Statistics Seminars: A grade of membership model for rank data
30 November 2009 14:15 in CM221
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.
Rank data arise when a set of judges rank, in order of their preference, some or all of a set of objects. Such data arise in a wide range of contexts: in preferential voting systems, in market research surveys and in university application procedures. Modelling preference data in an appropriate manner is imperative when examining the behaviour of the set of judges who give rise to the data. Here the Plackett-Luce model for rank data is employed as an appropriate modelling tool. Combining the Plackett-Luce model with the GoM modelling framework gives rise to the GoM model for rank data.
Parameter inference for the GoM model for rank data is achieved in a Bayesian setting using a Markov Chain Monte Carlo (MCMC) algorithm. A Metropolis-within-Gibbs sampler is used for model fitting, but the intricate nature of the rank data model 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.
(joint research with Thomas Brendan Murphy)
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