Confidence Intervals in Generalized Regression Models

Abstract

Introduction Likelihood-Based Statistical Inference Statistical evidence Statistical inference Likelihood concepts and law of likelihood Likelihood-based methods Profile likelihood-based confidence intervals Likelihood ratio tests (LRTs) Maximum likelihood estimate (MLE) Model selection Generalized Regression Model Examples of regression data Definition of generalized regression models (GRMs) Special cases of GRM Likelihood inference MLE with iterative reweighted least squares Model checking General Linear Model Definition of the general linear model (GLM) Estimate of regression coefficients Test of linear hypotheses Confidence regions and intervals Model checking Nonlinear Regression Model Definition of the nonlinear regression model Estimate of regression parameters Approximate distribution of LRT statistic Profile likelihood-based confidence region Profile likelihood-based confidence interval LRT for a hypothesis on finite set of functions Model checking Generalized Linear Model Definition of generalized linear model (GLIM) MLE of regression coefficients Binomial and Logistic Regression Models Data Binomial distribution Link functions Likelihood inference Logistic regression model Models with other link functions Nonlinear binomial regression model Poisson Regression Model Data Poisson distribution Link functions Likelihood inference Log-linear model Multinomial Regression Data Multinomial distribution Likelihood function Logistic multinomial regression model Proportional odds regression model Other Generalized Linear Regressions Models Negative binomial regression model Gamma regression model Other Generalized Regression Models Weighted GLM Weighted nonlinear regression model Quality design or Taguchi model Lifetime regression model Cox regression model Appendix A: Data Sets Appendix B: Notation Used for Statistical Models Bibliographic notes appear at the end of each chapter.