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

摘要

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