The Annals of Applied Statistics

A mixture of experts model for rank data with applications in election studies

Isobel Claire Gormley and Thomas Brendan Murphy

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Abstract

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.

Article information

Source
Ann. Appl. Stat., Volume 2, Number 4 (2008), 1452-1477.

Dates
First available in Project Euclid: 8 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1231424218

Digital Object Identifier
doi:10.1214/08-AOAS178

Mathematical Reviews number (MathSciNet)
MR2655667

Zentralblatt MATH identifier
05505363

Keywords
Rank data mixture models generalized linear models EM algorithm MM algorithm

Citation

Gormley, Isobel Claire; Murphy, Thomas Brendan. A mixture of experts model for rank data with applications in election studies. Ann. Appl. Stat. 2 (2008), no. 4, 1452--1477. doi:10.1214/08-AOAS178. https://projecteuclid.org/euclid.aoas/1231424218


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