Generalized Linear Models, Second EditionThe 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
An outline of generalized linear models | 24 |
Models for continuous data with constant variance | 48 |
Binary data | 98 |
Models for polytomous data | 149 |
Loglinear models | 193 |
Conditional likelihoods | 245 |
Models with constant coefficient of variation | 285 |
Quasilikelihood functions | 323 |
Model checking | 391 |
Models for survival data | 419 |
Components of dispersion | 432 |
Further topics | 455 |
Appendices | 469 |
References | 479 |
500 | |
506 | |
Joint modelling of mean and dispersion | 357 |
Models with additional nonlinear parameters | 372 |
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Common terms and phrases
algorithm analysis approximation assumption asymptotic B₁ Biometrika bivariate Chapter coefficient of variation components computed conditional distribution consider constant contrasts corresponding covariance matrix cumulants degrees of freedom density depends derivative deviance discussed dispersion parameter effect estimating equations estimating functions example exponential factor Fisher information Fisher information matrix fitted values gamma distribution given independent information matrix interaction inverse iteration J. R. Statist 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 Nelder non-linear nuisance parameters observed obtained over-dispersion parameter estimates plot Poisson Poisson distribution probabilities quadratic quasi-likelihood random variables regression models residual response sample scale score score statistic Show standard errors sum of squares Suppose Table totals transformation usually variance function vector weights Y₁ zero