Multidimensional Scaling Of Derived Dissimilarities

In past research, a matrix of squared profile distances, δ, has sometimes been multidimensionally scaled rather than the matrix of original dissimilarities, D. It is thought that scaling solutions derived from δ have lower stress and enhanced interpretability when applied to data generated by sorting. Two experiments were performed to investigate the consequences of the delta transformation. First, random numbers resembling data collected by the method of sorting were simulated. Scaling solutions derived from δ matrices invariably had lower stress than solutions computed from the associated D matrices. This result suggests that the delta transformation may reduce stress irrespective of any change in interpretability. Simulated dissimilarity matrices were then generated from known stimulus configurations. It was found that: (1) nonmetric multidimensional scaling solutions for δ matrices had relatively lower stress; but under low error conditions (2) solution based on D were more closely related to the underlying configurations; and (3) determination of dimensionality by inspection of the stress plot was somewhat more difficult for solutions based on δ. These results can be understood by observing that the delta transformation tends to increase the size of large distances in the derived configurations relative to small distances.