STA428 GENERALIZED LINEAR MODELS

2 Hours/Week, 2 Credits

Introduction to the concepts of modeling. Model fitting: examples, some principles of statistical modeling (exploratory data analysis), model formulation, parameter estimation, residuals and model checking), estimation and tests based on specific problems Sampling distribution for score statistics, MLEs, deviance; log-likelihood ratio statistic. Exponential family and generalized linear models (Bernoulli, binomial, Poisson, exponential, gamma, normal, etc.) Properties of distributions in the exponential family, expected value, variance, expected value and variance of score statistic, examples for various distributions. Components of generalized linear models random, systematic and link functions, Poisson regression. Maximum likelihood estimation using chain rules, random component, mean and variance of the outcome variable, variance function, dispersion parameter, applications. Systematic component and link function: identity link, logit link, log link, parameter estimation. Score function and information matrix, estimation using the method of scoring, iteratively reweighted least squares. Inference procedures, deviance for logit, identity, log link functions, scaled deviance, sampling distributions, hypothesis testing. Generalized Pearson chi-square statistic, residuals for glm, Pearson residual, Anscombe residuals. Logit link function, iteratively reweighted least squares, tests; nominal and ordinal logistic regression. Goodness of fit tests, Hosmer-Lemeshow test, pseudo R square, AIC and BIC. Quasi likelihood, construction of quasi likelihood for correlated outcomes, parameter estimation, variance-covariance of estimators, estimation of variance function. Quasi likelihood estimating equations, generalized estimating equations for repeated measures data, repeated measures models for normal data, repeated measures models for non-normal data, working correlation matrix, robust variance estimation or information sandwich estimator, hypothesis testing. Comparison between likelihood and quasi likelihood methods, mixed effect models.