Generalized linear models

Author(s)

• McCullagh, Peter
• Nelder, John A.

Bibliographic Information

Generalized linear models

P. McCullagh and J.A. Nelder

（Monographs on statistics and applied probability, 37）

Chapman and Hall, 1989

2nd ed

Note

Bibliography: p. 479-499

Includes indexes

Description and Table of Contents

Description

The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications. The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables. The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions. Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference.

Table of Contents

Preface Introduction Background The Origins of Generalized Linear Models Scope of the Rest of the Book An Outline of Generalized Linear Models Processes in Model Fitting The Components of a Generalized Linear Model Measuring the goodness of Fit Residuals An Algorithm for Fitting Generalized Linear Models Models for Continuous Data with Constant Variance Introduction Error Structure Systematic Component (Linear Predictor) Model Formulae for Linear Predictors Aliasing Estimation Tables as Data Algorithms for Least Squares Selection of Covariates Binary Data Introduction Binomial Distribution Models for Binary Responses Likelihood functions for Binary Data Over-Dispersion Example Models for Polytomous Data Introduction Measurement scales The Multinomical Distribution Likelihood Functions Over-Dispersion Examples Log-Linear Models Introduction Likelihood Functions Examples Log-Linear Models and Multinomial Response Models Multiple responses Example Conditional Likelihoods Introduction Marginal and conditional Likelihoods Hypergeometric Distributions Some Applications Involving Binary data Some Aplications Involving Polytomous Data Models with Constant Coefficient of Variation Introduction The Gamma Distribution Models with Gamma-distributed Observations Examples Quasi-Likelihood Functions Introduction Independent Observations Dependent Observations Optimal Estimating Functions Optimality Criteria Extended Quasi-Likelihood Joint Modelling of Mean and Dispersion Introduction Model Specification Interaction between Mean and Dispersion Effects Extended Quasi-Likelihood as a Criterion Adjustments of the Estimating Equations Joint Optimum Estimating Equations Example: The Production of Leaf-Springs for Trucks Models with Additional Non-Linear Parameters Introduction Parameters in the Variance function Parameters in the Link Function Nonlinear Parameters in the Covariates Examples Model Checking Introduction Techniqes in Model Checking Score Tests for Extra Parameters Smoothing as an Aid to Informal Checks The Raw Materials of Model Checking Checks for systematic Departure from Model Check for isolated Departures from the Model Examples A Strategy for Model Checking? Models for Survival Data Introduction Proportional-Hazards Models Estimation with a Specified Survival distribution Example: Remission Times for Leukemia Cox's Proportional-Hazards Model Components of Dispersion Introduction Linear Models Nonlinear Models Parameter Estimation Example: A Salamander mating Experiment Further Topics Introduction Bias Adjustment Computation of Bartlett Adjustments Generalized Additive Models Appendices Elementary Likelihood Theory Edgeworth Series Likelihood-Ratio Statistics References Index of Data Sets Author Index Subject Index Each chapter also contains Bibliographic Notes and Exercises

by "Nielsen BookData"

Details

• NCID: BA07288691
• ISBN:
  • 0412317605
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: London ; New York
• Pages/Volumes: xix, 511 p.
• Size: 23 cm
• Classification:
  • LCC : QA276
  • DC19 : 519.5
• Subject Headings:
  • LCSH : Linear models (Statistics)
• Parent Bibliography ID:
  • BA00231539