Pseudo R-squared measures for Poisson regression models with over- or underdispersion

The Poisson regression model is frequently used to analyze count data. Pseudo R-squared measures for Poisson regression models have recently been proposed and bias adjustments recommended in the presence of small samples and/or a large number of covariates. In practice, however, data are often over- or sometimes even underdispersed as compared to the standard Poisson model. The definition of Poisson R-squared measures can be applied in these situations as well, albeit with bias adjustments accordingly adapted. These adjustments are motivated by arguments of quasi-likelihood theory. Properties of unadjusted and adjusted R-squared measures are studied by simulation under standard Poisson; over- and underdispersed Poisson regression models and their use is exemplified and discussed with popcorn data. (C) 2003 Elsevier B.V. All rights reserved.