Germán Rodríguez

Generalized Linear Models
Princeton University
The following is a tentative list of the topics to be covered in the lectures scheduled for this fall. The overall pace or the distribution of lectures within each topic may be altered, if it seems advisable during the course of the term.

Wednesday, September 14 |
Introduction and overview of the course. Responses and predictors. Factors and covariates. The generalized linear model. Review of likelihood theory. | |

Monday, September 19 | Linear models. Ordinary least squares estimation. Testing the general linear hypothesis: t-tests and F-tests. Simple linear regression. | |

Wednesday, September 21 | Multiple linear regression. Interpretation of the coefficients. Gross and net effects. Hierarchical anova for multiple regression. Partial and multiple correlation. | |

Monday, September 26 |
Analysis of variance models. One-way anova and regression with dummy variables. Two-way anova. The additive model. Main effects and interactions. | |

Wednesday, September 28 | Analysis of covariance models. The additive model. The assumption of parallelism. Models with different intercepts and different slopes. Interpretation. | |

Monday, October 3 |
Regression diagnostics. Analysis of residuals. Influential observations, leverage and influence. Q-Q plots. | |

Wednesday, October 5 | Regression remedies. Transforming the response. The Box-Cox family of transformations. Transforming the predictors. | |

Monday, October 10 | Binary data. The binomial distribution. Grouped and ungrouped data. Odds and log-odds. The logit transformation. Logistic regression. | |

Wednesday, October 12 | Maximum likelihood estimation and testing in logistic regression models. The comparison of two groups. The odds ratio. Comparison of several groups. The one-factor model. The one-variate model. | |

Monday, October 17 | Regression models for binary data. Models with two predictors. Main effects and interactions. Multifactor models. Model selection. | |

Wednesday, October 19 | Alternative links for binary data. Probit analysis. The c-log-log link. Regression diagnostics with binary data. | |

Monday, October 24 | Count data. The Poisson distribution. The log link. Maximum likelihood estimation and testing in Poisson regression. The Poisson deviance. Modelling heteroscedastic counts. | |

Wednesday, October 26 | First Partial Exam. | |

Monday, November 7 | Models for rates of events. Exposure and the use of an offset in the linear predictor. | |

Wednesday, November 9 | Extra-Poisson variation. The negative binomial model. Zero-inflated models for counts | |

Monday, November 14 | Multinomial response models. Multinomial logits. Independence of irrelevant alternatives. Random utilities and the conditional logit model. | |

Wednesday, November 16 | Sequential logits. Sequential binary choice and continuation ratio models. Equivalence with logit models. | |

Monday, November 21 | Models for ordered categorical data. Ordered logits and probits. Latent variable formulation and interpretation of the coefficients. | |

Monday, November 28 | Survival and event history models. The survival and hazard functions. Censoring mechanisms. The likelihood function for non-informative censoring. | |

Wednesday, November 30 | The proportional hazards model. The baseline hazard. Relative risks. Time-varying covariates. Time-varying effects and models with interactions. | |

Monday, December 5 | Semi-parametric models. The piece-wise exponential model. Equivalence with Poisson regression and with models for contingency tables. | |

Wednesday, December 7 | Discrete time models and equivalence with logistic regression. Unobserved heterogeneity. Topics in survival analysis. | |

Monday, December 12 | The analysis of panel data. Random effects and fixed effects. Intraclass correlation. | |

Wednesday, December 14 | Fixed and random effect models for binary and count data. Hierarchical models. | |

Monday, January 23 | Second Partial Exam |

Continue with the Supplementary Readings