Statistica Sinica 11(2001), 445-461
BAYESIAN ANALYSIS OF WANDERING VECTOR MODELS
FOR DISPLAYING RANKING DATA
Philip L. H. Yu and Lucia K. Y. Chan
The University of Hong Kong
Abstract:
In a process of examining 
objects, each judge provides a ranking of them.
The aim of this paper is to investigate a probabilistic model for ranking
data--the wandering vector model. The model represents objects by points in a
-dimensional space, and the judges are represented by latent vectors
emanating from the origin in the same space. Each judge samples a vector from
a multivariate normal distribution; given this vector, the judge's utility
assigned to an object is taken to be the length of the orthogonal projection of
the object point onto the judge vector, plus a normally distributed random
error. The ordering of the
utilities given by the judge determines the
judge's ranking. A Bayesian approach and the Gibbs sampling technique are used
for parameter estimation. The method of computing the marginal likelihood
proposed by Chib (1995) is used to select the dimensionality of the model.
Simulations are done to demonstrate the proposed estimation and model selection
method. We then analyze the Goldberg data, in which 10 occupations are ranked
according to the degree of social prestige.
Key words and phrases:
Bayesian approach, Gibbs sampling, marginal likelihood, ranking data, wandering
vector model.