Testing and Adjusting for Departures from Nominal Dispersion in Generalized Linear Models

SUMMARY In this paper we describe a score test of the hypothesis of no departure from nominal dispersion in a generalized linear model. We also give a method for adjusting the nominal variance-covariance matrix of the estimated regression coefficients when overdispersion is suspected. This procedure is an alternative to the traditional method of adjusting each element of the variance-covariance matrix by the same factor. We illustrate our method for the one-parameter exponential family of distributions in a logistic analysis of a factorial experiment and a Poisson regression analysis of bioassay data.