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Estimating overdispersion when fitting a generalized linear model to sparse data

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  • D. J. Fletcher

Abstract

We consider the problem of fitting a generalized linear model to overdispersed data, focussing on a quasilikelihood approach in which the variance is assumed to be proportional to that specified by the model, and the constant of proportionality, φ, is used to obtain appropriate standard errors and model comparisons. It is common practice to base an estimate of φ on Pearson's lack-of-fit statistic, with or without Farrington's modification. We propose a new estimator that has a smaller variance, subject to a condition on the third moment of the response variable. We conjecture that this condition is likely to be achieved for the important special cases of count and binomial data. We illustrate the benefits of the new estimator using simulations for both count and binomial data. Copyright 2012, Oxford University Press.

Suggested Citation

  • D. J. Fletcher, 2012. "Estimating overdispersion when fitting a generalized linear model to sparse data," Biometrika, Biometrika Trust, vol. 99(1), pages 230-237.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:1:p:230-237
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    File URL: http://hdl.handle.net/10.1093/biomet/asr083
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    Cited by:

    1. Farzana Afroz & Matt Parry & David Fletcher, 2020. "Estimating overdispersion in sparse multinomial data," Biometrics, The International Biometric Society, vol. 76(3), pages 834-842, September.
    2. Yee, Thomas W., 2014. "Reduced-rank vector generalized linear models with two linear predictors," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 889-902.
    3. Kirsty J MacLeod & Tracy Langkilde & Cameron P Venable & David C Ensminger & Michael J Sheriff, 2021. "The influence of maternal glucocorticoids on offspring phenotype in high- and low-risk environments," Behavioral Ecology, International Society for Behavioral Ecology, vol. 32(6), pages 1330-1338.

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