M7222 Generalized linear models

Faculty of Science
autumn 2021
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
Mgr. Andrea Kraus, M.Sc., Ph.D. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Wed 14:00–15:50 M6,01011
  • Timetable of Seminar Groups:
M7222/01: Mon 12:00–13:50 MP1,01014, A. Kraus
Prerequisites
Probability and mathematical statistics, in particular theory of estimation and testing statistical hypotheses: at the level of the course M4122. Statistical software R: at the level of the course M4130. Linear models: at the level of the course M5120.
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 course introduces generalized linear models as a generalization of the linear model for situations, where the assumption of normality, linearity and/or homoskedasticity is violated. The course covers theory, software implementation, applications and interpretation, and lays foundations for the study of more advanced regression models.
Learning outcomes
After the course, the students
- are able to recognize the situations that can be addressed by generalized linear models;
- are able to choose, formulate and implement an appropriate model from this class, and interpret the results;
- to this aim, the students develop a deeper understanding of the theory of modelling, estimation and testing than what is sufficient for linear models;
- at the same time, the students are made aware of the limitations of generalized linear models and are offered an overview of the models that can be used in situations that cannot be addressed by generalized linear models.
Syllabus
  • Overview.
  • Exponential families of distributions.
  • Maximum likelihood and quasi-likelihood.
  • Theory and practice of estimation in generalized linear models.
  • Deviance and residuals, and their role in model diagnostics and model selection.
  • Logistic regression, generalizations for multicategory response, applications in classification.
  • Poisson and multinomial regression, contingency tables.
  • Generalized linear models for continuous response.
Literature
    recommended literature
  • WOOD, Simon N. Generalized additive models : an introduction with R. Second edition. Boca Raton, FL: CRC Press/Taylor & Francis Group, 2017. xx, 476. ISBN 9781498728331. info
  • FARAWAY, Julian James. Extending the linear model with R : generalized linear, mixed effects and nonparametric regression models. Second edition. Boca Raton, FL: CRC Press/Taylor & Francis Group, 2016. xiii, 399. ISBN 9781498720960. info
  • AGRESTI, Alan. Categorical data analysis. 2nd ed. Hoboken: John Wiley & Sons, 2002. xv, 710. ISBN 0471360937. info
  • 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
    not specified
  • 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: exercises focused on in-depth understanding of the theory and on practical data analysis
Assessment methods
Semestral data project, written final exam, possibly with a bonus for an optional written midterm exam. The form of the exam will be adjusted to the epidemiological situation preceding the date of the exam.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
https://is.muni.cz/auth/el/sci/podzim2021/M7222/index.qwarp
https://is.muni.cz/auth/el/sci/podzim2021/M7222/index-KFhemy.qwarp
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 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2021/M7222