A grade of membership model for rank data

Abstract

A grade of membership (GoM) model is an individual level mixture model which allows individuals have partial membership of the groups that characterize a population. A GoM model for rank data is developed to model the particular case when the response data is ranked in nature. A Metropolis-within-Gibbs sampler provides the framework for model fitting, but the intricate nature of the rank data models makes the selection of suitable proposal distributions difficult. `Surrogate' proposal distributions are constructed using ideas from optimization transfer algorithms. Model fitting issues such as label switching and model selection are also addressed. The GoM model for rank data is illustrated through an analysis of Irish election data where voters rank some or all of the candidates in order of preference. Interest lies in highlighting distinct groups of voters with similar preferences (i.e. `voting blocs') within the electorate, taking into account the rank nature of the response data, and in examining individuals' voting bloc memberships. The GoM model for rank data is fitted to data from an opinion poll conducted during the Irish presidential election campaign in 1997.