Single Subject Incomplete Designs for Nonmetric Multidimensional Scaling

Monte Carlo procedures were used to investigate the properties of a nonmetric multidimensional scaling algorithm when used to scale an incomplete matrix of dissimilarities. Various recommendations for users who wish to scale incomplete matrices are made: (a) recovery was found to be satisfactory provided that the “degrees of freedom” ratio exceeded 3.5, irrespective of error level; (b) cyclic designs were found to provide best recovery, although random patterns of deletion performed almost as well; and (c) strongly locally connected designs, specifically overlapping cliques, were generally inferior. These conclusions are based on 837 scaling solutions and are applicable to stimulus sets containing more than 30 objects.