Download
1 / 5
60 likes | 174 Views
STA.216 is an advanced course on Generalized Linear Models, covering GLM basics including model fitting, frequentist inference, and Bayesian approaches. Key topics include binary and categorical response data analysis, latent variable models, count data, Bayesian variable selection, hypothesis testing, and survival analysis. Students will engage in practical assignments and a data analysis project. The course emphasizes both computational strategies and theoretical foundations, providing a comprehensive understanding of the application of generalized linear models in various contexts.
E N D
STA 216Generalized Linear Models Meets: 2:50-4:05 T/TH (Old Chem 025) Instructor: David Dunson 221 Old Chemistry, 684-8025 dunson@stat.duke.edu Teaching Assistant: Eric Vance 222 Old Chemistry, 684-8840 ervance@stat.duke.edu
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
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
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
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 will have both in-class (15%) & out of class problems (15%)
