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Biometrika 1978 65(3):591-602; doi:10.1093/biomet/65.3.591
© 1978 by Biometrika Trust
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Inference sensitivity for Poisson mixtures

S. R. PAUL and R. L. PLACKETT

Department of Statistics, University of Newcastle upon Tyne

Data presented as contingency tables and classified by qualitative or quantitative methods are usually analysed on the basis of a Poisson log linear model. We examine the effect of Poisson mixtures, especially as represented by the negative binomial distribution, on statistical inference. The main finding is that probabilities of rejection are increased, sometimes considerably. In the case of heterogeneous binary data, attention is also given to the problems of analysis implied by Poisson mixtures.

Key Words: Beta-binomial • Binary data • Compound multinomial • Contingency table • Heterogeneity • Log linear models • Negative binomial • Poisson mixture


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