Generalized Linear Models, Second Edition
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.
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Preface to the first edition xvi
An outline of generalized linear models
Models for continuous data with constant variance
Models for polytomous data
Models with constant coefficient of variation
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algorithm analysis approximation assumed assumption asymptotic bivariate Chapter coefficient of variation column components computed conditional distribution consider constant contrasts corresponding covariance matrix cumulants defined degrees of freedom density depends derivative deviance discussed dispersion parameter dose effect estimating equations estimating functions example exponential factor Fisher information Fisher information matrix fitted values gamma gamma distribution given gives independent information matrix interaction inverse iteration levels likelihood function linear logistic model linear models linear predictor link function log likelihood log-linear model logistic model marginal maximum maximum-likelihood estimate mean method model formula multinomial multinomial distribution non-linear Normal distribution nuisance parameters observed obtained over-dispersion parameter estimates plot Poisson Poisson distribution probabilities quadratic quasi-likelihood random variables regression models response sample scale score score statistic Show standard errors statistic sum of squares Suppose Table totals transformation usually var(Y variance function vector weights zero