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Preface to the second edition1 Introduction1£®1 What is a negative binomial model 1£®2 A brief history of the negative binomial1£®3 Overview of the book2 The concept of risk2£®1 Risk and 2¡Á2 tables2£®2 Risk and 2¡Ák tables2£®3 Risk ratio confidence intervals2£®4 Risk difference2£®5 The relationship of risk to odds ratios2£®6 Marginal probabilities£º joint and conditional3 Overview of count response models3£®1 Varieties of count response model3£®2 Estimation3£®3 Fit considerations4 Methods of estimation4£®1 Derivation of the IRLS algorithm4£®1£®1 Solving for ¡õl or U¡ª the gradient4£®1£®2 Solving for ¡õ2L4£®1£®3 The IRLS fitting algorithm4£®2 Newton¡ªRaphson algorithms4£®2£®1 Derivation of the Newton¡ªRaphson4£®2£®2 GLM with OIM4£®2£®3 Parameterizing from£¯z to x'¦Â4£®2£®4 Maximum likelihood estimators5 Assessment of count models5£®1 Residuals for count response models5£®2 Model fit tests5£®2£®1 Traditional fit tests5£®2£®2 Information criteria fit tests5£®3 Validation models6 Poisson regression6£®1 Derivation of the Poisson model6£®1£®1 Derivation of the Poisson from the binomial distribution6£®1£®2 Derivation of the Poisson model6£®2 Synthetic Poisson models6£®2£®1 Construction of synthetic models6£®2£®2 Changing response and predictor values6£®2£®3 Changing multivariable predictor values6£®3 Example£º Poisson model6£®3£®1 Coefficient parameterization6£®3£®2 Incidence rate ratio parameterization6£®4 Predicted counts6£®5 Effects plots6£®6 Marginal effects£¬ elasticities£¬ and discrete change6£®6£®1 Marginal effects for Poisson and negative binomial effects models6£®6£®2 Discrete change for Poisson and negative binomial models6£®7 Parameterization as a rate model6£®7£®1 Exposure in time and area6£®7£®2 Synthetic Poisson with offset6£®7£®3 Example7 Overdispersion7£®1 What is overdispersion 7£®2 Handling apparent overdispersion7£®2£®1 Creation of a simulated base Poisson model7£®2£®2 Delete a predictor7£®2£®3 Outliers in data7£®2£®4 Creation of interaction7£®2£®5 Testing the predictor scale7£®2£®6 Testing the link7£®3 Methods of handling real overdispersion7£®3£®1 Scaling of standard errors/quasi-Poisson7£®3£®2 Quasi-likelihood variance multipliers7£®3£®3 Robust variance estimators7£®3£®4 Bootstrapped and jackknifed standard errors7£®4 Tests of overdispersion7£®4£®1 Score and Lagrange multiplier tests7£®4£®2 Boundary likelihood ratio test7£®4£®3 Rp2 and Rpd2 tests for Poisson and negative binomial models7£®5 Negative binomial overdispersion8 Negative binomial regression8£®1 Varieties of negative binomial8£®2 Derivation of the negative binomial8£®2£®1 Poisson¡ªgamma mixture model8£®2£®2 Derivation of the GLM negative binomial8£®3 Negative binomial distributions8£®4 Negative binomial algorithms8£®4£®1 NB-C£º canonical negative binomial8£®4£®2 NB2£º expected information matrix8£®4£®3 NB2£º observed information matrix8£®4£®4 NB2£º R maximum likelihood function9 Negative binomial regression£º modeling9£®1 Poisson versus negative binomial9£®2 Synthetic negative binomial9£®3 Marginal effects and discrete change9£®4 Binomial versus count models9£®5 Examples£º negative binomial regressionExample 1£ºModeling number of marital affairsExample 2£ºHeart proceduresExample 3£ºTitanic survival dataExample 4£ºHealth reform data10 Alternative variance parameterizations10£®1 Geometric regression£º NB ¦Á=110£®1£®1 Derivation of the geometric10£®1£®2 Synthetic geometric models10£®1£®3 Using the geometric model10£®1£®4 The canonical geometric model10£®2 NB 1£º The linear negative binomial model10£®2£®1 NBI as QL-Poisson10£®2£®2 Derivation of NB110£®2£®3 Modeling with NB110£®2£®4 NB I£ºR maximum likelihood function10£®3 NB-C£º Canonical negative binomial regression10£®3£®1 NB-C overview and formulae10£®3£®2 Synthetic NB¡ªC models10£®3£®3 NB-C models10£®4 NB-H£º Heterogeneous negative binomial regression10£®5 The NB-P model£º generalized negative binomial10£®6 Generalized Waring regression10£®7 Bivariate negative binomial10£®8 Generalized Poisson regression10£®9 Poisson inverse Gaussian regression £¨PIG£©10£®10 Other count models11 Problems with zero counts11£®1 Zero-truncated count models11£®2 Hurdle models11£®2£®1 Theory and formulae for hurdle models11£®2£®2 Synthetic hurdle models11£®2£®3 Applications11£®2£®4 Marginal effects11£®3 Zero-inflated negative binomial models11£®3£®1 Overview of ZIP£¯ZINB models11£®3£®2 ZINB algorithms11£®3£®3 Applications11£®3£®4 Zero-altered negative binomial11£®3£®5 Tests of comparative fit11£®3£®6 ZINB marginal effects11£®4 Comparison of models12 Censored and truncated count models12£®1 Censored and truncated models-econometric parameterization12£®1£®1 Truncation12£®1£®2 Censored models12£®2 Censored Poisson and NB2 models-survival parameterization13 Handling endogeneity and latent class models13£®1 Finite mixture models13£®1£®1 Basics of finite mixture modeling13£®1£®2 Synthetic finite mixture models13£®2 Dealing with endogeneity and latent class models13£®2£®1 Problems related to endogeneity13£®2£®2 Two-stage instrumental variables approach13£®2£®3 Generalized method of moments £¨GMM£©13£®2£®4 NB2 with an endogenous multinomial treatment variable13£®2£®5 Endogeneity resulting from measurement error13£®3 Sample selection and stratification13£®3£®1 Negative binomial with endogenous stratification13£®3£®2 Sample selection models13£®3£®3 Endogenous switching models13£®4 Quantile count models14 Count panel models14£®1 Overview of count panel models14£®2 Generalized estimating equations£º negative binomial14£®2£®1 The GEE algorithm14£®2£®2 GEE correlation structures14£®2£®3 Negative binomial GEE models14£®2£®4 GEE goodness-of-fit14£®2£®5 GEE marginal effects14£®3 Unconditional fixed-effects negative binomial model14£®4 Conditional fixed-effects negative binomial model14£®5 Random-effects negative binomial14£®6 Mixed-effects negative binomial models14£®6£®1 Random-intercept negative binomial models14£®6£®2 Non-parametric random-intercept negative binomial14£®6£®3 Random-coefficient negative binomial models14£®7 Multilevel models15 Bayesian negative binomial models15£®1 Bayesian versus frequentist methodology15£®2 The logic of Bayesian regression estimation15£®3 ApplicationsAppendix A£ºConstructing and interpreting interaction termsAppendix B£ºData sets£¬ commands£¬ functionsReferences and further readingIndex