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

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  • Philip J. Smith
  • Daniel F. Heitjan

Abstract

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.

Suggested Citation

  • Philip J. Smith & Daniel F. Heitjan, 1993. "Testing and Adjusting for Departures from Nominal Dispersion in Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(1), pages 31-41, March.
    • Handle: RePEc:bla:jorssc:v:42:y:1993:i:1:p:31-41
    DOI: 10.2307/2347407
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    Cited by:

    1. Vanegas, Luis Hernando & Rondón, Luz Marina & Cysneiros, Francisco José A., 2012. "Diagnostic procedures in Birnbaum–Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1662-1680.
    2. Bo-Cheng Wei & Jian-Qing Shi & Wing-Kam Fung & Yue-Qing Hu, 1998. "Testing for Varying Dispersion in Exponential Family Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 277-294, June.
    3. Zhu, Zhongyi & Fung, Wing K., 2004. "Variance component testing in semiparametric mixed models," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 107-118, October.

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