Generalized Linear Models and Applications

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Department of Mathematics

Synopsis:

1.Generalized linear models: exponential family, regularity conditions, score function.

2.Estimation of parameters: maximum likelihood estimates, numerical methods used for their calculation, Newton-Raphson, Fisher-scoring algorithm.

3.Testing of models: asymptotic distribution of the score function and the MLE estimates, models comparisons, residual analysis, diagnostic of influential observations.

4.Analysis of covariance (ANCOVA), general model of analysis of covariance, one factor ANCOVA, multiple comparisons.

5.Models for binary data: logistic model, normal model, Gumbel model, model parameters interpretation, odds ratio, tests, residuals.

6.Poisson regression: univariate and multivariate Poisson regression, model parameters interpretation, tests and residuals.

7. Probability models for contingency tables, log-linear models.

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Key references:

[1] Dobson, A. J.: An Introduction to Generalized Linear Models. CRC Press, 2018.

[2] Dunn, P. K., Smyth, G. K.: Generalized linear models with examples in R. Springer, 2018.

Recommended references:

[3] Lindsey, J. K.: Applying Generalized Linear Models. Springer, 1998.

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Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikované matematicko-stochastické metody (compulsory course in the program)