Negative Binomial Regression Review

Negative Binomial Regression
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The first edition of this book was one of the first on this topic. The text is is very comprehensive, covering count models in general, the common Poisson regression model and its generalization to over-and-under dispersion with all the various forms of the negative binomial regression model. The Poisson distribution has the property that its mean and variance are the same. When sample estimates of variance are significantly higher (lower) than the estimated mean, the model is said to be overdispersed (underdispersed).
The main additions in the second edition of the book are the advances in software to estimate parameters of the various negative binomial models. Hilbe describes the currently available software in SAS, SPSS and STATA as well as the econometric package LIMDEP.
The book covers the historical development of the negative binomial regression model. It is primarily an applied text with numerous examples and demonstration of the various software products. As with all of Joe Hilbe's books, this text is thorough and scholarly with an extensive list of references. Important theorems and other theoretical results are given but are presented to be imformative rather than to develop and teach the theory. The text is well-written and for the most part easy to understand. Emphasis is on computation and goodness of fit of the models. Although both overdispersion and underdispersion are covered overdispersion is emphasized as Hilbe sees it as the most common departure from the Poisson model.

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This second edition of Hilbe's Negative Binomial Regression is a substantial enhancement to the popular first edition. The only text devoted entirely to the negative binomial model and its many variations, nearly every model discussed in the literature is addressed. The theoretical and distributional background of each model is discussed, together with examples of their construction, application, interpretation and evaluation. Complete Stata and R codes are provided throughout the text, with additional code (plus SAS), derivations and data provided on the book's website. Written for the practising researcher, the text begins with an examination of risk and rate ratios, and of the estimating algorithms used to model count data. The book then gives an in-depth analysis of Poisson regression and an evaluation of the meaning and nature of overdispersion, followed by a comprehensive analysis of the negative binomial distribution and of its parameterizations into various models for evaluating count data.

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