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基本説明
Features: Addresses a class of statistical models that generalizes classical linear models-extending them to include many other models useful in statistical analysis. Incorporates numerous exercises, both theoretical and data-analytic. Holds particular interest for statisticians in medicine, biology, agriculture, social science, and engineering.
Full 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.
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, Pa
