Generalized Linear Models and Extensions, Second Edition

Generalized Linear Models and Extensions, Second Edition provides a comprehensive overview of the nature and scope of generalized linear models (GLMs) and of the major changes to the basic GLM algorithm that allow modeling of data that violate GLM distributional assumptions. Deftly balancing theory and application, the book stands out in its coverage of the derivation of the GLM families and their foremost links, while also guiding readers in the application of the various models to real data. This edition has new sections on discrete response models, including zero-truncated, zero-inflated, censored, and hurdle count models, as well as heterogeneous negative binomial, generalized Poisson, and generalized binomial models. The book also includes a substantially expanded discussion of both proportional-odds and generalized ordered models, making it easy for readers to use these models in their own research.

Table of Contents:
From the first edition: Introduction Origins and motivation Notational conventions Applied or theoretical? Road map PART I: FOUNDATIONS OF GENERALIZED LINEAR MODELS Generalized Linear Models Components Assumptions Exponential family Example: Using an offset in a GLM Summary GLM Estimation Algorithms Newton-Raphson Starting values for Newton-Raphson Fisher scoring Starting values for IRLS Goodness of fit Estimated variance matrices Estimation algorithms Summary Analysis of Fit Deviance Diagnostics Assessing the link function Checks for systematic departure from the model Residual analysis Model statistics PART II: CONTINUOUS RESPONSE MODELS The Gaussian Family Derivation of the GLM Gaussian family Derivation in terms of the mean IRLS GLM algorithm (non-binomial) Maximum likelihood estimation GLM log-normal models Expected versus observed information matrix Other Gaussian links Example: Relation to OLS The Gamma Family Derivation of the gamma model Example: Reciprocal link Maximum likelihood estimation Log-gamma models Identity-gamma models Using the gamma model for survival analysis The Inverse Gaussian Family Derivation of the inverse Gaussian model The inverse Gaussian algorithm Maximum likelihood algorithm Example: The canonical inverse Gaussian Non-canonical links The Power Family and Link Power links Example: Power link The power family PART III: BINOMIAL RESPONSE MODELS The Binomial-Logit Family Derivation of the binomial model Derivation of the Bernoulli model The binomial regression algorithm Example: Logistic regression Goodness-of-fit statistics Interpretation of parameter estimates The General Binomial Family Non-canonical binomial models Non-canonical binomial links (binary form) The probit model The complementary log-log and log-log models Other links Interpretation of coefficients The Problem of Overdispersion Overdispersion Scaling of standard errors Williams' procedure Robust standard errors PART IV: COUNT RESPONSE MODELS The Poisson Family Count response regression models Derivation of the Poisson algorithm Poisson regression: Examples Example: Testing overdispersion in the Poisson model Using the Poisson model for survival analysis Using offsets to compare models Interpretation of coefficients The Negative Binomial Family Constant overdispersion Variable overdispersion The log-negative binomial parameterization Negative binomial examples The geometric family Generalized negative binomial Interpretation of coefficients PART V: MULTINOMIAL RESPONSE MODELS The Ordered Response Family Ordered outcomes for general link Ordered logit Ordered probit Generalized ordered logit Example: Synthetic data Example: Automobile data Unordered Response Family The multinomial logit model The multinomial probit model PART VI: EXTENSIONS TO THE GLM Extending the Likelihood The quasi-likelihood Example: Wedderburn's leaf blotch data Generalized additive models Clustered Data Generalization from individual to clustered data Pooled estimators PART VII: STATA SOFTWARE Programs for Stata Syntax Syntax for predict Description Options User-written programs Remarks Tables References Author Index Subject Index