichotomous) variable from a set of
predictor variables. With a categorical dependent variable, discriminant function analysis is usually
employed if all of the predictors are continuous and nicely distributed; logit analysis is usually
employed if all of the predictors are categorical; and logistic regression is often chosen if the predictor
variables are a mix of continuous and categorical variables and/or if they are not nicely distributed
(logistic regression makes no assumptions about the distributions of the predictor variables). Logistic
regression has been especially popular with medical research in which the dependent variable is
whether or not a patient has a disease.
For a logistic regression, the predicted dependent variable is a function of the probability that a
particular subject will be in one of the categories (for example, the probability that Suzie Cue has the
disease, given her set of scores on the predictor variables).
Description of the Research Used to Generate Our Data
As an example of the use of logistic regression in psychological research, consider the
research done by Wuensch and Poteat and published in the Journal of Social Behavior and
Personality, 1998, 13, 139-150. College students (N = 315) were asked to pretend that they were
serving on a university research committee hearing a complaint against animal research being
conducted by a member of the university faculty. The complaint included a description of the
research in simple but emotional language. Cats were being subjected to stereotaxic surgery in
which a cannula was implanted into their brains. Chemicals were then introduced into the cats’ brains
via the cannula and the cats given various psychological tests. Following completion of testing, the
cats’ brains were subjected to histological analysis. The complaint asked that the researcher's
authorization to conduct this research be withdrawn and the cats turned over to the animal rights
group that was filing the complaint. It was suggested that the research could just as well be done
with computer simulations.
In defense of his research, the researcher provided an explanation of how steps had been
taken to assure that no animal felt much pain at any time, an explanation that computer simulation
was not an adequate substitute for animal research, and an explanation of what the benefits of the
research were. Each participant read one of five different scenarios which described the goals and
benefits of the research. They were:
 COSMETIC -- testing the toxicity of chemicals to be used in new lines of hair care products.
 THEORY -- evaluating two competing theories about the function of a particular nucleus in the
brain.
 MEAT -- testing a synthetic growth hormone said to have the potential of increasing meat
production.
 VETERINARY -- attempting to find a cure for a brain disease that is killing both domestic cats
and endangered species of wild cats.
 MEDICAL -- evaluating a potential cure for a debilitating disease that afflicts many young adult
humans.
After reading the case materials, each participant was asked to decide whether or not to
withdraw Dr. Wissen’s authorization to conduct the research and, among other things, to fill out D. R.
Forysth’s Ethics Position Questionnaire (Journal of Personality and Social Psychology, 1980, 39, 175-
184), which consists of 20 Likert-type items, each with a 9-point response scale from “completely

Copyright 2014 Karl L. Wuensch - All rights reserved.
2
disagree” to “completely agree.” Persons who score high on the relativism dimension of this
instrument reject the notion of universal moral principles, preferring personal and situational analysis
of behavior. Persons who score high on the idealism dimension believe that ethical behavior will
always lead only to good consequences, never to bad consequences, and never to a mixture of good
and bad consequences.
Having committed the common error of projecting myself onto others, I once assumed that all
persons make ethical decisions by weighing good consequences against bad consequences -- but for
the idealist the presence of any bad consequences may make a behavior unethical, regardless of
good consequences. Research by Hal Herzog and his students at Western Carolina has shown that
animal rights activists tend to be high in idealism and low in relativism (see me for references if
interested). Are idealism and relativism (and gender and purpose of the research) related to attitudes
towards animal research in college students? Let’s run the logistic regression and see.
Using a Single Dichotomous Predictor, Gender of Subject
Let us first consider a simple (bivariate) logistic regression, using subjects' decisions as the
dichotomous criterion variable and their gender as a dichotomous predictor variable. I have coded
gender with 0 = Female, 1 = Male, and decision with 0 = "Stop the Research" and 1 = "Continue the
Research".
Our regression model will be predicting the logit, that is, the natural log of the odds of having
made one or the other decision. That is,
  bXa
Y
Y
ODDS 









ˆ1
ˆ
lnln , where Yˆ is the predicted probability of the event which is
coded with 1 (continue the research) rather than with 0 (stop the research), Yˆ1 is the predicted
probability of the other decision, and X is our predictor variable, gender. Some statistical programs
(such as SAS) predict the event which is coded with the smaller of the two numeric codes. By the
way, if you have ever wondered what is "natural" about the natural log, you can find an answer of
sorts at http://www.math.toronto.edu/mathnet/answers/answers_13.html.
Our model will be constructed by an iterative maximum likelihood procedure. The program
will start with arbitrary values of the regression coefficients and will construct an initial model for
predicting the observed data. It will then evaluate errors in such prediction and change the
regression coefficients so as make the likelihood of the observed data greater under the new model.
This procedure is repeated until the model converges -- that is, until the differences between the
newest model and the previous model are trivial.
Open the data file at http://core.ecu.edu/psyc/wuenschk/SPSS/Logistic.sav. Click Analyze,
Regression, Binary Logistic. Scoot the decision variable into the Dependent box and the gender
variable into the Covariates box. The dialog box should now look like this:
Open the data file at
http://core.ecu.edu/psyc/wuenschk/SPSS/Logistic.sav.
Click Analyze, Regression, Binary Logistic. Scoot
the decision variable into the Dependent box and the
gender variable into the Covariates box. The dialog
box should now look like this:
3
Click OK.
Look at the statistical output. We see that there are 315 cases used in the analysis.
The Block 0 output is for a model that includes only the intercept (which SPSS calls the
constant). Given the base rates of the two decision options (187/315 = 59% decided to stop the
research, 41% decided to allow it to continue), and no other information, the best strategy is to
predict, for every case, that the subject will decide to stop the research. Using that strategy, you
would be correct 59% of the time.
Under Variables in the Equation you see that the intercept-only model is ln(odds) = -.379. If
we exponentiate both sides of this expression we find that our predicted odds [Exp(B)] = .684. That
is, the predicted odds of deciding to continue the research is .684. Since 128 of our subjects decided
to continue the research and 187 decided to stop the research, our observed odds are 128/187 =
.684.
Now look at the Block 1 output. Here SPSS has added the gender variable as a predictor.
Omnibus Tests of Model Coefficients gives us a Chi-Square of 25.653 on 1 df, significant beyond
.001. This is a test of the null hypothesis that adding the gender variable to the model has not
significantly increased our ability to predict the decisions made by our subjects.
Case Processing Summary
315 100.0
0 .0
315 100.0
0 .0
315 100.0
Unweighted Cases
a
Included in Analysis
Missing Cases
Total
Selected Cases
Unselected Cases
Total
N Percent
If weight is in eff ect, see classification table for the total
number of cases.
a.
Classification Tablea,b
187 0 100.0
128 0 .0
59.4
Observed
stop
continue
decision
Overall Percentage
Step 0
stop continue
decision Percentage
Correct
Predicted
Constant is included in the model.a.
The cut value is .500b.
Variables in the Equation
-.379 .115 10.919 1 .001 .684ConstantStep 0
B S.E. Wald df Sig. Exp(B)
4
Under Model Summary we see that the -2 Log Likelihood statistic is 399.913. This statistic
measures how poorly the model predicts the decisions -- the smaller the statistic the better the
model. Although SPSS does not give us this statistic for the model that had only the intercept, I know
it to be 425.666. Adding the gender variable reduced the -2 Log Likelihood statistic by 425.666 -
399.913 = 25.653, the 2
statistic we just discussed in the previous paragraph. The Cox & Snell R2
can be interpreted like R2
in a multiple regression, but cannot reach a maximum value of 1. The
Nagelkerke R2
can reach a maximum of 1.
The Variables in the Equation output shows us that the regression equation is
  GenderODDS 217.1847.ln  .
We can now use this model to predict the odds that a subject of a given gender will decide to
continue the research. The odds prediction equation is bXa
eODDS 
 . If our subject is a woman
(gender = 0), then the 429.0847.)0(217.1847.
 
eeODDS . That is, a woman is only .429 as likely
to decide to continue the research as she is to decide to stop the research. If our subject is a man
(gender = 1), then the 448.137.)1(217.1847.
 
eeODDS . That is, a man is 1.448 times more likely to
decide to continue the research than to decide to stop the research.
We can easily convert odds to probabilities. For our women,
30.0
429.1
429.0
1
ˆ 


ODDS
ODDS
Y . That is, our model predicts that 30% of women will decide to
continue the research. For our men, 59.0
448.2
448.1
1
ˆ 


ODDS
ODDS
Y . That is, our model predicts that
59% of men will decide to continue the research
The Variables in the Equation output also gives us the Exp(B). This is better known as the
odds ratio predicted by the model. This odds ratio can be computed by raising the base of the
natural log to the bth
power, where b is the slope from our logistic regression equation. For
Omnibus Tests of Model Coefficients
25.653 1 .000
25.653 1 .000
25.653 1 .000
Step
Block
Model
Step 1
Chi-square df Sig.
Model Summary
399.913a .078 .106
Step
1
-2 Log
likelihood
Cox & Snell
R Square
Nagelkerke
R Square
Estimation terminated at iteration number 3 because
parameter estimates changed by less than .001.
a.
Variables in the Equation
1.217 .245 24.757 1 .000 3.376
-.847 .154 30.152 1 .000 .429
gender
Constant
Step
1
a
B S.E. Wald df Sig. Exp(B)
Variable(s) entered on step 1: gender.a.
5
our model, 376.3217.1
e . That tells us that the model predicts that the odds of deciding to
continue the research are 3.376 times higher for men than they are for women. For the men, the
odds are 1.448, and for the women they are 0.429. The odds ratio is
1.448 / 0.429 = 3.376 .
The results of our logistic regression can be used to classify subjects with respect to what
decision we think they will make. As noted earlier, our model leads to the prediction that the
probability of deciding to continue the research is 30% for women and 59% for men. Before we can
use this information to classify subjects, we need to have a decision rule. Our decision rule will take
the following form: If the probability of the event is greater than or equal to some threshold, we shall
predict that the event will take place. By default, SPSS sets this threshold to .5. While that seems
reasonable, in many cases we may want to set it higher or lower than .5. More on this later. Using
the default threshold, SPSS will classify a subject into the “Continue the Research” category if the
estimated probability is .5 or more, which it is for every male subject. SPSS will classify a subject into
the “Stop the Research” category if the estimated probability is less than .5, which it is for every
female subject.
The Classification Table shows us that this rule allows us to correctly classify 68 / 128 = 53%
of the subjects where the predicted event (deciding to continue the research) was observed. This is
known as the sensitivity of prediction, the P(correct | event did occur), that is, the percentage of
occurrences correctly predicted. We also see that this rule allows us to correctly classify 140 / 187 =
75% of the subjects where the predicted event was not observed. This is known as the specificity of
prediction, the P(correct | event did not occur), that is, the percentage of nonoccurrences correctly
predicted. Overall our predictions were correct 208 out of 315 times, for an overall success rate of
66%. Recall that it was only 59% for the model with intercept only.
We could focus on error rates in classification. A false positive would be predicting that the
event would occur when, in fact, it did not. Our decision rule predicted a decision to continue the
research 115 times. That prediction was wrong 47 times, for a false positive rate of 47 / 115 = 41%.
A false negative would be predicting that the event would not occur when, in fact, it did occur. Our
decision rule predicted a decision not to continue the research 200 times. That prediction was wrong
60 times, for a false negative rate of 60 / 200 = 30%.
It has probably occurred to you that you could have used a simple Pearson Chi-Square
Contingency Table Analysis to answer the question of whether or not there is a significant
relationship between gender and decision about the animal research. Let us take a quick look at
such an analysis. In SPSS click Analyze, Descriptive Statistics, Crosstabs. Scoot gender into the
rows box and decision into the columns box. The dialog box should look like this:
Classification Tablea
140 47 74.9
60 68 53.1
66.0
Observed
stop
continue
decision
Overall Percentage
Step 1
stop continue
decision Percentage
Correct
Predicted
The cut value is .500a.
6
Now click the Statistics box. Check Chi-Square and then click Continue.
Now click the Cells box. Check Observed Counts and Row Percentages and then click
Continue.
Back on the initial page, click OK.
In the Crosstabulation output you will see that 59% of the men and 30% of the women
decided to continue the research, just as predicted by our logistic regression.
7
You will also notice that the Likelihood Ratio Chi-Square is 25.653 on 1 df, the same test of
significance we got from our logistic regression, and the Pearson Chi-Square is almost the same
(25.685). If you are thinking, “Hey, this logistic regression is nearly equivalent to a simple Pearson
Chi-Square,” you are correct, in this simple case. Remember, however, that we can add additional
predictor variables, and those additional predictors can be either categorical or continuous -- you
can’t do that with a simple Pearson Chi-Square.
Multiple Predictors, Both Categorical and Continuous
Now let us conduct an analysis that will better tap the strengths of logistic regression. Click
Analyze, Regression, Binary Logistic. Scoot the decision variable in the Dependent box and
gender, idealism, and relatvsm into the Covariates box.
gender * decision Crosstabulation
140 60 200
70.0% 30.0% 100.0%
47 68 115
40.9% 59.1% 100.0%
187 128 315
59.4% 40.6% 100.0%
Count
% within gender
Count
% within gender
Count
% within gender
Female
Male
gender
Total
stop continue
decision
Total
Chi-Square Tests
25.685b
1 .000
25.653 1 .000
315
Pearson Chi-Square
Likelihood Ratio
N of Valid Cases
Value df
Asy mp. Sig.
(2-sided)
Computed only f or a 2x2 tablea.
0 cells (.0%) hav e expected count less than 5. The
minimum expected count is 46.73.
b.
8
Click Options and check “Hosmer-Lemeshow goodness of fit” and “CI for exp(B) 95%.”
Continue, OK. Look at the output.
In the Block 1 output, notice that the -2 Log Likelihood statistic has dropped to 346.503,
indicating that our expanded model is doing a better job at predicting decisions than was our onepredictor
model. The R2
statistics have also increased.
We can test the significance of the difference between any two models, as long as one model
is nested within the other. Our one-predictor model had a 2 Log Likelihood statistic of 399.913.
Adding the ethical ideology variables (idealism and relatvsm) produced a decrease of 53.41. This
difference is a 2
on 2 df (one df for each predictor variable).
To determine the p value associated with this 2
, just click Transform, Compute. Enter the
letter p in the Target Variable box. In the Numeric Expression box, type 1-CDF.CHISQ(53.41,2).
The dialog box should look like this:
Click OK and then go to the SPSS Data Editor, Data View. You will find a new column, p,
with the value of .00 in every cell. If you go to the Variable View and set the number of decimal
points to 5 for the p variable you will see that the value of p is.00000. We conclude that adding the
ethical ideology variables significantly improved the model, 2
(2, N = 315) = 53.41, p < .001.
Note that our overall success rate in classification has improved from 66% to 71%.
Model Summary
346.503a .222 .300
Step
1
-2 Log
likelihood
Cox & Snell
R Square
Nagelkerke
R Square
Estimation terminated at iteration number 4 because
parameter estimates changed by less than .001.
a.
9
The Hosmer-Lemeshow tests the null hypothesis that predictions made by the model fit
perfectly with observed group memberships. Cases are arranged in order by their predicted
probability on the criterion variable. These ordered cases are then divided into ten (usually) groups of
equal or near equal size ordered with respect to the predicted probability of the target event. For
each of these groups we then obtain the predicted group memberships and the actual group
memberships This results in a 2 x 10 contingency table, as shown below. A chi-square statistic is
computed comparing the observed frequencies with those expected under the linear model. A
nonsignificant chi-square indicates that the data fit the model well.
This procedure suffers from several problems, one of which is that it relies on a test of
significance. With large sample sizes, the test may be significant, even when the fit is good. With
small sample sizes it may not be significant, even with poor fit. Even Hosmer and Lemeshow have
acknowledged problems with this test.
Box-Tidwell Test. Although logistic regression is often thought of as having no assumptions,
we do assume that the relationships between the continuous predictors and the logit (log odds) is
linear. This assumption can be tested by including in the model interactions between the continuous
predictors and their logs. If such an interaction is significant, then the assumption has been violated.
I should caution you that sample size is a factor here too, so you should not be very concerned with a
just significant interaction when sample sizes are large.
Classification Tablea
151 36 80.7
55 73 57.0
71.1
Observed
stop
continue
decision
Overall Percentage
Step 1
stop continue
decision Percentage
Correct
Predicted
The cut value is .500a.
Hosmer and Lemeshow Test
8.810 8 .359
Step
1
Chi-square df Sig.
Contingency Table for Hosmer and Lemeshow Test
29 29.331 3 2.669 32
30 27.673 2 4.327 32
28 25.669 4 6.331 32
20 23.265 12 8.735 32
22 20.693 10 11.307 32
15 18.058 17 13.942 32
15 15.830 17 16.170 32
10 12.920 22 19.080 32
12 9.319 20 22.681 32
6 4.241 21 22.759 27
1
2
3
4
5
6
7
8
9
10
Step
1
Observed Expected
decision = stop
Observed Expected
decision = continue
Total
10
Below I show how to create the natural log of a predictor. If the predictor has values of 0 or
less, first add to each score a constant such that no value will be zero or less. Also shown below is
how to enter the interaction terms. In the pane on the left, select both of the predictors to be included
in the interaction and then click the >a*b> button.
Variables in the Equation
B S.E. Wald df Sig. Exp(B)
Step 1
a
gender 1.147 .269 18.129 1 .000 3.148
idealism 1.130 1.921 .346 1 .556 3.097
relatvsm 1.656 2.637 .394 1 .530 5.240
idealism by idealism_LN -.652 .690 .893 1 .345 .521
relatvsm by relatvsm_LN -.479 .949 .254 1 .614 .620
Constant -5.015 5.877 .728 1 .393 .007
a. Variable(s) entered on step 1: gender, idealism, relatvsm, idealism * idealism_LN , relatvsm * relatvsm_LN .
11
Bravo, neither of the interaction terms is significant. If one were significant, I would try
adding to the model powers of the predictor (that is, going polynomial). For an example, see my
document Independent Samples T Tests versus Binary Logistic Regression.
Using a K > 2 Categorical Predictor
We can use a categorical predictor that has more than two levels. For our data, the stated
purpose of the research is such a predictor. While SPSS can dummy code such a predictor for you, I
prefer to set up my own dummy variables. To see how to get SPSS to create the dummy variables,
go here. You will need K-1 dummy variables to represent K groups. Since we have five levels of
purpose of the research, we shall need 4 dummy variables. Each of the subjects will have a score of
either 0 or 1 on each of the dummy variables. For each dummy variable a score of 0 will indicate that
the subject does not belong to the group represented by that dummy variable and a score of 1 will
indicate that the subject does belong to the group represented by that dummy variable. One of the
groups will not be represented by a dummy variable. If it is reasonable to consider one of your
groups as a reference group to which each other group should be compared, make that group
the one which is not represented by a dummy variable.
I decided that I wanted to compare each of the cosmetic, theory, meat, and veterinary groups
with the medical group, so I set up a dummy variable for each of the groups except the medical
group. Take a look at our data in the data editor. Notice that the first subject has a score of 1 for the
cosmetic dummy variable and 0 for the other three dummy variables. That subject was told that the
purpose of the research was to test the safety of a new ingredient in hair care products. Now scoot to
the bottom of the data file. The last subject has a score of 0 for each of the four dummy variables.
That subject was told that the purpose of the research was to evaluate a treatment for a debilitating
disease that afflicts humans of college age.
Click Analyze, Regression, Binary Logistic and add to the list of covariates the four dummy
variables. You should now have the decision variable in the Dependent box and all of the other
variables (but not the p value column) in the Covariates box. Click OK.
The Block 0 “Variables not in the Equation” show how much the -2LL would drop if a single
predictor were added to the model (which already has the intercept)
Look at the output, Block 1. Under Omnibus Tests of Model Coefficients we see that our
latest model is significantly better than a model with only the intercept.
Variables not in the Equation
25.685 1 .000
47.679 1 .000
7.239 1 .007
.003 1 .955
2.933 1 .087
.556 1 .456
.013 1 .909
77.665 7 .000
gender
idealism
relatvsm
cosmetic
theory
meat
veterin
Variables
Overall Statistics
Step
0
Score df Sig.
12
Under Model Summary we see that our R2
statistics have increased again and the -2 Log
Likelihood statistic has dropped from 346.503 to 338.060. Is this drop statistically significant? The
2
, is the difference between the two -2 log likelihood values, 8.443, on 4 df (one df for each dummy
variable). Using 1-CDF.CHISQ(8.443,4), we obtain an upper-tailed p of .0766, short of the usual
standard of statistical significance. I shall, however, retain these dummy variables, since I have an a
priori interest in the comparison made by each dummy variable.
In the Classification Table, we see a small increase in our overall success rate, from 71% to
72%.
I would like you to compute the values for Sensitivity, Specificity, False Positive Rate, and
False Negative Rate for this model, using the default .5 cutoff.
Sensitivity percentage of occurrences correctly predicted
Specificity percentage of nonoccurrences correctly predicted
False Positive Rate percentage of predicted occurrences which are incorrect
False Negative Rate percentage of predicted nonoccurrences which are incorrect
Remember that the predicted event was a decision to continue the research.
Under Variables in the Equation we are given regression coefficients and odds ratios.
Omnibus Tests of Model Coefficients
87.506 7 .000
87.506 7 .000
87.506 7 .000
Step
Block
Model
Step 1
Chi-square df Sig.
Model Summary
338.060a .243 .327
Step
1
-2 Log
likelihood
Cox & Snell
R Square
Nagelkerke
R Square
Estimation terminated at iteration number 5 because
parameter estimates changed by less than .001.
a.
Classification Tablea
152 35 81.3
54 74 57.8
71.7
Observed
stop
continue
decision
Overall Percentage
Step 1
stop continue
decision Percentage
Correct
Predicted
The cut value is .500a.
13
We are also given a statistic I have ignored so far, the Wald Chi-Square statistic, which tests
the unique contribution of each predictor, in the context of the other predictors -- that is, holding
constant the other predictors -- that is, eliminating any overlap between predictors. Notice that each
predictor meets the conventional .05 standard for statistical significance, except for the dummy
variable for cosmetic research and for veterinary research. I should note that the Wald 2
has been
criticized for being too conservative, that is, lacking adequate power. An alternative would be to test
the significance of each predictor by eliminating it from the full model and testing the significance of
the increase in the -2 log likelihood statistic for the reduced model. That would, of course, require
that you construct p+1 models, where p is the number of predictor variables.
Let us now interpret the odds ratios.
 The .496 odds ratio for idealism indicates that the odds of approval are more than cut in half for
each one point increase in respondent’s idealism score. Inverting this odds ratio for easier
interpretation, for each one point increase on the idealism scale there was a doubling of the odds
that the respondent would not approve the research.
 Relativism’s effect is smaller, and in the opposite direction, with a one point increase on the ninepoint
relativism scale being associated with the odds of approving the research increasing by a
multiplicative factor of 1.39.
 The odds ratios of the scenario dummy variables compare each scenario except medical to the
medical scenario. For the theory dummy variable, the .314 odds ratio means that the odds of
approval of theory-testing research are only .314 times those of medical research.
 Inverted odds ratios for the dummy variables coding the effect of the scenario variable indicated
that the odds of approval for the medical scenario were 2.38 times higher than for the meat
scenario and 3.22 times higher than for the theory scenario.
Let us now revisit the issue of the decision rule used to determine into which group to classify
a subject given that subject's estimated probability of group membership. While the most obvious
decision rule would be to classify the subject into the target group if p > .5 and into the other group if p
< .5, you may well want to choose a different decision rule given the relative seriousness of making
one sort of error (for example, declaring a patient to have breast cancer when she does not) or the
other sort of error (declaring the patient not to have breast cancer when she does).
Repeat our analysis with classification done with a different decision rule. Click Analyze,
Regression, Binary Logistic, Options. In the resulting dialog window, change the Classification
Cutoff from .5 to .4. The window should look like this:
Variables in the Equation
1.255 20.586 1 .000 3.508 2.040 6.033
-.701 37.891 1 .000 .496 .397 .620
.326 6.634 1 .010 1.386 1.081 1.777
-.709 2.850 1 .091 .492 .216 1.121
-1.160 7.346 1 .007 .314 .136 .725
-.866 4.164 1 .041 .421 .183 .966
-.542 1.751 1 .186 .581 .260 1.298
2.279 4.867 1 .027 9.766
gender
idealism
relatvsm
cosmetic
theory
meat
veterin
Constant
Step
1
a
B Wald df Sig. Exp(B) Lower Upper
95.0% C.I.f or EXP(B)
Variable(s) entered on step 1: gender, idealism, relatv sm, cosmetic, theory , meat, v eterin.a.
14
Click Continue, OK.
Now SPSS will classify a subject into the "Continue the Research" group if the estimated
probability of membership in that group is .4 or higher, and into the "Stop the Research" group
otherwise. Take a look at the classification output and see how the change in cutoff has changed the
classification results. Fill in the table below to compare the two models with respect to classification
statistics.
Value When Cutoff = .5 .4
Sensitivity
Specificity
False Positive Rate
False Negative Rate
Overall % Correct
SAS makes it much easier to see the effects of the decision rule on sensitivity etc. Using the
ctable option, one gets output like this:
------------------------------------------------------------------------------------
The LOGISTIC Procedure
Classification Table
Correct Incorrect Percentages
Prob Non- Non- Sensi- Speci- False False
Level Event Event Event Event Correct tivity ficity POS NEG
0.160 123 56 131 5 56.8 96.1 29.9 51.6 8.2
0.180 122 65 122 6 59.4 95.3 34.8 50.0 8.5
0.200 120 72 115 8 61.0 93.8 38.5 48.9 10.0
0.220 116 84 103 12 63.5 90.6 44.9 47.0 12.5
15
0.240 113 93 94 15 65.4 88.3 49.7 45.4 13.9
0.260 110 100 87 18 66.7 85.9 53.5 44.2 15.3
0.280 108 106 81 20 67.9 84.4 56.7 42.9 15.9
0.300 105 108 79 23 67.6 82.0 57.8 42.9 17.6
0.320 103 115 72 25 69.2 80.5 61.5 41.1 17.9
0.340 100 118 69 28 69.2 78.1 63.1 40.8 19.2
0.360 97 120 67 31 68.9 75.8 64.2 40.9 20.5
0.380 96 124 63 32 69.8 75.0 66.3 39.6 20.5
0.400 94 130 57 34 71.1 73.4 69.5 37.7 20.7
0.420 88 134 53 40 70.5 68.8 71.7 37.6 23.0
0.440 86 140 47 42 71.7 67.2 74.9 35.3 23.1
0.460 79 141 46 49 69.8 61.7 75.4 36.8 25.8
0.480 75 144 43 53 69.5 58.6 77.0 36.4 26.9
0.500 71 147 40 57 69.2 55.5 78.6 36.0 27.9
0.520 69 152 35 59 70.2 53.9 81.3 33.7 28.0
0.540 67 157 30 61 71.1 52.3 84.0 30.9 28.0
0.560 65 159 28 63 71.1 50.8 85.0 30.1 28.4
0.580 61 159 28 67 69.8 47.7 85.0 31.5 29.6
0.600 56 162 25 72 69.2 43.8 86.6 30.9 30.8
0.620 50 165 22 78 68.3 39.1 88.2 30.6 32.1
0.640 48 166 21 80 67.9 37.5 88.8 30.4 32.5
0.660 43 170 17 85 67.6 33.6 90.9 28.3 33.3
0.680 40 170 17 88 66.7 31.3 90.9 29.8 34.1
0.700 36 173 14 92 66.3 28.1 92.5 28.0 34.7
0.720 30 177 10 98 65.7 23.4 94.7 25.0 35.6
0.740 28 178 9 100 65.4 21.9 95.2 24.3 36.0
0.760 23 180 7 105 64.4 18.0 96.3 23.3 36.8
0.780 22 180 7 106 64.1 17.2 96.3 24.1 37.1
0.800 18 181 6 110 63.2 14.1 96.8 25.0 37.8
0.820 17 182 5 111 63.2 13.3 97.3 22.7 37.9
0.840 13 184 3 115 62.5 10.2 98.4 18.8 38.5
0.860 12 185 2 116 62.5 9.4 98.9 14.3 38.5
0.880 8 185 2 120 61.3 6.3 98.9 20.0 39.3
0.900 7 185 2 121 61.0 5.5 98.9 22.2 39.5
0.920 5 187 0 123 61.0 3.9 100.0 0.0 39.7
0.940 1 187 0 127 59.7 0.8 100.0 0.0 40.4
0.960 1 187 0 127 59.7 0.8 100.0 0.0 40.4
0.980 0 187 0 128 59.4 0.0 100.0 . 40.6
------------------------------------------------------------------------------------
The classification results given by SAS are a little less impressive because SAS uses a
jackknifed classification procedure. Classification results are biased when the coefficients used to
classify a subject were developed, in part, with data provided by that same subject. SPSS'
classification results do not remove such bias. With jackknifed classification, SAS eliminates the
subject currently being classified when computing the coefficients used to classify that subject. Of
course, this procedure is computationally more intense than that used by SPSS. If you would like to
learn more about conducting logistic regression with SAS, see my document at
http://core.ecu.edu/psyc/wuenschk/MV/MultReg/Logistic-SAS.pdf.
Beyond An Introduction to Logistic Regression
I have left out of this handout much about logistic regression. We could consider logistic
regression with a criterion variable with more than two levels, with that variable being either
qualitative or ordinal. We could consider testing of interaction terms. We could consider sequential
and stepwise construction of logistic models. We could talk about detecting outliers among the
cases, dealing with multicollinearity and nonlinear relationships between predictors and the logit, and
so on. If you wish to learn more about logistic regression, I recommend, as a starting point, Chapter
10 in Using Multivariate Statistics, 5th
edition, by Tabachnick and Fidell (Pearson, 2007).
Presenting the Results
Let me close with an example of how to present the results of a logistic regression. In the
example below you will see that I have included both the multivariate analysis (logistic regression)
16
and univariate analysis. I assume that you all already know how to conduct the univariate analyses
I present below.
Table 1
Effect of Scenario on Percentage of Participants Voting to Allow the Research to Continue and
Participants’ Mean Justification Score
Scenario Percentage
Support
Theory 31
Meat 37
Cosmetic 40
Veterinary 41
Medical 54
As shown in Table 1, only the medical research received support from a majority of the
respondents. Overall a majority of respondents (59%) voted to stop the research. Logistic regression
analysis was employed to predict the probability that a participant would approve continuation of the
research. The predictor variables were participant’s gender, idealism, relativism, and four dummy
variables coding the scenario. A test of the full model versus a model with intercept only was
statistically significant, 2
(7, N = 315) = 87.51, p < .001. The model was able correctly to classify 73%
of those who approved the research and 70% of those who did not, for an overall success rate of
71%.
Table 2 shows the logistic regression coefficient, Wald test, and odds ratio for each of the
predictors. Employing a .05 criterion of statistical significance, gender, idealism, relativism, and two
of the scenario dummy variables had significant partial effects. The odds ratio for gender indicates
that when holding all other variables constant, a man is 3.5 times more likely to approve the research
than is a woman. Inverting the odds ratio for idealism reveals that for each one point increase on the
nine-point idealism scale there is a doubling of the odds that the participant will not approve the
research. Although significant, the effect of relativism was much smaller than that of idealism, with a
one point increase on the nine-point idealism scale being associated with the odds of approving the
research increasing by a multiplicative factor of 1.39. The scenario variable was dummy coded using
the medical scenario as the reference group. Only the theory and the meat scenarios were approved
significantly less than the medical scenario. Inverted odds ratios for these dummy variables indicate
that the odds of approval for the medical scenario were 2.38 times higher than for the meat scenario
and 3.22 times higher than for the theory scenario.
Univariate analysis indicated that men were significantly more likely to approve the research
(59%) than were women (30%), 2
(1, N = 315) = 25.68, p < .001, that those who approved the
research were significantly less idealistic (M = 5.87, SD = 1.23) than those who didn’t (M = 6.92, SD =
1.22), t(313) = 7.47, p < .001, that those who approved the research were significantly more
relativistic (M = 6.26, SD = 0.99) than those who didn’t (M = 5.91, SD = 1.19), t(313) = 2.71, p = .007,
and that the omnibus effect of scenario fell short of significance, 2
(4, N = 315) = 7.44, p = .11.
17
Table 2
Logistic Regression Predicting Decision From Gender, Ideology, and Scenario
Predictor B Wald 2
p Odds Ratio
Gender 1.25 20.59 < .001 3.51
Idealism -0.70 37.89 < .001 0.50
Relativism 0.33 6.63 .01 1.39
Scenario
Cosmetic -0.71 2.85 .091 0.49
Theory -1.16 7.35 .007 0.31
Meat -0.87 4.16 .041 0.42
Veterinary -0.54 1.75 .186 0.58
Interaction Terms
Interaction terms can be included in a logistic model. When the variables in an interaction are
continuous they probably should be centered. Consider the following research: Mock jurors are
presented with a criminal case in which there is some doubt about the guilt of the defendant. For half
of the jurors the defendant is physically attractive, for the other half she is “plain.” Half of the jurors
are asked to recommend a verdict without having deliberated, the other half are asked about their
recommendation only after a short deliberation with others. The deliberating mock jurors were primed
with instructions predisposing them to change their opinion if convinced by the arguments of others.
We could use a logit analysis here, but elect to use a logistic regression instead. The article in which
these results were published is: Patry, M. W. (2008). Attractive but guilty: Deliberation and the
physical attractiveness bias. Psychological Reports, 102, 727-733.
The data are in Logistic2x2x2.sav at my SPSS Data Page. Download the data and bring them
into SPSS. Each row in the data file represents one cell in the three-way contingency table. Freq is
the number of scores in the cell.
Tell SPSS to weight cases by Freq. Data, Weight Cases:
18
Analyze, Regression, Binary Logistic. Slide Guilty into the Dependent box and Delib and Plain
into the Covariates box. Highlight both Delib and Plain in the pane on the left and then click the
>a*b> box.
This creates the interaction term. It could also be created by simply creating a new variable,
Interaction = DelibPlain.
Under Options, ask for the Hosmer-Lemeshow test and confidence intervals on the odds
ratios.
19
You will find that the odds ratios are .338 for Delib, 3.134 for Plain, and 0.030 for the
interaction.
Those who deliberated were less likely to suggest a guilty verdict (15%) than those who did not
deliberate (66%), but this (partial) effect fell just short of statistical significance in the logistic
regression (but a 2 x 2 chi-square would show it to be significant).
Plain defendants were significantly more likely (43%) than physically attractive defendants
(39%) to be found guilty. This effect would fall well short of statistical significance with a 2 x 2 chi-
square.
We should not pay much attention to the main effects, given that the interaction is powerful.
The interaction odds ratio can be simply computed, by hand, from the cell frequencies.
 For those who did deliberate, the odds of a guilty verdict are 1/29 when the defendant was
plain and 8/22 when she was attractive, yielding a conditional odds ratio of 0.09483.
 For those who did not deliberate, the odds of a guilty verdict are 27/8 when the defendant was
plain and 14/13 when she was attractive, yielding a conditional odds ratio of 3.1339.
Variables in the Equation
3.697 1 .054 .338 .112 1.021
4.204 1 .040 3.134 1.052 9.339
8.075 1 .004 .030 .003 .338
.037 1 .847 1.077
Delib
Plain
Delib by Plain
Constant
Step
1
a
Wald df Sig. Exp(B) Lower Upper
95.0% C.I.f or EXP(B)
Variable(s) entered on step 1: Delib, Plain, Delib * Plain .a.
Plain * Guilty Crosstabulationa
22 8 30
73.3% 26.7% 100.0%
29 1 30
96.7% 3.3% 100.0%
51 9 60
85.0% 15.0% 100.0%
Count
% within Plain
Count
% within Plain
Count
% within Plain
Attrractive
Plain
Plain
Total
No Yes
Guilty
Total
Delib = Yesa.
20
 The interaction odds ratio is simply the ratio of these conditional odds ratios – that is,
.09483/3.1339 = 0.030.
Follow-up analysis shows that among those who did not deliberate the plain defendant was
found guilty significantly more often than the attractive defendant, 2
(1, N = 62) = 4.353, p = .037, but
among those who did deliberate the attractive defendant was found guilty significantly more often
than the plain defendant, 2
(1, N = 60) = 6.405, p = .011.
Interaction Between a Dichotomous Predictor and a Continuous Predictor
Suppose that I had some reason to suspect that the effect of idealism differed between men
and women. I can create the interaction term just as shown above.
Variables in the Equation
B S.E. Wald df Sig. Exp(B)
Step 1
a
idealism -.773 .145 28.572 1 .000 .461
gender -.530 1.441 .135 1 .713 .589
gender by idealism .268 .223 1.439 1 .230 1.307
Constant 4.107 .921 19.903 1 .000 60.747
a. Variable(s) entered on step 1: idealism, gender, gender * idealism .
Plain * Guilty Crosstabulationa
13 14 27
48.1% 51.9% 100.0%
8 27 35
22.9% 77.1% 100.0%
21 41 62
33.9% 66.1% 100.0%
Count
% within Plain
Count
% within Plain
Count
% within Plain
Attrractive
Plain
Plain
Total
No Yes
Guilty
Total
Delib = Noa.
21
As you can see, the interaction falls short of significance.
Partially Standardized B Weights and Odds Ratios
The value of a predictor’s B (and the associated odds ratio) is highly dependent on the unit of
measure. Suppose I am predicting whether or not an archer hits the target. One predictor is distance
to the target. Another is how much training the archer has had. Suppose I measure distance in
inches and training in years. I would not expect much of an increase in the logit when decreasing
distance by an inch, but I would expect a considerable increase when increasing training by a year.
Suppose I measured distance in miles and training in seconds. Now I would expect a large B for
distance and a small B for training. For purposes of making comparisons between the predictors, it
may be helpful to standardize the B weights.
Suppose that a third predictor is the archer’s score on a survey of political conservatism and
that a photo of Karl Marx appears on the target. The unit of measure here is not intrinsically
meaningful – how much is a one point change in score on this survey. Here too it may be helpful to
standardize the predictors. Menard (The American Statistician, 2004, 58, 218-223) discussed several
ways to standardize B weights. I favor simply standardizing the predictor, which can be simply
accomplished by converting the predictor scores to z scores or by multiplying the unstandardized B
weight by the predictor’s standard deviation. While one could also standardize the dichotomous
outcome variable (group membership), I prefer to leave that unstandardized.
In research here at ECU, Cathy Hall gathered data that is useful in predicting who will be
retained in our engineering program. Among the predictor variables are high school GPA, score on
the quantitative section of the SAT, and one of the Big Five personality measures, openness to
experience. Here are the results of a binary logistic regression predicting retention from high school
GPA, quantitative SAT, and openness (you can find more detail here).
Unstandardized Standardized
Predictor B Odds Ratio B Odds Ratio
HS-GPA 1.296 3.656 0.510 1.665
SAT-Q 0.006 1.006 0.440 1.553
Openness 0.100 1.105 0.435 1.545
The novice might look at the unstandardized statistics and conclude that SAT-Q and openness
to experience are of little utility, but the standardized coefficients show that not to be true. The three
predictors differ little in their unique contributions to predicting retention in the engineering program.
Practice Your Newly Learned Skills
Now that you know how to do a logistic regression, you should practice those skills. I have
presented below three exercises designed to give you a little practice.
Exercise 1: What is Beautiful is Good, and Vice Versa
Castellow, Wuensch, and Moore (1990, Journal of Social Behavior and Personality, 5, 547-
562) found that physically attractive litigants are favored by jurors hearing a civil case involving
22
alleged sexual harassment (we manipulated physical attractiveness by controlling the photos of the
litigants seen by the mock jurors). Guilty verdicts were more likely when the male defendant was
physically unattractive and when the female plaintiff was physically attractive. We also found that
jurors rated the physically attractive litigants as more socially desirable than the physically
unattractive litigants -- that is, more warm, sincere, intelligent, kind, and so on. Perhaps the jurors
treated the physically attractive litigants better because they assumed that physically attractive people
are more socially desirable (kinder, more sincere, etc.).
Our next research project (Egbert, Moore, Wuensch, & Castellow, 1992, Journal of Social
Behavior and Personality, 7, 569-579) involved our manipulating (via character witness testimony) the
litigants' social desirability but providing mock jurors with no information on physical attractiveness.
The jurors treated litigants described as socially desirable more favorably than they treated those
described as socially undesirable. However, these jurors also rated the socially desirable litigants as
more physically attractive than the socially undesirable litigants, despite having never seen them!
Might our jurors be treating the socially desirable litigants more favorably because they assume that
socially desirable people are more physically attractive than are socially undesirable people?
We next conducted research in which we manipulated both the physical attractiveness and the
social desirability of the litigants (Moore, Wuensch, Hedges, & Castellow, 1994, Journal of Social
Behavior and Personality, 9, 715-730). Data from selected variables from this research project are in
the SPSS data file found at http://core.ecu.edu/psyc/wuenschk/SPSS/Jury94.sav. Please download
that file now.
You should use SPSS to predict verdict from all of the other variables. The variables in the file
are as follows:
 VERDICT -- whether the mock juror recommended a not guilty (0) or a guilty (1) verdict -- that
is, finding in favor of the defendant (0) or the plaintiff (1)
 ATTRACT -- whether the photos of the defendant were physically unattractive (0) or physically
attractive (1)
 GENDER -- whether the mock juror was female (0) or male (1)
 SOCIABLE -- the mock juror's rating of the sociability of the defendant, on a 9-point scale, with
higher representing greater sociability
 WARMTH -- ratings of the defendant's warmth, 9-point scale
 KIND -- ratings of defendant's kindness
 SENSITIV -- ratings of defendant's sensitivity
 INTELLIG -- ratings of defendant's intelligence
You should also conduct bivariate analysis (Pearson Chi-Square and independent samples ttests)
to test the significance of the association between each predictor and the criterion variable
(verdict). You will find that some of the predictors have significant zero-order associations with the
criterion but are not significant in the full model logistic regression. Why is that?
You should find that the sociability predictor has an odds ratio that indicates that the odds of a
guilty verdict increase as the rated sociability of the defendant increases -- but one would expect that
greater sociability would be associated with a reduced probability of being found guilty, and the
univariate analysis indicates exactly that (mean sociability was significantly higher with those who
were found not guilty). How is it possible for our multivariate (partial) effect to be opposite in direction
to that indicated by our univariate analysis? You may wish to consult the following documents to help
understand this:
Redundancy and Suppression
Simpson's Paradox
23
Exercise 2: Predicting Whether or Not Sexual Harassment Will Be Reported
Download the SPSS data file found at http://core.ecu.edu/psyc/wuenschk/SPSS/HarassHowell.sav.
This file was obtained from David Howell's site,
http://www.uvm.edu/~dhowell/StatPages/Methods/DataMethods5/Harass.dat. I have added value
labels to a couple of the variables. You should use SPSS to conduct a logistic regression predicting
the variable "reported" from all of the other variables. Here is a brief description for each variable:
 REPORTED -- whether (1) or not (0) an incident of sexual harassment was reported
 AGE -- age of the victim
 MARSTAT -- marital status of the victim -- 1 = married, 2 = single
 FEMinist ideology -- the higher the score, the more feminist the victim
 OFFENSUV -- offensiveness of the harassment -- higher = more offensive
I suggest that you obtain, in addition to the multivariate analysis, some bivariate statistics,
including independent samples t-tests, a Pearson chi-square contingency table analysis, and simple
Pearson correlation coefficients for all pairs of variables.
Exercise 3: Predicting Who Will Drop-Out of School
Download the SPSS data file found at http://core.ecu.edu/psyc/wuenschk/SPSS/Dropout.sav.
I simulated these data based on the results of research by David Howell and H. R. Huessy
(Pediatrics, 76, 185-190). You should use SPSS to predict the variable "dropout" from all of the other
variables. Here is a brief description for each variable:
 DROPOUT -- whether the student dropped out of high school before graduating -- 0 = No, 1 =
Yes.
 ADDSC -- a measure of the extent to which each child had exhibited behaviors associated with
attention deficit disorder. These data were collected while the children were in the 2nd
, 4th
, and
5th
grades combined into one variable in the present data set.
 REPEAT -- did the child ever repeat a grade -- 0 = No, 1 = Yes.
 SOCPROB -- was the child considered to have had more than the usual number of social
problems in the 9th
grade -- 0 = No, 1 = Yes.
I suggest that you obtain, in addition to the multivariate analysis, some bivariate statistics,
including independent samples t-tests, a Pearson chi-square contingency table analysis, and simple
Pearson correlation coefficients for all pairs of variables. Imagine that you were actually going to use
the results of your analysis to decide which children to select as "at risk" for dropping out before
graduation. Your intention is, after identifying those children, to intervene in a way designed to make
it less likely that they will drop out. What cutoff would you employ in your decision rule?
Having SPSS Create the Dummy Variables for You
Dependent Variable Encoding
Original Value Internal Value
stop 0
continue 1
The predicted event is that the subject will vote to continue the research. The scenario
variable is categorical, with five levels. SPSS allows you to select as the reference group either the
24
group with the lowest numeric code or that with the highest numeric code. I selected the highest
(last) code, the medical scenario.
SPSS shows you the coding of the k-1 = 4 dummy variables it has created
Categorical Variables Codings
Frequency Parameter coding
(1) (2) (3) (4)
scenario
1.00 62 1.000 .000 .000 .000
2.00 64 .000 1.000 .000 .000
3.00 63 .000 .000 1.000 .000
4.00 63 .000 .000 .000 1.000
5.00 63 .000 .000 .000 .000
Block 0: Beginning Block
Classification Table
a,b
Observed Predicted
decision Percentage
Correctstop continue
Step 0
decision
stop 187 0 100.0
continue 128 0 .0
Overall Percentage 59.4
a. Constant is included in the model.
b. The cut value is .500
25
Variables in the Equation
B S.E. Wald df Sig. Exp(B)
Step 0 Constant -.379 .115 10.919 1 .001 .684
Block 1: Method = Enter
Omnibus Tests of Model Coefficients
Chi-square df Sig.
Step 1
Step 7.417 4 .115
Block 7.417 4 .115
Model 7.417 4 .115
Addition of the four scenario dummy variables has lowered the -2 Log Likelihood by 7.417.
Model Summary
Step -2 Log
likelihood
Cox & Snell R
Square
Nagelkerke R
Square
1 418.149
a
.023 .031
a. Estimation terminated at iteration number 3 because
parameter estimates changed by less than .001.
Classification Table
a
Observed Predicted
decision Percentage
Correctstop continue
Step 1
decision
stop 158 29 84.5
continue 94 34 26.6
Overall Percentage 61.0
Variables in the Equation
B S.E. Wald df Sig. Exp(B)
Step 1
a
scenario 7.291 4 .121
scenario(1) -.551 .362 2.320 1 .128 .576
scenario(2) -.948 .370 6.571 1 .010 .388
scenario(3) -.712 .364 3.835 1 .050 .490
scenario(4) -.512 .360 2.025 1 .155 .599
Constant .159 .253 .396 1 .529 1.172
a. Variable(s) entered on step 1: scenario.
26
The Wald chi-square is more conservative than the drop in the -2 Log Likelihood chi-square
(7.291 rather than 7.417). SPSS gives a Wald chi-square for each of the four dummy variables. The
second and third contrasts are significant. Inverting the odds ratio for ease of interpretation, the odds
of voting to continue the research were 2.58 times higher when the scenario was medical than when
the scenario was neuroscience research and 2.04 times higher when medical than when agricultural
(feed the poor). Distressingly, approval of the research was not significantly different between the
cosmetic scenario and the medical scenario. Our students are reluctant to condone animal research
intended to feed the poor or to investigate brain function, but they condone animal research that is
used to gain approval of new cosmetic products.
Here is some of the output from the analysis where I
created the dummy variables myself.
Chi-square df Sig.
Step 1 Step 7.417 4 .115
As earlier, adding the dummy variables lowered the
-2 Log Likelihood by 7.417, an effect short of
significance.
Variables in the Equation
B S.E. Wald df Sig. Exp(B)
Step 1
a
cosmetic -.551 .362 2.320 1 .128 .576
theory -.948 .370 6.571 1 .010 .388
meat -.712 .364 3.835 1 .050 .490
veterin -.512 .360 2.025 1 .155 .599
Constant .159 .253 .396 1 .529 1.172
a. Variable(s) entered on step 1: cosmetic, theory, meat, veterin.
Notice that we obtain a Wald chi-square for each of the four dummy variables. We do not get
a Wald chi-square for the omnibus effect of scenario, nor do we need one, since the reduction in the -
2 Log Likelihood chi-square tests the omnibus effect of scenario.
27
Types of Contrasts Available in SPSS Binary Logistic Regression
 Indicator. Contrasts indicate the presence or absence of category membership. The reference
category is represented in the contrast matrix as a row of zeros.
 Simple. Each category of the predictor variable (except the reference category) is compared to
the reference category.
 Difference. Each category of the predictor variable except the first category is compared to the
average effect of previous categories. Also known as reverse Helmert contrasts.
 Helmert. Each category of the predictor variable except the last category is compared to the
average effect of subsequent categories.
 Repeated. Each category of the predictor variable except the first category is compared to the
category that precedes it.
 Polynomial. Orthogonal polynomial contrasts. Categories are assumed to be equally spaced.
Polynomial contrasts are available for numeric variables only.
 Deviation. Each category of the predictor variable except the reference category is compared
to the overall effect.
 If you select Deviation, Simple, or Indicator, select either First or Last as the reference
category.
 Note that the method is not actually changed until you click Change.
Here is an example. Sudden heart failure patients are the subjects here. They were asked
whether or not anxiety had been a problem for them recently (this is the predicted event). Our
predictor variables were sex and group, where group was (1) No ICD, (2) ICD but no history of shock
from it, and (3) ICD with history of shock from it.
We first tested a model with Group, Sex, and Group x Sex predictors.
LOGISTIC REGRESSION VARIABLES AnxietyNow
/METHOD=ENTER Sex Group Group*Sex
/CONTRAST (Sex)=Helmert
/CONTRAST (Group)=Helmert
/CRITERIA=PIN(.05) POUT(.10) ITERATE(20) CUT(.5).
The output showed that the Group X Sex interaction fell just short of statistical significance.
Variables in the Equation
B S.E. Wald df Sig. Exp(B) 95% C.I.for EXP(B)
Lower Upper
Group * Sex 5.258 2 .072
Group(1) by
Sex(1)
2.202 1.305 2.847 1 .092 9.045 .701 116.743
Group(2) by
Sex(1)
-1.078 .711 2.300 1 .129 .340 .085 1.370
Constant .363 .296 1.507 1 .220 1.438
28
Accordingly, we dropped the interaction from the model. Here is the output for the main
effects model.
Variables in the Equation
B S.E. Wald df Sig. Exp(B) 95% C.I.for EXP(B)
Lower Upper
Step 1
a
Group 8.065 2 .018
Group(1) 1.315 .569 5.352 1 .021 3.727 1.223 11.359
Group(2) .591 .354 2.784 1 .095 1.805 .902 3.614
Sex(1) .585 .338 2.995 1 .084 1.795 .925 3.482
Constant .655 .281 5.429 1 .020 1.925
The effect of sex fell just short of significance, but group had a significant effect. Recall that
we used Helmert contrasts for the effect of group.
Categorical Variables Codings
Frequency Parameter coding
(1) (2)
Group
No ICD 32 .667 .000
ICD No Shock 80 -.333 .500
ICD Shock 63 -.333 -.500
Sex
Male 97 1.000
Female 78 .000
The first contrast compares those who did not have an ICD (Group 1) with those who did
(Groups 2 and 3). That contrast was significant. Those who had an ICD were 3.7 times more likely
to identify anxiety as a problem than were those who did not have an ICD. The second contrast
compared those who had an ICD but no history of shock with those who had an ICD with a history of
shock. This contrast fell short of statistical significance.
Variables in the Equation
B S.E. Wald df Sig. Exp(B) 95% C.I.for EXP(B)
Lower Upper
Step 1
a
Group 8.065 2 .018
Group(1) 1.315 .569 5.352 1 .021 3.727 1.223 11.359
Group(2) .591 .354 2.784 1 .095 1.805 .902 3.614
Sex(1) .585 .338 2.995 1 .084 1.795 .925 3.482
Constant .655 .281 5.429 1 .020 1.925
Copyright 2016, Karl L. Wuensch - All rights reserved.
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