STA 216STA 216Generalized Linear ModelsGeneralized Linear Models

MeetsMeets: 2:50-4:05 T/TH (Old Chem 025): 2:50-4:05 T/TH (Old Chem 025)

InstructorInstructor: David Dunson : David Dunson

219A Old Chemistry, 684-8025219A Old Chemistry, 684-8025

dunson@stat.duke.edudunson@stat.duke.edu

Teaching AssistantTeaching Assistant: Dawn Barnard: Dawn Barnard

112 Old Chemistry, 684-4365112 Old Chemistry, 684-4365

dawn@stat.duke.edudawn@stat.duke.edu

STA 216 SyllabusSTA 216 Syllabus Topics to be covered:Topics to be covered:

GLM BasicsGLM Basics: : components, exponential family, model fitting, components, exponential family, model fitting, frequent inference: analysis of deviance, stepwise selection, frequent inference: analysis of deviance, stepwise selection, goodness of fitgoodness of fit

Bayesian Inference in GLMs (basics)Bayesian Inference in GLMs (basics): : priors, posterior, priors, posterior, comparison with frequentist approach, posterior computation, comparison with frequentist approach, posterior computation, MCMC strategies (Gibbs, Metropolis-Hastings)MCMC strategies (Gibbs, Metropolis-Hastings)

Binary & categorical response dataBinary & categorical response data: : • BasicsBasics: link functions, form of posterior, approximations, Gibbs : link functions, form of posterior, approximations, Gibbs

sampling via adaptive rejection sampling via adaptive rejection • Latent variable modelsLatent variable models: Threshold formulations, probit models, : Threshold formulations, probit models,

discrete choice models, logistic regression & generalizations, data discrete choice models, logistic regression & generalizations, data augmentation algorithms (Albert & Chib + other forms)augmentation algorithms (Albert & Chib + other forms)

Count DataCount Data: Poisson & over-dispersed Poisson log-linear : Poisson & over-dispersed Poisson log-linear models, prior distributions, applicationsmodels, prior distributions, applications

STA 216 SyllabusSTA 216 Syllabus Topics to be covered (continued):Topics to be covered (continued):

Bayesian Variable SelectionBayesian Variable Selection: problem formulation, mixture : problem formulation, mixture priors, stochastic search algorithms, examples, approximationspriors, stochastic search algorithms, examples, approximations

Bayesian hypothesis testing in GLMsBayesian hypothesis testing in GLMs: one- and two-sided : one- and two-sided alternatives, basic decision theoretic approaches, mixture priors, alternatives, basic decision theoretic approaches, mixture priors, computation, order restricted inferencecomputation, order restricted inference

Survival analysisSurvival analysis: censoring definitions, form of likelihood, : censoring definitions, form of likelihood, parametric models, discrete-time & continuous time parametric models, discrete-time & continuous time formulations, proportional hazards, priors for hazard functions, formulations, proportional hazards, priors for hazard functions, computationcomputation

Missing dataMissing data: problem formulation, selection & pattern mixture : problem formulation, selection & pattern mixture models, shared variable approaches, examplesmodels, shared variable approaches, examples

Multistate & stochastic modelingMultistate & stochastic modeling: motivating examples : motivating examples (epidemiologic studies with periodic observations of a disease (epidemiologic studies with periodic observations of a disease process), discrete time approaches, joint models, computationprocess), discrete time approaches, joint models, computation

STA 216 SyllabusSTA 216 Syllabus Topics to be covered (continued):Topics to be covered (continued):

Correlated data (basics)Correlated data (basics): mixed models for longitudinal, : mixed models for longitudinal, frequentist alternatives (marginal models, GEEs, etc)frequentist alternatives (marginal models, GEEs, etc)

Generalized linear mixed models (GLMM)Generalized linear mixed models (GLMM): : definition, definition, examples, normal linear case - induced correlation structure, examples, normal linear case - induced correlation structure, priors, computation, multi-level models, covariance selectionpriors, computation, multi-level models, covariance selection

Generalized additive modelsGeneralized additive models: definition, frequentist : definition, frequentist approaches for inference & computation (Hastie & Tibshirani), approaches for inference & computation (Hastie & Tibshirani), Bayesian approaches using basis functions, priors, computationBayesian approaches using basis functions, priors, computation

Factor analytic modelsFactor analytic models: Underlying normal formulations, : Underlying normal formulations, mixed discrete & continuous outcomes, generalized factor mixed discrete & continuous outcomes, generalized factor models, joint models for longitudinal and event time data, models, joint models for longitudinal and event time data, covariance selection, model identifiability issues, computationcovariance selection, model identifiability issues, computation

Student ResponsibilitiesStudent Responsibilities:: AssignmentsAssignments: Outside reading and problems sets will : Outside reading and problems sets will

typically be assigned after each class (10%)typically be assigned after each class (10%) Mid-term ExaminationMid-term Examination: An in-class closed-book mid : An in-class closed-book mid

term examination will be given (30%)term examination will be given (30%) ProjectProject: Students will be expected to write-up and : Students will be expected to write-up and

present results from a data analysis project (30%)present results from a data analysis project (30%) Final ExaminationFinal Examination: The final examination be out of : The final examination be out of

class (30%)class (30%)

Comments on ComputingComments on Computing Course will have an applied emphasis Course will have an applied emphasis Students will be expected to implement frequentist & Students will be expected to implement frequentist &

Bayesian analyses of real and simulated data examplesBayesian analyses of real and simulated data examples It is not required that students use a particular computing It is not required that students use a particular computing

packagepackage However, emphasis will be given to R/S-PLUS & Matlab, However, emphasis will be given to R/S-PLUS & Matlab,

with code sometimes providedwith code sometimes provided