Probabilistic Multidimensional Scaling: Complete and Incomplete Data

Abstract

Simple procedures are described for obtaining maximum likelihood estimates of the location and uncertainty parameters of the Hefner model. This model is a probabilistic, multidimensional scaling model, which assigns a multivariate normal distribution to each stimulus point. It is shown that for such a model, standard nonmetric and metric algorithms are not appropriate. A procedure is also described for constructing incomplete data sets, by taking into consideration the degree of familiarity the subject has for each stimulus. Maximum likelihood estimates are developed both for complete and incomplete data sets.