Hypothesis Tests on Mixture Model Components with Applications in Ecology and Agriculture

Abstract

Multiple comparisons are widely used to compare gross features of distributions across populations. However, often a scientific hypothesis is more easily couched in terms of more focused null and alternative statistical hypotheses. For example, among distributions exhibiting clusters of continuous measurements across strata, are there clusters of measurements similar in terms of location, spread, or weight? We propose testing such hypotheses using a sequence of nested finite mixture models. Reasonable, data-driven priors are suggested based on estimates of the sample spreads and midpoints. Formal hypothesis testing is carried out through the computation of Bayes factors. The method is illustrated on Holling’s (Ecological Monographs 62:447–502, 1992) forest and prairie bird body mass data, and data on the time-to-abortion in dairy cows. Supplemental simulations are available online.