Negative Binomial Regression
by Joseph M. Hilbe
Negative Binomial Regression, by
Joseph M. Hilbe, reviews the negative binomial model and its
variations. Negative binomial regression—a recently popular alternative
to Poisson regression—is used to account for overdispersion, which is
often encountered in many real-world applications with count responses.
Negative Binomial Regression covers the count response models, their
estimation methods, and the algorithms used to fit these models. Hilbe
details the problem of overdispersion and ways to handle it. The book
emphasizes the application of the negative binomial models to various
research problems involving overdispersed count data. Much of the book
is devoted to discussing model-selection techniques, the interpretation
of the results, regression diagnostics, and methods of assessing
goodness-of-fit.
Hilbe uses Stata extensively throughout the book to display examples.
He describes various extensions of the negative binomial model: those
that handle excess zeros, censored and truncated data,
panel/longitudinal data, and data from sample selection.
Negative Binomial Regression is aimed at those statisticians,
econometricians, and practicing researchers analyzing count-response
data. The book is written for a reader with a general background in
maximum likelihood estimation and generalized linear models, but Hilbe
includes enough mathematical details to satisfy the more
theoretically-minded reader.
Table of contents
Preface
Introduction
1 Overview of count response models
- 1.1 Varieties of count response model
1.2 Estimation
1.3 Fit considerations
1.4 Brief history of the negative binomial
1.5 Summary
2 Methods of estimation
2.1 Derivation of the IRLS algorithm
2.2 Newton–Raphson algorithms
2.3 The exponential family
2.4 Residuals for count response models
2.5 Summary
3 Poisson regression
- 3.1 Derivation of the Poisson model
3.2 Parameterization as a rate
3.3 Testing overdispersion
3.4 Summary
4 Overdispersion
- 4.1 What is overdispersion?
4.2 Handling apparent overdispersion
4.3 Methods of handling real overdispersion
4.4 Summary
5 Negative binomial regression
5.1 Varieties of negative binomial
5.2 Derivation of the negative binomial
5.3 Negative binomial distributions
5.4 Algorithms
5.5 Summary
6 Negative binomial regression: modeling
- 6.1 Poisson versus negative binomial
6.2 Binomial versus count models
6.3 Examples: negative binomial regression
6.4 Summary
7 Alternative variance parameterization
- 7.1 Geometric regression
7.2 NB-1: The linear constant model
7.3 NB-H: Heterogeneous negative binomial regression
7.4 The NB-P model
7.5 Generalized Poisson regression
7.6 Summary
8 Problems with zero counts
- 8.1 Zero-truncated negative binomial
8.2 Negative binomial with endogenous stratification
8.3 Hurdle models
8.4 Zero-inflated count models
8.5 Summary 9 Negative binomial with censoring, truncation, and sample selection
- 9.1 Censored and truncated models—econometric parameterization
9.2 Censored poisson and NB-2 models—survival parameterization
9.3 Sample selection models
9.4 Summary
10 Negative binomial panel models
- 10.1 Unconditional fixed-effects negative binomial model
10.2 Conditional fixed-effects negative binomial model
10.3 Random-effects negative binomial
10.4 Generalized estimating equation
10.5 Multilevel negative binomial models
10.6 Summary Appendix A: Negative binomial log-likelihood functions
Appendix B: Deviance functions
Appendix C: Stata negative binomial—ML algorithm
Appendix D: Negative binomial variance functions
Appendix E: Data sets
References
Author Index
Subject Index
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