Regression analysis of count data - Cameron, Adrian Colin; Trivedi, P. K. (2013)
"Students in both social and natural sciences often seek regression methods to explain the frequency of events, such as visits to a doctor, auto accidents, or new patents awarded. This book provides the most comprehensive and up-to-date account of models and methods to interpret such data. The authors have conducted research in the field for more than twenty-five years. In this book, they combine theory and practice to make sophisticated methods of analysis accessible to researchers and practitioners working with widely different types of data and software in areas such as applied statistics, econometrics, marketing, operations research, actuarial studies, demography, biostatistics, and quantitative social sciences. The book may be used as a reference work on count models or by students seeking an authoritative overview. Complementary material in the form of data sets, template programs, and bibliographic resources can be accessed on the Internet through the authors' homepages. This second edition is an expanded and updated version of the first, with new empirical examples and more than one hundred new references added. The new material includes new theoretical topics, an updated and expanded treatment of cross-section models, coverage of bootstrap-based and simulation-based inference, expanded treatment of time series, multivariate and panel data, expanded treatment of endogenous regressors, coverage of quantile count regression, and a new chapter on Bayesian methods"--
"Introduction God made the integers, all the rest is the work of man. - Kronecker. This book is concerned with models of event counts. An event count refers to the number of times an event occurs, for example the number of airline accidents or earthquakes. An event count is the realization of a nonnegative integer-valued random variable. A univariate statistical model of event counts usually specifies a probability distribution of the number of occurrences of the event known up to some parameters. Estimation and inference in such models is concerned with the unknown parameters, given the probability distribution and the count data. Such a specification involves no other variables and the number of events is assumed to be independently identically distributed (iid). Much early theoretical and applied work on event counts was carried out in the univariate framework. The main focus of this book, however, is regression analysis of event counts. The statistical analysis of counts within the framework of discrete parametric distributions for univariate iid random variables has a long and rich history (Johnson, Kemp, and Kotz, 2005). The Poisson distribution was derived as a limiting case of the binomial by Poisson (1837). Early applications include the classic study of Bortkiewicz (1898) of the annual number of deaths from being kicked by mules in the Prussian army. A standard generalization of the Poisson is the negative binomial distribution. It was derived by Greenwood and Yule (1920), as a consequence of apparent contagion due to unobserved heterogeneity, and by Eggenberger and Polya (1923) as a result of true contagion"--
Includes bibliographical references (pages 511-541) and indexes.
Keywords: Regression analysis; Econometrics; BUSINESS & ECONOMICS / Econometrics