Confidence Intervals in Generalized Regression Models

Series:
Statistics: A Series of Textbooks and Monographs
Published:
July 25, 2008 by Chapman and Hall/CRC - 328 Pages
Author(s):
Esa Uusipaikka, University of Turku, Finland

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$104.95
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ISBN 9781420060270
Cat# C6027
 

Features

  • Provides the first comprehensive text entirely devoted to handling GRMs
  • Presents a unified way of calculating likelihood-based confidence intervals in GRMs
  • Introduces the concept of residuals in GRMs
  • Includes a DVD with restricted versions of Mathematica® and the author’s own Statistical Inference Package (SIP) for Windows, Linux, and Mac
  • Supplies SIP and R code for several likelihood-based inference examples online

    • Summary

    A Cohesive Approach to Regression Models

    Confidence Intervals in Generalized Regression Models introduces a unified representation—the generalized regression model (GRM)—of various types of regression models. It also uses a likelihood-based approach for performing statistical inference from statistical evidence consisting of data and its statistical model.

    Provides a Large Collection of Models

    The book encompasses a number of different regression models, from very simple to more complex ones. It covers the general linear model (GLM), nonlinear regression model, generalized linear model (GLIM), logistic regression model, Poisson regression model, multinomial regression model, and Cox regression model. The author also explains methods of constructing confidence regions, profile likelihood-based confidence intervals, and likelihood ratio tests.

    Uses Statistical Inference Package to Make Inferences on Real-Valued Parameter Functions

    Offering software that helps with statistical analyses, this book focuses on producing statistical inferences for data modeled by GRMs. It contains numerical and graphical results while providing the code online.

    Table of Contents

    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.

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