| Vast amount of preference data arise from daily life or scientific research, where observations consist of preferences on a set of available objects. The observations are usually recorded by ranking data or multinomial data. Sometimes, there is not a clear preference between two objects, which will result in ranking data with ties, also called censored rank-ordered data. To study such kind of data, we develop a symmetric Bayesian probit model based on Thurstone's random utility (discriminal process) assumption. However, parameter identification is always an unavoidable problem for probit model, i.e., determining the location and scale of latent utilities. The standard identification method need to specify one of the utilities as a base, and then model the differences of the other utilities subtracted by the base. However, Bayesian predictions have been verified to be sensitive to specification of the base in the case of multinomial data. In this thesis, we set the average of the whole set of utilities as a base which is symmetric to any relabeling of objects. Based on this new base, we propose a symmetric identification approach to fully identify multinomial probit model. Furthermore, we design a Bayesian algorithm to fit that model. By simulation study and real data analysis, we find that this new probit model not only can be identified well, but also remove sensitivities mentioned above. In what follows, we generalize this probit model to fit general censored rank-ordered data. Correspondingly, we get the symmetric Bayesian censored rank-ordered probit model. At last, we apply this model to analyze Hong Kong horse racing data successfully.;Keywords: Discrete Choice model, Censored Rank-Ordered Probit model, Bayesian Analysis, Ranking data, Multinomial data, MNP. |
