Statistical Modelling 9 (2009), 137–150
Clustered binary data with random cluster sizes:
a dual poisson modelling approach
Renjun Ma
Department of Mathematics and Statistics,
University of New Brunswick,
Fredericton, E3B 5A3 New Brunswick
Canada
eMail:
renjun@unb.ca
Bent Jørgensen
Department of Statistics,
University of Southern Denmark
Denmark
Jon Douglas Willms
Canadian Research Institute for Social Policy,
University of New Brunswick
Canada
Abstract:
In the analysis of clustered binary data with random cluster sizes,
traditional approaches assuming fixed cluster sizes are generally used.
Appropriate inference should take account of both intra-cluster
correlation and extra-variation arising from the random cluster sizes.
We introduce a dual Poisson random effects model for performing
appropriate analyses of such data. Our orthodox best linear unbiased
predictor approach to this model depends only on the first- and
second-moment assumptions of unobserved random effects. This approach
is illustrated with analyses of seed germination data and developmental
toxicity data.
Keywords:
Best linear unbiased predictor; logistic regression; mixed model;
overdispersion; random effects
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