Statistical models for rank data

Abstract

Rank data arise when a set of judges rank some or all of a set of objects. Rank data emerges in many areas of society; the list of the world’s most cited scientists or the final ordering of horses in a race provide examples of such data. Irish society generates a wealth of rank data in two specific contexts: applicants to Irish third level educational institutions rank degree courses in order of preference and under the Irish electoral system voters rank candidates in order of preference. The relationships that may exist between the set of objects ranked and between the judges who rank them are explored in this thesis. The set of applicants to Irish third level institutions in the year 2000 are investigated to determine if groups of similar applicants exist and if so, what characteristics they share. Voters and candidates from the 1997 Irish presidential election and from the 2002 Irish general election are examined. The (dis)similarities that the Irish electorate deem to exist between candidates are revealed. Complex rank data models are developed which take account of the ranked nature of the data. Mixture models, and extensions thereof, are used to model heteroge­neous populations which generate rank data; a latent space model is also proposed which locates the ranked objects in an unobservable space. Model fitting is performed in both classical and Bayesian frameworks. Unique model fitting techniques are necessary due to the complex nature of the models. Examining fitted model parameters provides insight to the underlying mecha­nisms which drive Irish social opinions. Applicants to Irish third level institutions are in.uenced by course discipline, an institutions’ geographical location and by course prestige. Evidence of both candidate orientated and politically driven voters is also presented.