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