M7222 Generalized linear models

Faculty of Science
Autumn 2010
Extent and Intensity
2/1. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Forbelská, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 M5,01013
  • Timetable of Seminar Groups:
M7222/01: Wed 16:00–16:50 M5,01013
Prerequisites
M6120 Linear Models in Statistics II
Basic knowledge of the theory of estimation and knowledge of linear statistical models of full rank (regression analysis) and not full rank (ANOVA).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of this course is to consider generalized linear models as a broad class of statistical models applying the general principles of likelihood inference to a variety of commonly encountered data analysis problems in many branches such as in biology, medicine, sociology and others. For computer labs the MATLAB software environment is used. Upon successful completion of the course students should be able to understand principles of parameter estimation and hypotheses testing in a generalized linear model; apply the methods to build models to address practical objectives; learn to interpret the results properly.
Syllabus
  • Selected topics of statistical estimation theory: family of regular densities, exponential family of distributions, maximal likelihood estimation and its properties. Theory of generalized linear models: generalization of classical linear regression model, construction of generalized linear model and its description, model fitting, minimal, maximal models, submodels, goodness-of-fit measures and residua, testing of adequacy of a model, diagnostics. Gamma regression, models for binary and binomial data, logistic regression, dose response models, models for nominal and ordinal data, Poisson regresion, log-linear models and contingency tables.
Literature
  • An introduction to generalized linear models. Edited by Annette J. Dobson. 2nd ed. Boca Raton: CRC Press, 2002, vii, 225 s. ISBN 1-58488-165-8. info
  • FAHRMEIR, Ludwig and Gerhard TUTZ. Multivariate statistical modelling based on generalized linear models. New York: Springer-Verlag, 1994, 425 s. ISBN 0387942335. info
Teaching methods
Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems.
Assessment methods
Lecture with a seminar. Active work in seminars. Oral examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2010, recent)
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