A Bayesian approach to modeling group and individual differences in multidimensional scaling

Abstract

Multidimensional scaling (MDS) models of mental representation assume stimuli are represented by points in a low-dimensional space, such that more similar stimuli are represented by points closer to each other. We consider possible individual differences in MDS representations, using the recently proposed K-INDSCAL model, which allows for both sub-groups of people with different representations, and individual differences in the attention people give to different stimulus dimensions. We develop a novel Bayesian implementation of the K-INDSCAL model, and demonstrate in a simulation study it is capable of inferring meaningful individual differences for the sorts of data sets typically available in psychology. We then apply the model to three existing data sets, involving the taste of colas, images of cats, and colors of different hues. Collectively, the results demonstrate the flexibility of the K-INDSCAL model in finding both group- and individual-level differences, and highlight the need for Bayesian methods to make these inferences.