Introduction to generalised linear models

• Data types.

• Review of linear regression model.

• Exponential family of distributions: introduction.

• Natural and scale parameters. Mean and variance. Variance function.

• Introduction to Generalized Linear Models: link functions, canonical link function, linear predictor.

• Variables, factors, interactions. Parametrisation.

• Deviance and scaled deviance. 

• Pearson and deviance residuals.

Statistical inference in the GLM

• Review of Maximum Likelihood theory.

• Point and interval estimation.

• Test of hypotheses on individual parameters.

• Test of linear restrictions - nested models.

• Model fit and model comparison.

• Estimation of dispersion parameter.

Continuous response models

• The Normal model.

• The Exponential and Gamma models.

Discrete response models

• The Binomial model.

• The Poisson model.

• Modelling of proportions.

• Poisson modelling of rates. Offest.

Quasi-likelihood and overdispersion

• Introduction to quasi-likelihood estimation.

• Likelihood equations for the general and regression models.

• Choice of mean value and variance functions.

• Estimation of the dispersion parameter.