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 □2L 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／z 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/quasi-Poisson 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 7.4.1 Score and Lagrange multiplier tests 7.4.2 Boundary likelihood ratio test 7.4.3 Rp2 and Rpd2 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 NB-C： 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 NB 1： The linear negative binomial model 10.2.1 NBI as QL-Poisson
10.2.2 Derivation of NB1 10.2.3 Modeling with NB1 10.2.4 NB I：R maximum likelihood function 10.3 NB-C： Canonical negative binomial regression 10.3.1 NB-C overview and formulae 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 Problems with zero counts 11.1 Zero-truncated 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 Zero-inflated negative binomial models 11.3.1 Overview of ZIP／ZINB 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 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 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 13.3.1 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 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 14.6.1 Random-intercept 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 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
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