STA 216 Generalized Linear Models

1. STA 216Generalized Linear Models Meets: 2:50-4:05 T/TH (Old Chem 025) Instructor: David Dunson 219A Old Chemistry, 684-8025 dunson@stat.duke.edu Teaching Assistant: Dawn Barnard 112 Old Chemistry, 684-4365 dawn@stat.duke.edu

2. STA 216 Syllabus • Topics to be covered: • GLM Basics: components, exponential family, model fitting, frequent inference: analysis of deviance, stepwise selection, goodness of fit • Bayesian Inference in GLMs (basics): priors, posterior, comparison with frequentist approach, posterior computation, MCMC strategies (Gibbs, Metropolis-Hastings) • Binary & categorical response data: • Basics: link functions, form of posterior, approximations, Gibbs sampling via adaptive rejection • Latent variable models: Threshold formulations, probit models, discrete choice models, logistic regression & generalizations, data augmentation algorithms (Albert & Chib + other forms) • Count Data: Poisson & over-dispersed Poisson log-linear models, prior distributions, applications

3. STA 216 Syllabus • Topics to be covered (continued): • Bayesian Variable Selection: problem formulation, mixture priors, stochastic search algorithms, examples, approximations • Bayesian hypothesis testing in GLMs: one- and two-sided alternatives, basic decision theoretic approaches, mixture priors, computation, order restricted inference • Survival analysis: censoring definitions, form of likelihood, parametric models, discrete-time & continuous time formulations, proportional hazards, priors for hazard functions, computation • Missing data: problem formulation, selection & pattern mixture models, shared variable approaches, examples • Multistate & stochastic modeling: motivating examples (epidemiologic studies with periodic observations of a disease process), discrete time approaches, joint models, computation

4. STA 216 Syllabus • Topics to be covered (continued): • Correlated data (basics): mixed models for longitudinal, frequentist alternatives (marginal models, GEEs, etc) • Generalized linear mixed models (GLMM): definition, examples, normal linear case - induced correlation structure, priors, computation, multi-level models, covariance selection • Generalized additive models: definition, frequentist approaches for inference & computation (Hastie & Tibshirani), Bayesian approaches using basis functions, priors, computation • Factor analytic models: Underlying normal formulations, mixed discrete & continuous outcomes, generalized factor models, joint models for longitudinal and event time data, covariance selection, model identifiability issues, computation

5. Student Responsibilities: • Assignments: Outside reading and problems sets will typically be assigned after each class (10%) • Mid-term Examination: An in-class closed-book mid term examination will be given (30%) • Project: Students will be expected to write-up and present results from a data analysis project (30%) • Final Examination: The final examination be out of class (30%)

6. Comments on Computing • Course will have an applied emphasis • Students will be expected to implement frequentist & Bayesian analyses of real and simulated data examples • It is not required that students use a particular computing package • However, emphasis will be given to R/S-PLUS & Matlab, with code sometimes provided