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 func tional relationships between sample size and metric recovery. This paper develops answers to two im portant sample-size questions in nonmetric weight ed 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 recov ery ? The graphs developed to answer the second question illustrate how such functional relation ships can be defined empirically in a wide range of MDS and other complicated nonlinear models.