Now showing 1 - 4 of 4
  • Publication
    A mixture of experts model for rank data with applications in election studies
    (Institute of Mathematical Statistics, 2008-12) ;
    A voting bloc is defined to be a group of voters who have similar voting preferences. The cleavage of the Irish electorate into voting blocs is of interest. Irish elections employ a 'single transferable vote' electoral system; under this system voters rank some or all of the electoral candidates in order of preference. These rank votes provide a rich source of preference information from which inferences about the composition of the electorate may be drawn. Additionally, the influence of social factors or covariates on the electorate composition is of interest. A mixture of experts model is a mixture model in which the model parameters are functions of covariates. A mixture of experts model for rank data is developed to provide a model-based method to cluster Irish voters into voting blocs, to examine the influence of social factors on this clustering and to examine the characteristic preferences of the voting blocs. The Benter model for rank data is employed as the family of component densities within the mixture of experts model; generalized linear model theory is employed to model the influence of covariates on the mixing proportions. Model fitting is achieved via a hybrid of the EM and MM algorithms. An example of the methodology is illustrated by examining an Irish presidential election. The existence of voting blocs in the electorate is established and it is determined that age and government satisfaction levels are important factors in influencing voting in this election.
      336Scopus© Citations 82
  • Publication
    A grade of membership model for rank data
    (International Society for Bayesian Analysis (ISBA), 2009-06) ;
    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-withinGibbs 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.
    Scopus© Citations 35  301
  • Publication
    Clustering ranked preference data using sociodemographic covariates
    Ranked preference data arise when a set of judges rank, in order of their preference, a set of objects. Such data arise in preferential voting systems and market research surveys. Covariate data associated with the judges are also often recorded. Such covariate data should be used in conjunction with preference data when drawing inferences about judges. To cluster a population of judges, the population is modelled as a collection of homogeneous groups. The Plackett-Luce model for ranked data is employed to model a judge’s ranked preferences within a group. A mixture of Plackett-Luce models is employed to model the population of judges, where each component in the mixture represents a group of judges. Mixture of experts models provide a framework in which covariates are included in mixture models. Covariates are included through the mixing proportions and the component density parameters. A mixture of experts model for ranked preference data is developed by combining a mixture of experts model and a mixture of Plackett-Luce models. Particular attention is given to the manner in which covariates enter the model. The mixing proportions and group specific parameters are potentially dependent on covariates. Model selection procedures are employed to choose optimal models. Model parameters are estimated via the ‘EMM algorithm’, a hybrid of the Expectation-Maximization and the Minorization-Maximization algorithms. Examples are provided through a menu survey and through Irish election data. Results indicate mixture modelling using covariates is insightful when examining a population of judges who express preferences.
      648