title: Finite mixture models for proportions.
abstract: Six data sets recording fetal control mortality in mouse litters are presented. 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 beta-binomial model provides a reasonable description but that the fit can be significantly improved by using a mixture of a beta-binomial model with a binomial distribution. This mixture provides two alternative solutions, in one of which the binomial component indicates a high probability of death but is selected infrequently; this accounts for outlying litters with high mortality. The influence of the outliers on the beta-binomial fits is also demonstrated. The location and nature of the two main maxima to the likelihood are investigated through profile log-likelihoods. Comparisons are made with the performance of finite mixtures of binomial distributions.
authors.affiliation: School of Mathematics, University of Bristol, U.K.
authors.forename: S P
authors.initials: SP
authors.lastname: Brooks
authors.forename: B J
authors.initials: BJ
authors.lastname: Morgan
authors.forename: M S
authors.initials: MS
authors.lastname: Ridout
authors.forename: S E
authors.initials: SE
authors.lastname: Pack
mesh_terms: D000818:Animals; D016010:Binomial Distribution; D001699:Biometry / Q000379:methods; D005260:Female; D005313:Fetal Death; D008098:Litter Size; D051379:Mice; D015233:Models, Statistical; D009010:Monte Carlo Method; D011247:Pregnancy; D011336:Probability; D015203:Reproducibility of Results; D012107:Research Design