This book presents statistical methods for the analysis of events. The primary focus is on single equation cross section models. The book addresses both the methodology and the practice of the subject and it provides both a synthesis of a diverse body of literature that hitherto was available largely in pieces, as well as a contribution to the progress of the methodology, establishing several new results and introducing new models. Starting from the standard Poisson regression model as a benchmark, the causes, symptoms and consequences of misspecification are worked out. Both parametric and semi-parametric alternatives are discussed. While semi-parametric models allow for robust interference, parametric models can identify features of the underlying data generation process.
Evaluates the most useful models for categorical and limited dependent variables (CLDVs), emphasizing the links among models and applying common methods of derivation, interpretation, and testing. The author also explains how models relate to linear regression models whenever possible. Annotation c.
This study presents several extensions of the most familiar models for count data, the Poisson and negative binomial models. We develop an encompassing model for two well-known variants of the negative binomial model (the NB1 and NB2 forms). We then analyze some alternative approaches to the standard log gamma model for introducing heterogeneity into the loglinear conditional means for these models. The lognormal model provides a versatile alternative specification that is more flexible (and more natural) than the log gamma form, and provides a platform for several "two part" extensions, including zero inflation, hurdle, and sample selection models. (We briefly present some alternative approaches to modeling heterogeneity.) We also resolve some features in Hausman, Hall and Griliches (1984, Economic models for count data with an application to the patents-R & D relationship, Econometrica 52, 909-938) widely used panel data treatments for the Poisson and negative binomial models that appear to conflict with more familiar models of fixed and random effects. Finally, we consider a bivariate Poisson model that is also based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed methods using the data employed in one of the two aforementioned bivariate Poisson studies
Statistical Methods for Overdispersed Count Data provides a review of the most recent methods and models for such data, including a description of R functions and packages that allow their implementation. All methods are illustrated on datasets arising in the field of health economics. As several tools have been developed to tackle over-dispersed and zero-inflated data (such as adjustment methods and zero-inflated models), this book covers the topic in a comprehensive and interesting manner. - Includes reading on several levels, including methodology and applications - Presents the state-of-the-art on the most recent zero-inflated regression models - Contains a single dataset that is used as a common thread for illustrating all methodologies - Includes R code that allows the reader to apply methodologies
The goal of the book is to make easier to carry out the computations necessary for the full interpretation of regression nonlinear models for categorical outcomes usign Stata.
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.
The goal of this book is multidimensional: a) to help reviving Statistics education in many parts in the world where it is in crisis. For the first time authors from many developing countries have an opportunity to write together with the most prominent world authorities. The editor has spent several years searching for the most reputable statisticians all over the world. International contributors are either presidents of the local statistical societies, or head of the Statistics department at the main university, or the most distinguished statisticians in their countries. b) to enable any non-statistician to obtain quick and yet comprehensive and highly understandable view on certain statistical term, method or application c) to enable all the researchers, managers and practicioners to refresh their knowledge in Statistics, especially in certain controversial fields. d) to revive interest in statistics among students, since they will see its usefulness and relevance in almost all branches of Science.