FINITE MIXTURE-MODELS FOR PROPORTIONS

Six data sets recording fetal control mortality in mouse litters are p resented. The data are clearly overdispersed, and a standard approach would be to describe the data by means of a beta-binomial model or to use quasi-likelihood methods. For five of the examples, we show that t he beta-binomial model provides a reasonable description but that the fit can be significantly improved by using a mixture of a beta-binomia l model with a binomial distribution. This mixture provides two altern ative solutions, in one of which the binomial component indicates a hi gh probability of death but is selected infrequently; this accounts fo r outlying litters with high mortality. The influence of the outliers on the beta-binomial fits is also demonstrated. The location and natur e of the two main maxima to the likelihood are investigated through pr ofile log-likelihoods. Comparisons are made with the performance of fi nite mixtures of binomial distributions.