Matrix and stimulus sample sizes in the weighted MDS model: Empirical metric recovery functions

Abstract

The only guidelines for sample size that exist in the multidimensional scaling (MDS) literature are a set of heuristic "rules-of-thumb" that have failed to live up to Young’s (1970) goal of finding functional relationships between sample size and metric recovery. This paper develops answers to two important sample-size questions in nonmetric weighted MDS settings, both of which are extensions of work reported in MacCallum and Cornelius (1977): (1) are the sample size requirements for number of stimuli and number of matrices compensatory? and (2) what type of functional relationships exist between the number of matrices and metric recovery ? The graphs developed to answer the second question illustrate how such functional relationships can be defined empirically in a wide range of MDS and other complicated nonlinear models. Index terms: metnc recovery, monte carlo study, multidimensional scaling, sample size, weighted multidimensional scaling.