# Course: Generalized Linear Models

Course type: elective
Lecturer: Maja Pohar Perme, Ph.D., Associate Professor

Study programme and level Study field Academic year Semester
Applied statistics, second level All modules 1st or 2nd 1st or 2nd

For the timeline see Curriculum.

Prerequisites:

• Enrollment into the first year of the programme.
• Prerequisites to the written exam are successfully completed homeworks.

Content (Syllabus outline):

• Recap of linear regression models
• Box-Cox transformation family
• Exponential family of distributions: properties and members, maximum (quasi-) likelihood estimation
• Generalized linear models: maximum likelihood estimation, deviance and Pearson's chi-square statistic
• Logistic regression with emphasis on binomial logit models and log odds ratio modelling, loglinear Poisson models
• Multinomial responses (contingency tables)
• Dispersion models: quasi-likelihood and quasi-deviane, over- and underdispersion
• Extended quasi-likelihood technique : additional parameters in the variance structure of the responses
• Random effect models: EM algorithms, extra variability in the data, Gauss-Hermite quadrature methods
• Nonparametric maximum likelihood estimation
• Modelling sets of correlated data: generalized estimating equation approaches (GEE & GEE2) and the class of generalized linear mixed models

Objectives and competences:
In statistical practice statistician often tackles problems that go beyond the frame of linear models. The course deals with the nature of the data and the concepts of the models that obey these specialities. The students learns the methods for the analysis of that kind of data and tests them on practical examples.

Intended learning outcomes:
By the end of the course students should be able to recognize and understand the nature of the additional structure of problems for which statistical techniques met earlier in the study programme are insufficient; understand the basic concepts of models that can address these problems; develop functional knowledge of modelling techniques that are appropriate for such problems; understand the way these techniques relate to each other in specific contexts and be able to generalize from these contexts to new situations.

### Contact

Main contact:
e-mail: info.stat (at) uni-lj.si

Contact for administrative questions (enrolment, technical questions):
Katarina Erjavec Drešar
University of Ljubljana, Faculty of electrical engineering, Tržaška cesta 25, 1000 Ljubljana.
room num.: AN012C-ŠTU
phone: 01 4768 209
e-mail: katarina.erjavec-dresar (at) fe.uni-lj.si