Generalized linear models

Subject description

  • Recap of linear regression models;
  • Box-Cox transformation family;
  • Exponential family of distributions: properties and members, maximum 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;
  • Dispersion models: quasi-likelihood and quasi-deviance, over- and underdispersion;
  • Multilevel models: random effect models, hierarchical linear models, generalized linear mixed models, connections to social network analysis.

The subject is taught in programs

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.

Teaching and learning methods

Lectures, labs, homeworks.

Part of the pedagogical process will be carried out with the help of ICT technologies and the opportunities they offer.

Expected study results

By the end of the course students should be able to  recognise and understand the nature of the additional structure of problems for which statistical techniques met earlier in the study programe 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 generalise from these contexts to new situations.

Basic sources and literature

  • Aitkin, M., Francis, B., Hinde, J., and Darnell R. (2009): Statistical Modelling in R. Oxford University Press:Oxford.
  • Agresti, A. (2002): Categorical Data Analysis, 2nd ed., Wiley:New York.
  • McCullagh, Peter and Nelder, John (1989). Generalized Linear Models,
    Second Edition. Boca Raton: Chapman and Hall/CRC. ISBN 0-412-31760-5

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