Journal Article

On the use of corrections for overdispersion

Lindsey, J. K.

1999

Overview

In studying fluctuations in the size of a blackgrouse (Tetrao tetrix) population, an autoregressive model using climatic conditions appears to follow the changes quite well. However, the deviance of the model is considerably larger than its number of degrees of freedom. A widely used statistical rule of thumb holds that overdispersion is present in such situations, but model selection based on a direct likelihood approach can produce opposing results. Two further examples, of binomial and of Poisson data, have models with deviances that are almost twice the degrees of freedom and yet various overdispersion models do not fit better than the standard model for independent data. This can arise because the rule of thumb only considers a point estimate of dispersion, without regard for any measure of its precision. A reasonable criterion for detecting overdispersion is that the deviance be at least twice the number of degrees of freedom, the familiar Akaike information criterion, but the actual presence of overdispersion should then be checked by some appropriate modelling procedure.

• Publisher: Blackwell Publishers Ltd,Blackwell Publishers,Blackwell,Royal Statistical Society
• Subject: Akaike information criterion / Beta-binomial distribution / Binomial distributions / Binomials / Birds / Climate models / Correlations / Degrees of freedom / Direct likelihood inference / Exact sciences and technology / Frequentism / Habitats / Inference / Mathematical foundations / Mathematics / Modelling / Negative binomial distribution / Overdispersion / Parametric inference / Parametric models / Population / Probability and statistics / Sciences and techniques of general use / Standard error / Statistical methods / Statistical models / Statistical variance / Statistics