Fall 2012 PH1916 Generalized linear models
This is a course on methods for generalized linear models (GLMs), rather than a course on using software for data analysis with GLMs. This course is designed to provide students with a fundamental understanding of theory and applications of the GLMs. Emphasis will be placed on statistical modeling, building from standard normal linear models, extending to GLMs, and going beyond GLMs. The main subjects are logit models for nominal and ordinal data, log-linear models, models for repeated categorical data, generalized linear mixed models and other mixture models for categorical data. Methods of maximum likelihood, weighted least squares, and generalized estimating equations will be used for estimation and inference.”
1. Agresti, A. (2002). Categorical Data Analysis (Second Edition). Wiley. ISBN-10: 0471360937.
2. McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models (Second Edition). Chapman and Hall. ISBN-10: 0412317605.
Regression analysis has been developed for many years and remains one of the most commonly used statistical tools to help scientists address their scientific questions. Generalized linear models (GLMs) were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including ANCOVA, linear regression, logistic regression and log-linear models for contingency tables and count data. This lecture will introduce GLMs and some recent developments of regression techniques with focus on generalized linear models, quasi likelihood methods and estimating function approaches.
List of topics:
Generalized linear models and maximum likelihood method
Quasi-likelihood method and estimating equation
Analysis of binary data
Analysis of polytomous responses
Analysis of count data: log linear models
Analysis of contingency table
Generalized linear mixed effect models
Analysis of matched data
Inference for correlated responses: marginal models and random effect models
By the end of the course, the students are expected to: 1) understand the main components of GLMs; 2) build and apply appropriate models to binary, nominal, ordinal or count data; 3) build and apply appropriate models to correlated outcomes; 4) make inference for a given model and interpret the results in the scientific context.