A latent variable model for multidimensional unfolding

In multidimensional unfolding technique, preference data are fitted to the distances between the points associated with subjects and stimuli, but the joint estimation of subject and stimulus points is statistically undesirable. To avoid this difficulty, we propose a latent variable model for metric unfolding, in which subject points are regarded as normally-distributed random variables, whereas stimulus ones are treated as unknown fixed parameters. Marginal likelihood, defined by integrating out subject points, is maximized over stimulus point parameters, using an EM algorithm. After stimulus points are obtained, subject points are given by Bayes posterior means. The proposed method recovered true points well in a simulation study and showed better fitting to real data than factor analysis. Finally, its relations to other unfolding methods are discussed.