Negative Binomial Regression, Second Edition
Author: 
Joseph M. Hilbe 
Publisher: 
Cambridge University Press 
Copyright: 
2011 
ISBN13: 
9780521198158 
Pages: 
553; hardcover 
Price: 
$74.50 



Comment from the Stata technical group
Negative Binomial Regression, Second Edition, 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 realworld 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 negative binomial models to various
research problems involving overdispersed count data. Much of the book is
devoted to discussing modelselection techniques, the interpretation of
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 and longitudinal data,
and data from sample selection.
Negative Binomial Regression is aimed at those statisticians,
econometricians, and practicing researchers analyzing countresponse 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.
This second edition includes added material on finitemixture models;
quantilecount models; bivariate negative binomial models; and various
methods of handling endogeneity, including the generalized method of moments.
Table of contents
Preface to the second edition
1. Introduction
1.1 What is a negative binomial model?
1.2 A brief history of the negative binomial
1.3 Overview of the book
2. The concept of risk
2.1 Risk and 2 × 2 tables
2.2 Risk and 2 × k tables
2.3 Risk ratio confidence intervals
2.4 Risk difference
2.5 The relationship of risk to odds ratios
2.6 Marginal probabilities: joint and conditional
3. Overview of count response models
3.1 Varieties of count response model
3.2 Estimation
3.3 Fit considerations
4. Methods of estimation
4.1 Derivation of the IRLS algorithm
4.1.1 Solving for ∂ L or U — the gradient
4.1.2 Solving for ∂^{2} L
4.1.3 The IRLS fitting algorithm
4.2 Newton–Raphson algorithms
4.2.1 Derivation of the Newton–Raphson
4.2.2 GLM with OIM
4.2.3 Parameterizing from μ to x′Β
4.2.4 Maximum likelihood estimators
5. Assessment of count models
5.1 Residuals for count response models
5.2 Model fit tests
5.2.1 Traditional fit tests
5.2.2 Information criteria fit tests
5.3 Validation models
6. Poisson regression
6.1 Derivation of the Poisson model
6.1.1 Derivation of the Poisson from the binomial distribution
6.1.2 Derivation of the Poisson model
6.2 Synthetic Poisson models
6.2.1 Construction of synthetic models
6.2.2 Changing response and predictor values
6.2.3 Changing multivariable predictor values
6.3 Example: Poisson model
6.3.1 Coefficient parameterization
6.3.2 Incidence rate ratio parameterization
6.4 Predicted counts
6.5 Effects plots
6.6 Marginal effects, elasticities, and discrete change
6.6.1 Marginal effects for Poisson and negative binomial effects models
6.6.2 Discrete change for Poisson and negative binomial models
6.7 Parameterization as a rate model
6.7.1 Exposure in time and area
6.7.2 Synthetic Poisson with offset
6.7.3 Example
7. Overdispersion
7.1 What is overdispersion?
7.2 Handling apparent overdispersion
7.2.1 Creation of a simulated base Poisson model
7.2.2 Delete a predictor
7.2.3 Outliers in data
7.2.4 Creation of interaction
7.2.5 Testing the predictor scale
7.2.6 Testing the link
7.3 Methods of handling real overdispersion
7.3.1 Scaling of standard errors / quasiPoisson
7.3.2 Quasilikelihood variance multipliers
7.3.3 Robust variance estimators
7.3.4 Bootstrapped and jackknifed standard errors
7.4 Tests of overdispersion
7.4.1 Score and Lagrange multiplier tests
7.4.2 Boundary likelihood ratio test
7.4.3 R^{2}_{p} and R^{2}_{pd} tests for Poisson and negative binomial models
7.5 Negative binomial overdispersion
8. Negative binomial regression
8.1 Varieties of negative binomial
8.2 Derivation of the negative binomial
8.2.1 Poisson–gamma mixture model
8.2.2 Derivation of the GLM negative binomial
8.3 Negative binomial distributions
8.4 Negative binomial algorithms
8.4.1 NBC: canonical negative binomial
8.4.2 NB2: expected information matrix
8.4.3 NB2: observed information matrix
8.4.4 NB2: R maximum likelihood function
9. Negative binomial regression: modeling
9.1 Poisson versus negative binomial
9.2 Synthetic negative binomial
9.3 Marginal effects and discrete change
9.4 Binomial versus count models
9.5 Examples: negative binomial regression
Example 1: Modeling number of marital affairs
Example 2: Heart procedures
Example 3: Titanic survival data
Example 4: Health reform data
10. Alternative variance parameterizations
10.1 Geometric regression: NB α = 1
10.1.1 Derivation of the geometric
10.1.2 Synthetic geometric models
10.1.3 Using the geometric model
10.1.4 The canonical geometric model
10.2 NB1: The linear negative binomial model
10.2.1 NB1 as QLPoisson
10.2.2 Derivation of NB1
10.2.3 Modeling with NB1
10.2.4 NB1: R maximum likelihood function
10.3 NBC: Canonical negative binomial regression
10.3.1 NBC overview and formulae
10.3.2 Synthetic NBC models
10.3.3 NBC models
10.4 NBH: Heterogeneous negative binomial regression
10.5 The NBP model: generalized negative binomial
10.6 Generalized Waring regression
10.7 Bivariate negative binomial
10.8 Generalized Poisson regression
10.9 Poisson inverse Gaussian regression (PIG)
10.10 Other count models
11. Problems with zero counts
11.1 Zerotruncated count models
11.2 Hurdle models
11.2.1 Theory and formulae for hurdle models
11.2.2 Synthetic hurdle models
11.2.3 Applications
11.2.4 Marginal effects
11.3 Zeroinflated negative binomial models
11.3.1 Overview of ZIP/ZINB models
11.3.2 ZINB algorithms
11.3.3 Applications
11.3.4 Zeroaltered negative binomial
11.3.5 Tests of comparative fit
11.3.6 ZINB marginal effects
11.4 Comparison of models
12. Censored and truncated count models
12.1 Censored and truncated models — econometric parameterization
12.1.1 Truncation
12.1.2 Censored models
12.2 Censored Poisson and NB2 models — survival parameterization
13. Handling endogeneity and latent class models
13.1 Finite mixture models
13.1.1 Basics of finite mixture modeling
13.1.2 Synthetic finite mixture models
13.2 Dealing with endogeneity and latent class models
13.2.1 Problems related to endogeneity
13.2.2 Twostage instrumental variables approach
13.2.3 Generalized method of moments (GMM)
13.2.4 NB2 with an endogenous multinomial treatment variable
13.2.5 Endogeneity resulting from measurement error
13.3 Sample selection and stratification
13.3.1 Negative binomial with endogenous stratification
13.3.2 Sample selection models
13.3.3 Endogenous switching models
13.4 Quantile count models
14. Count panel models
14.1 Overview of count panel models
14.2 Generalized estimating equations: negative binomial
14.2.1 The GEE algorithm
14.2.2 GEE correlation structures
14.2.3 Negative binomial GEE models
14.2.4 GEE goodnessoffit
14.2.5 GEE marginal effects
14.3 Unconditional fixedeffects negative binomial model
14.4 Conditional fixedeffects negative binomial model
14.5 Randomeffects negative binomial
14.6 Mixedeffects negative binomial models
14.6.1 Randomintercept negative binomial models
14.6.2 Nonparametric randomintercept negative binomial
14.6.3 Randomcoefficient negative binomial models
14.7 Multilevel models
15. Bayesian negative binomial models
15.1 Bayesian versus frequentist methodology
15.2 The logic of Bayesian regression estimation
15.3 Applications
Appendix A: Constructing and interpreting interaction terms
Appendix B: Data sets, commands, functions
References and further reading
Index