At last - a book devoted to the negative binomial model and its many variations. Every model currently offered in commercial statistical software packages is discussed in detail - how each is derived, how each resolves a distributional problem, and numerous examples of their application. Many have never before been thoroughly examined in a text on count response models: the canonical negative binomial; the NB-P model, where the negative binomial exponent is itself parameterized; and negative binomial mixed models. As the models address violations of the distributional assumptions of the basic Poisson model, identifying and handling overdispersion is a unifying theme. For practising researchers and statisticians who need to update their knowledge of Poisson and negative binomial models, the book provides a comprehensive overview of estimating methods and algorithms used to model counts, as well as specific guidelines on modeling strategy and how each model can be analyzed to access goodness-of-fit.

• First book devoted entirely to the negative binomial model and all its varieties • Every model currently offered in a commercial statistical software package is discussed in detail; data sets and additional code on a companion website • Includes end of chapter review questions allowing readers to monitor their understanding of the material presented

### Contents

Preface; Introduction; 1. Overview of count response models; 2. Methods of estimation; 3. The Poisson model; 4. Overdispersion; 5. Negative binomial regression: basics; 6. Negative binomial regression: modeling; 7. Alternative variance parameterizations; 8. Problems with zero counts; 9. Negative binomial with censoring, truncation, and sample selection; 10. Negative binomial panel models; Appendix A: Negative binomial log-likelihood functions; Appendix B: Deviance functions; Appendix C: ML negative binomial Code; Appendix D: Negative binomial variance functions; Appendix E: Data sets; References; Author index; Index.

### Reviews

'I would recommend this book to researchers and students who would like to gain an overview of the negative binomial distribution and its extensions.' Fiona McElduff, University College London

'The text is well-written, easy-to-read but once started, is difficult to put down as each chapter unfolds the intricacies of the distribution.' International Statistical Review

'Every model currently offered in commercial statistical software is discussed in detail…well written and can serve as an excellent reference book for applied statisticians who would use negative binomial regression modelling for undergraduate students or graduate students.' Yuehua Wu, Zentralblatt MATH