Generalized Linear Models

ISBN-13: 9780412317606 / Angielski / Twarda / 1989 / 532 str.

A ccullagh P. Nel

Opis

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.

Recenzje

"... an important, useful book, well-written by two authorities in the field..."
-Times Higher Education Supplement
"... an enormous range of work is covered... represents, perhaps, the most important field of research in theoretical and practical statistics. For all statisticians working in this field, the book is essential."
-Short Book Reviews
"... this is a rich book; rich in theory, rich in examples, and rich in a statistical sense. I highly recommend it."
-Biometrics
"... a definitive and unified presentation...by the outstanding experts of this field."
-Statistics
"This is a wonderful book... Reading the book is like listening to a good lecturer. The authors present the material clearly, and they treat the reader with respect. There is a balance between discussion, mathematical presentation of models, and examples."
-Technometrics

"... a complete introduction to the topic in a single monograph... a very readable book that provides the reader with great insight into a vast array of data analysis techniques...
-Siam Review

"... a unique and useful text for intermediate undergraduate teaching."
-THES

Spis treści

PrefaceIntroductionBackgroundThe Origins of Generalized Linear ModelsScope of the Rest of the BookAn Outline of Generalized Linear ModelsProcesses in Model FittingThe Components of a Generalized Linear ModelMeasuring the goodness of FitResidualsAn Algorithm for Fitting Generalized Linear ModelsModels for Continuous Data with Constant VarianceIntroductionError StructureSystematic Component (Linear Predictor)Model Formulae for Linear PredictorsAliasingEstimationTables as DataAlgorithms for Least SquaresSelection of CovariatesBinary Data IntroductionBinomial DistributionModels for Binary ResponsesLikelihood functions for Binary DataOver-DispersionExampleModels for Polytomous DataIntroductionMeasurement scalesThe Multinomical DistributionLikelihood FunctionsOver-DispersionExamplesLog-Linear ModelsIntroductionLikelihood FunctionsExamplesLog-Linear Models and Multinomial Response ModelsMultiple responsesExampleConditional LikelihoodsIntroductionMarginal and conditional LikelihoodsHypergeometric DistributionsSome Applications Involving Binary dataSome Aplications Involving Polytomous DataModels with Constant Coefficient of VariationIntroductionThe Gamma DistributionModels with Gamma-distributed ObservationsExamplesQuasi-Likelihood FunctionsIntroductionIndependent ObservationsDependent ObservationsOptimal Estimating FunctionsOptimality CriteriaExtended Quasi-LikelihoodJoint Modelling of Mean and DispersionIntroductionModel SpecificationInteraction between Mean and Dispersion EffectsExtended Quasi-Likelihood as a CriterionAdjustments of the Estimating EquationsJoint Optimum Estimating EquationsExample: The Production of Leaf-Springs for TrucksModels with Additional Non-Linear ParametersIntroductionParameters in the Variance functionParameters in the Link FunctionNonlinear Parameters in the CovariatesExamplesModel CheckingIntroductionTechniqes in Model CheckingScore Tests for Extra ParametersSmoothing as an Aid to Informal ChecksThe Raw Materials of Model CheckingChecks for systematic Departure from ModelCheck for isolated Departures from the ModelExamplesA Strategy for Model Checking?Models for Survival DataIntroductionProportional-Hazards ModelsEstimation with a Specified Survival distributionExample: Remission Times for LeukemiaCox's Proportional-Hazards ModelComponents of DispersionIntroductionLinear ModelsNonlinear ModelsParameter EstimationExample: A Salamander mating ExperimentFurther TopicsIntroductionBias AdjustmentComputation of Bartlett AdjustmentsGeneralized Additive ModelsAppendicesElementary Likelihood TheoryEdgeworth SeriesLikelihood-Ratio StatisticsReferencesIndex of Data SetsAuthor IndexSubject Index Each chapter also contains Bibliographic Notes and Exercises

O autorze

P. McCullagh