Determining the Dimensionality of Multidimensional Scaling Representations for Cognitive Modeling

Michael D. Lee
2001 Journal of Mathematical Psychology  
Multidimensional scaling models of stimulus domains are widely used as a representational basis for cognitive modeling. These representations associate stimuli with points in a coordinate space that has some predetermined number of dimensions. Although the choice of dimensionality can significantly influence cognitive modeling, it is often made on the basis of unsatisfactory heuristics. To address this problem, a Bayesian approach to dimensionality determination, based on the Bayesian
more » ... n Criterion (BIC), is developed using a probabilistic formulation of multidimensional scaling. The BIC approach formalizes the trade-off between data-fit and model complexity implicit in the problem of dimensionality determination and allows for the explicit introduction of information regarding data precision. Monte Carlo simulations are presented that indicate, by using this approach, the determined dimensionality is likely to be accurate if either a significant number of stimuli are considered or a reasonable estimate of precision is available. The approach is demonstrated using an established data set involving the judged pairwise similarities between a set of geometric stimuli. Academic Press COGNITIVE MODELING AND MULTIDIMENSIONAL SCALING Multidimensional scaling techniques (Shepard, 1962; Kruskal, 1964; see Cox 6 Cox, 1994, for a recent overview) generate spatial representations of stimulus sets based on information regarding the similarity relationships existing between the stimuli. Typically, each stimulus is identified with a point in a coordinate space such that the distance between representative points decreases as the similarity of the corresponding stimuli increases. The spatial nature of these representations means that they are well suited to practical application in the context of data
doi:10.1006/jmps.1999.1300 pmid:11178927 fatcat:necqxxmd75gw3n24tlnkzu33jq