Analysis Of Ranking Data Based On Genralized Thurstone Model

In statistics, the statistical analysis of ranking data is a useful tool, playing an important role. The fields of application of this kind of analysis are quite wide, covering Marketing Research, Socio-Political studies, Quality Evaluation assessment, etc. In particular, according to research the ranking data, it can be easily exploited both to study the preferences of consumers towards different items or products with different combinations of attributes, and to assess the satisfaction of customers towards facilities, services, etc. Therefore, it is of practical significance to analyze the ranking data.Modeling how we choose among alternatives, or more generally, modeling preferences, is one of the core topics of study in Psychology. Preferences can be studied experimentally using a variety of procedures, one of the oldest being the method of paired comparisons.Thurstone proposed a class of models for paired comparison data, which produced a great impact. In 1931, he also suggested Thurstone model which is suitable for ranking data (ranking data can be transformed into paired comparison data). Based on the paired comparison method, Maydeu-Olivares model proposed Thurstone model (especially Thurstone V model). Thurstone's model is simply a multivariate normal density with an structured mean vector and covariance matrix that has been dichotomized. Thus, dealing with ranking data, the estimate of Thurstone model need to calculate high-dimensional integration of normal density function. The calculation of this high-dimensional integration is very difficult; in order not to calculate it, this paper presents three types of treatment:A stochastic approximation Monte Carlo (SAMC) algorithm; the preference distribution assumed to be extreme value distribution, and the preference distribution assumed to be negative extreme value distribution. And through the analysis of horse race data, we estimate the parameter and calculate the values of AIC respectively to compare these three treatment methods.