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 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 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 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 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.
This second edition includes added material on finite-mixture models; quantile-count models; bivariate negative binomial models; and various methods of handling endogeneity, including the generalized method of moments.
1.2 A brief history of the negative binomial
1.3 Overview of the book
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
3.2 Estimation
3.3 Fit considerations
4.1.2 Solving for ∂2 L
4.1.3 The IRLS fitting algorithm
4.2 Newton–Raphson algorithms
4.2.2 GLM with OIM
4.2.3 Parameterizing from μ to x′Β
4.2.4 Maximum likelihood estimators
5.2 Model fit tests
5.2.2 Information criteria fit tests
5.3 Validation models
6.1 Derivation of the Poisson model
6.1.2 Derivation of the Poisson model
6.2 Synthetic Poisson models
6.2.2 Changing response and predictor values
6.2.3 Changing multivariable predictor values
6.3 Example: Poisson model
6.3.2 Incidence rate ratio parameterization
6.4 Predicted counts
6.5 Effects plots
6.6 Marginal effects, elasticities, and discrete change
6.6.2 Discrete change for Poisson and negative binomial models
6.7 Parameterization as a rate model
6.7.2 Synthetic Poisson with offset
6.7.3 Example
7.2 Handling apparent overdispersion
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
7.3.2 Quasi-likelihood variance multipliers
7.3.3 Robust variance estimators
7.3.4 Bootstrapped and jackknifed standard errors
7.4 Tests of overdispersion
7.4.2 Boundary likelihood ratio test
7.4.3 R2p and R2pd tests for Poisson and negative binomial models
7.5 Negative binomial overdispersion
8.2 Derivation of the negative binomial
8.2.2 Derivation of the GLM negative binomial
8.3 Negative binomial distributions
8.4 Negative binomial algorithms
8.4.2 NB2: expected information matrix
8.4.3 NB2: observed information matrix
8.4.4 NB2: R maximum likelihood function
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 2: Heart procedures
Example 3: Titanic survival data
Example 4: Health reform data
10.1 Geometric regression: NB α = 1
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
10.2.2 Derivation of NB1
10.2.3 Modeling with NB1
10.2.4 NB1: R maximum likelihood function
10.3 NB-C: Canonical negative binomial regression
10.3.2 Synthetic NB-C models
10.3.3 NB-C models
10.4 NB-H: Heterogeneous negative binomial regression
10.5 The NB-P 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
11.2 Hurdle models
11.2.2 Synthetic hurdle models
11.2.3 Applications
11.2.4 Marginal effects
11.3 Zero-inflated negative binomial models
11.3.2 ZINB algorithms
11.3.3 Applications
11.3.4 Zero-altered negative binomial
11.3.5 Tests of comparative fit
11.3.6 ZINB marginal effects
11.4 Comparison of models
12.1 Censored and truncated models — econometric parameterization
12.1.2 Censored models
12.2 Censored Poisson and NB2 models — survival parameterization
13.1 Finite mixture models
13.1.2 Synthetic finite mixture models
13.2 Dealing with endogeneity and latent class models
13.2.2 Two-stage 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
13.3.2 Sample selection models
13.3.3 Endogenous switching models
13.4 Quantile count models
14.2 Generalized estimating equations: negative binomial
14.2.2 GEE correlation structures
14.2.3 Negative binomial GEE models
14.2.4 GEE goodness-of-fit
14.2.5 GEE marginal effects
14.3 Unconditional fixed-effects negative binomial model
14.4 Conditional fixed-effects negative binomial model
14.5 Random-effects negative binomial
14.6 Mixed-effects negative binomial models
14.6.2 Non-parametric random-intercept negative binomial
14.6.3 Random-coefficient negative binomial models
14.7 Multilevel models
15.2 The logic of Bayesian regression estimation
15.3 Applications
