# Regression Analysis of Count Data

## Synopsis

Students in both the natural and social sciences often seek regression models to explain the frequency of events, such as visits to a doctor, auto accidents or job hiring. This analysis provides a comprehensive account of models and methods to interpret such data. The authors have conducted research in the field for nearly fifteen years and in this work combine theory and practice to make sophisticated methods of analysis accessible to practitioners working with widely different types of data and software. The treatment will be useful to researchers in areas such as applied statistics, econometrics, operations research, actuarial studies, demography, biostatistics, quantitatively-oriented sociology and political science. The book may be used as a reference work on count models or by students seeking an authoritative overview. The analysis is complemented by template programs available on the Internet through the authors' homepages.

## Excerpt

This book describes regression methods for count data, where the response variable is a nonnegative integer. the methods are relevant for analysis of counts that arise in both social and natural sciences.

Despite their relatively recent origin, count data regression methods build on an impressive body of statistical research on univariate discrete distributions. Many of these methods have now found their way into major statistical packages, which has encouraged their application in a variety of contexts. Such widespread use has itself thrown up numerous interesting research issues and themes, which we explore in this book.

The objective of the book is threefold. First, we wish to provide a synthesis and integrative survey of the literature on count data regressions, covering both the statistical and econometric strands. the former has emphasized the framework of generalized linear models, exponential families of distributions, and generalized estimating equations; the latter has emphasized nonlinear regression and generalized method of moment frameworks. Yet between them there are numerous points of contact that can be fruitfully exploited. Our second objective is to make sophisticated methods of data analysis more accessible to practitioners with different interests and backgrounds. To this end we consider models and methods suitable for cross-section, time series, and longitudinal data. Detailed analyses of several data sets as well as shorter illustrations, implemented from a variety of viewpoints, are scattered throughout the book to put empirical flesh on theoretical or methodological discussion. We draw on examples from, and give references to, works in many applied areas. Our third objective is to highlight the potential for further research by discussion of issues and problems that need more analysis. We do so by embedding count data models in a larger body of econometric and statistical work on discrete variables and, more generally, on nonlinear regression.

The book can be divided into four parts. Chapters 1 and 2 contain introductory material on count data and a comprehensive review of statistical methods for nonlinear regression models. Chapters 3, 4, 5, and 6 present models and applications for cross-section count data. Chapters 7, 8, and 9 present methods for data other than cross-section data, namely time series, multivariate, and . . .

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