Factor analysis for ranking data

Abstract

(Uncorrected OCR) Abstract of thesis entitled ’FACTOR ANALYSIS FOR RANKING DATA’ Submitted by Lo Siu Ming For the Degree of Master of Philosophy at The University of Hong Kong in December 1998 This thesis aims at the analysis of preference rankings which allow people’s preference or behaviour to be studied. Some models proposed in the literature for modelling ranking data will be discussed. When the number of ranked items, k, is large, the number of parameters involved in model estimation may be too large which leads to computational infeasible. To solve this problem, an important objective is to reduce the dimensionality of the data. Factor analysis, which achieves much of the above objective, is a sensitive, informative method and is widely used in economical, psychological, sociological or marketing research as a powerful tool to identify the common characteristics among a set of variables. In the context of factor analysis for non-continuous type data, most application are restricted to item response data only. We extend factor analysis for item response data to accommodate ranking data by the Monte Carlo Expectation Maximization (MCEM) algorithm which is an estimation procedure with high efficiency and accuracy. The factor model for ranking data, the corresponding likelihood function and details on the MCEM algorithm for parameter estimation are described. The E-step is implemented via the Gibbs Sampler (Geman and Geman (1984)) which simu- i lates the response utilities based on the observed full rankings. A bridge sampling criterion will be introduced to monitor the convergence of the MCEM algorithm. A model selection method and a goodness-of-fit test of the factor model will also be discussed. The efficiency of the proposed estimation method, selection method and goodness-of-fit test will be illustrated by a simulation study. For illustrative purpose, the methods are used to analyse a set of ranking data collected from a parent and teacher interview survey on pre-school education in which respondents are requested to give their preferences on the relative importance of different goals of pre-school education. Extension to factor analysis for incomplete rankings (rank the top q out of k items and subset rankings) will also be discussed. To illustrate the feasibility of the proposed method, a simulation study is carried out for each of the two types of incomplete rankings. Also, the estimation procedure is applied to a set of incomplete ranking data obtained from a survey carried out in GuangZhou, a major city in Mainland China, to investigate the factors affecting the choice of a job. The MCEM algorithm is also applied to obtain estimates of the factor scores in a factor analysis model with ranking data. The covariance matrix of the estimates, given the observed rankings and factor model parameters, is also derived. Furthermore, the GuangZhou job selection dataset will be revisited and the factor scores of the respondents will be estimated. <