Introduction to generalized linear models

Introduction Background Scope Notation Distributions Related to the Normal Distribution Quadratic Forms Estimation Model Fitting Introduction Examples Some Principles of Statistical Modeling Notation and Coding for Explanatory Variables Exponential Family and Generalized Linear Models Introduction Exponential Family of Distributions Properties of Distributions in the Exponential Family Generalized Linear Models Examples Estimation Introduction Example: Failure Times for Pressure Vessels Maximum Likelihood Estimation Poisson Regression Example Inference Introduction Sampling Distribution for Score Statistics Taylor Series Approximations Sampling Distribution for MLEs Log-Likelihood Ratio Statistic Sampling Distribution for the Deviance Hypothesis Testing Normal Linear Models Introduction Basic Results Multiple Linear Regression Analysis of Variance Analysis of Covariance General Linear Models Binary Variables and Logistic Regression Probability Distributions Generalized Linear Models Dose Response Models General Logistic Regression Model Goodness-of-Fit Statistics Residuals Other Diagnostics Example: Senility and WAIS Nominal and Ordinal Logistic Regression Introduction Multinomial Distribution Nominal Logistic Regression Ordinal Logistic Regression General Comments Poisson Regression and Log-Linear Models Introduction Poisson Regression Examples of Contingency Tables Probability Models for Contingency Tables Log-Linear Models Inference for Log-Linear Models Numerical Examples Remarks Survival Analysis Introduction Survivor Functions and Hazard Functions Empirical Survivor Function Estimation Inference Model Checking Example: Remission Times Clustered and Longitudinal Data Introduction Example: Recovery from Stroke Repeated Measures Models for Normal Data Repeated Measures Models for Non-Normal Data Multilevel Models Stroke Example Continued Comments Bayesian Analysis Frequentist and Bayesian Paradigms Priors Distributions and Hierarchies in Bayesian Analysis WinBUGS Software for Bayesian Analysis Methods Why Standard Inference Fails Monte Carlo Integration Markov Chains Bayesian Inference Diagnostics of Chain Convergence Bayesian Model Fit: The DIC Example Bayesian Analyses Introduction Binary Variables and Logistic Regression Nominal Logistic Regression Latent Variable Model Survival Analysis Random Effects Longitudinal Data Analysis Some Practical Tips for WinBUGS Software References Index Exercises appear at the end of each chapter.