Department of Statistics

Recent Instructors B BHATTACHARYA	ST 762	Nonlinear Models for Univariate and Multivariate Response
	Course Description This course will provide a detailed treatment of regression models and associated inferential methods both for univariate and multivariate (e.g. repeated measures) response. The first 1/2 to 2/3 of the course will focus on nonlinear regression models for univariate response, including models for nonconstant response variance. The remainder of the course will be devoted to introduction to extension of the univariate model to two popular types of nonlinear regression models for multivariate response: (i) Marginal (population-averaged) models and models for covariance structure will discussed; methods for these models are popularly known in the literature as "generalized estimating equations," and (ii) Nonlinear mixed effects (subject-specific) models. Properties of competing inferential techniques and the effects of model misspecification will be studied via theoretical arguments carried out at a nonrigorous, heuristic level and via simulation exercises on the part of students. Although we will go through theoretical arguments in class in some detail, and students will be expected to understand and be able to carry out similar arguments at the same level, our main objective will be to appreciate the implication of the results for practice rather than the technical details. Implementation of the methods and application to data will be emphasized in the homework assignments. Course Syllabus Models for Univariate Response Introduction to nonlinear models Implementation of generalized least squares (GLS), iteratively reweighted least squares Generalized (non)linear models, quasilikelihood Normal theory maximum likelihood (ML) Unknown parameters in the variance function Detecting and modeling nonconstant variance Large sample theory -- a casual approach The "folklore" theorem and "optimality" of GLS Linear vs. quadratic estimating equations for the regression parameter Effect of estimating weights in GLS Estimation of unknown parameters in variance function models Models for multivariate response Modeling multivariate response -- sources of correlation and "subject-speciffic" vs. "population-averaged" approaches Generalized estimating equation methods for marginal (population-averaged) models Nonlinear and generalized linear mixed effects (subject-speciffic) models -- approximate and "exact" methods Course Prerequisites ST 512R and ST 552 Course Corequisites None Recent Textbooks None