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Testing and Adjusting for Departures from Nominal Dispersion in Generalized Linear Models
Author(s) -
Smith Philip J.,
Heitjan Daniel F.
Publication year - 1993
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347407
Subject(s) - mathematics , statistics , dispersion (optics) , econometrics , physics , optics
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.