Generalized Linear Models and Application

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

In this course we will consider a series of statistical models which generalize classical linear models with normally distributed objective variables. This course consists of the theory of generalized linear models (GLM), outline of the algorithms used for GLM estimation, and explanation how to determine which algorithm to use for a given data analysis.

Requirements:

Basic course of Calculus and Probability (in the extent of the courses 01MAB3, 01MAB4 and 01PRST held at the FNSPE CTU in Prague).

Syllabus of lectures:

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

3. Testing of models: asymptotical distribution of the score function and the MLE estimates, models comparisons, residual analysis

4. Analysis of covariance (ANCOVA), elements of matrix algebra, general model of analysis of covariance, one factor ANCOVA

5. Models for binary data: uniform model, logistic model, normal model, Gumbel model

6. Poisson regression: Poisson distribution, univariate and multivariate Poisson regression, tests and residua, Poisson model for small area estimation

7. Multivariate logistic regression: multivariate logit model, tests about estimated parameters, residua, logit area model

Syllabus of tutorials:

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

2. Testing of models, models comparisons, residual analysis

3. Analysis of covariance (ANCOVA)

4. Logistic regression

5. Poisson regression

6. Multivariate logistic regression.

Study Objective:

Knowledge:

Generalized linear statistical models and methods for estimation of their parameters.

Skills:

Application of theoretically studied statistical procedures to practical problems of data analysis including demonstration of use of these methods on computer in the MATLAB or R environment.

Study materials:

Key references:

[1] A.J. Dobson: An Introduction to Generalized Linear Models. London: Chapman and Hall, 1990

Recommended references:

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

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: