Modelos Lineares Generalizados (2 º Sem 2017/2018)

1. Review of linear regression model

1.1 Introduction.

1.2 Definition of the linear regression model.

1.3 Basic hypotheses of the model.

1.4 Coefficient estimation through the least squares method.

1.5 Coefficient of determination.

1.6 The normal linear regression model.

1.7 Inference in the linear regression model.

2. Introduction to generalised linear models

2.1 Data types.

2.2 Exponential family of distributions: introduction.

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

2.4 Introduction to Generalized Linear Models: link functions, canonical

link function, linear predictor.

2.5 Variables, factors, interactions. Parametrisation.

2.6 Deviance and scaled deviance. 

2.7 Pearson and deviance residuals.

3. Statistical inference in the GLM

3.1 Review of Maximum Likelihood theory.

3.2 Point and interval estimation.

3.3 Test of hypotheses on individual parameters.

3.4 Test of linear restrictions - nested models.

3.5 Model fit and model comparison.

3.6 Estimation of dispersion parameter.

4. Continuous response models

4.1 The Normal model.

4.2 The Exponential and Gamma models.

5. Discrete response models

5.1 The Binomial model.

5.2 The Poisson model.

5.3 Modelling of proportions.

5.4 Poisson modelling of rates. Offest.

6. Quasi-likelihood and overdispersion

6.1 Introduction to quasi-likelihood estimation.

6.2 Likelihood equations for the general and regression models.

6.3 Choice of mean value and variance functions.

6.4 Estimation of the dispersion parameter.