Multidimensional Scaling of Binary Dissimilarities: Direct and Derived Approaches

Given a matrix of dissimilarities, it has been debated whether researchers should perform multidimensional scaling on this original matrix or on a new one derived by comparing rows in the original matrix. Careful comparison studies (Drasgow & Jones, 1979; Van der Kloot & Van Herk, 1991) in the context of sorting data indicated that most of the initial enthusiasm for the derivative approach was unfounded. The current work, a Monte Carlo study of structured binary data derived from known two-dimensional configurations using ALSCAL, complements and extends the previous studies. We discuss a weakness in the squared difference (δ) row-comparison rule used previously and propose an alternative row-comparison measure based on the Jaccard coefficient. Scaling the binary data directly gave better performance, as gauged by Procrustes statistics, than did scaling A data across a range of noise levels. The quality of solutions obtained by scaling Jaccard data was always better or essentially equal to that from scaling δ data, and in certain parameter regions improved upon that of direct scaling. Another alternative approach, applying the δ rule after first row-centering the binary data, was found to be generally ineffective. These findings are pertinent to the analysis not just of stimulus sorting data but of coarse dissimilarities generally, for example from direct pairwise judgment tasks and in fields outside statistical psychology.