Class 12, Module II

13 Abril 2021, 14:30 • Jorge Filipe Campinos Landerset Cadima

Onli ne class Monday, April 26, from 14h30 and 17h00
[GLM slides 114-173] (The slides 174 - 202 are suplementary material, which is not considered course material). Exercises GLM 1 and 10: ANCOVA-type GLM models, in a probit regression context. Interpretation in a toxicological context and the likelihood ratio test. The Akaike Information Criterion (AIC) in a GLM context. Subselect selection heuristics using the AIC criterion: the R function 'step'. An example. The Gamma distribution: a parametrization suited for GLMs; the natural and dispersion parameters of a Gamma distribution as a member of the exponential family of distributions; the relation between the variance and the mean in a Gamma distribution; the canonical link for Gamma distributions and some specific contexts with a single numerical predictor. The problem of estimating unknown dispersion parameters, phi. Deviance and scaled deviances: definition; the case of Normal distribution and of Gamma distribution. Residuals in GLMs: the concept of the variance function; Pearson residuals and deviance residuals. How each of these concepts depends on the distribution of Y and on the link function used. The generalized Pearson statistic, X^2.  An estimator for the dispersion parameter phi, based on the generalized Pearson statistic. Standardized residuals. A very brief discussion of the use of residuals and other diagnostics for model checking in GLMs. Log-linear models and contingency tables: the case of two-way contingency tables with Poisson counts; an ANOVA-type log-linear model (without interaction effects) and independence; the bridge between this model and the chi-squared test for independence. A brief word on log-linear models for contingency tables with three or more factors.