A. Colin Cameron

Regression Analysis of Count Data: Author Index

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 25 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 two 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.

Regression Analysis of Count Data: List of Tables

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 25 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 two 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.

Robust Inference with Multi-way Clustering

In this article we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit, and GMM. This variance estimator enables cluster-robust inference when there is two-way or multiway clustering that is nonnested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g., Liang and Zeger 1986; Arellano 1987) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state–year effects example of Bertrand, Duflo, and Mullainathan (2004) to two dimensions; and by application to studies in the empirical literature where two-way clustering is present.

Bootstrap-Based Improvements for Inference with Clustered Errors

Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (5-30) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo and Mullainathan (2004). Rejection rates of ten percent using standard methods can be reduced to the nominal size of five percent using our methods.

A Practitioner's Guide to Cluster-Robust Inference

We consider statistical inference for regression when data are grouped into clusters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year differences-in-differences studies with clustering on state. In such settings, default standard errors can greatly overstate estimator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specific fixed effects, few clusters, multiway clustering, and estimators other than OLS.

Regression-based tests for overdispersion in the Poisson model

Abstract A property of the Poisson regression model is mean-variance equality, conditional on explanatory variables. ‘Regression-based’ tests for this property are proposed in a very general setting. Unlike classical statistical tests, these tests require specification of only the mean-variance relationship under the alternative, rather than the complete distribution whose choice is usually arbitrary. The optimal regression-based test is easily computed as the t-test from an auxiliary regression. If a distribution under the alternative hypothesis is in fact specified and is in the Katz system of distributions or is Coxs local approximation to the Poisson, the score test for the Poisson distribution is equivalent to the optimal regression-based test.

An R-squared measure of goodness of fit for some common nonlinear regression models

Abstract For regression models other than the linear model, R -squared type goodness-of-fit summary statistics have been constructed for particular models using a variety of methods. We propose an R -squared measure of goodness of fit for the class of exponential family regression models, which includes logit, probit, Poisson, geometric, gamma, and exponential. This R -squared is defined as the proportionate reduction in uncertainty, measured by Kullback-Leibler divergence, due to the inclusion of regressors. Under further conditions concerning the conditional mean function it can also be interpreted as the fraction of uncertainty explained by the fitted model.

R-Squared Measures for Count Data Regression Models With Applications to Health-Care Utilization

R-squared measures of goodness of fit for count data are rarely, if ever, reported in empirical studies or by statistical packages. We propose several R-squared measures based on various definitions of residuals for the basic Poisson regression model and for more general models such as negative binomial that accommodate overdispersed data. The preferred R-squared measure is based on the deviance residual. An application to data on health-care-service utilization measured in counts illustrates the performance and usefulness of the various R-squared measures.

Count Data Regression Using Series Expansions: With Applications

Most research on count data regression models, i.e. models for there the dependent variable takes only non-negative integer values or count values, has focused on the univariate case. Very little attention has been given to joint modeling of two or more counts. We propose parametric regression models for bivariate counts based on squared polynomial expansions around a baseline density. The models are more flexible than the current leading bivariate count model, the bivariate Poisson. The models are applied to data on the use of prescribed and nonprescribed medications.

The role of income and health risk in the choice of health insurance: Evidence from Australia

Abstract Health insurance choice is investigated using individual data from Australia where all people faced a common limited set of possible health insurance policies. The data cover two separate regimes: one in which insurance choice was for a more generous level of coverage; and one in which the choice was a more dramatic one between insurance and no insurance coverage. In determining health insurance choice, the results indicate a major role for income; a major role for premium, notably in the first regime; and a minor role for observed factors related to health risk, aside from age and sex.