Modelos Lineares Generalizados (2 º Sem 2014/2015)

CA (Actuarial Science)

Detailed Programme Link

     

    1. 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.

    2. Statistical inference

      • 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.

    3. Continuous response models

      • The Normal model.

      • The Exponential and Gamma models.

    4. Discrete response models

      • The Binomial model.

      • The Poisson model.

      • Modelling of proportions.

      • Poisson modelling of rates. Offest.

    5. 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.