Canadian Journal of Statistics

Overdispersed poisson regression models for studies of air pollution and human health

Journal Article

Abstract

This paper presents results from a simulation study motivated by a recent study of the relationships between ambient levels of air pollution and human health in the community of Prince George, British Columbia. The simulation study was designed to evaluate the performance of methods based on overdispersed Poisson regression models for the analysis of series of count data. Aspects addressed include estimation of the dispersion parameter, estimation of regression coefficients and their standard errors, and the performance of model selection tests. The effects of varying amounts of overdispersion and differing underlying variance structure on this performance were of particular interest. This study is related to work reported by Breslow (1990) although the context is quite different. Preliminary work led to the conclusion that estimation of the dispersion parameter should be based on Pearson's chi‐square statistic rather than the Poisson deviance. Regression coefficients are well estimated, even in the présence of substantial overdispersion and when the model for the variance function is incorrectly specified. Despite potential greater variability, the empirical estimator of the covariance matrix is preferred because the model‐based estimator is unreliable in general. When the model for the variance function is incorrect, model‐based test statistics may perform poorly, in sharp contrast to empirical test statistics, which performed very well in this study.

Related Topics

Related Publications

Related Content

Site Footer

Address:

This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on StatisticsViews.com are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and StatisticsViews.com express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.