TY - JOUR
T1 - Multidimensional scaling of derived dissimilarities
AU - Drasgow, Fritz
AU - Jones, Lawrence E.
N1 - Funding Information:
The research reported herein was supported by National Science Foundation Grant No. NSF-GS 42801 to L. E. Jones and N,.H irschberg. Computing fhnds were provided by the University of Illinois Research Board. The authors wish to thank Drs. Ledyard R Tucker, Michael V. Levine and J. Douglas Ca~rroll for their helpful comments and suggestions. Address reprint requests to Fritz Drasgow, Department of Psychology, University of Illinois, Champaign, Illinois 61820.
PY - 1979/1/4
Y1 - 1979/1/4
N2 - In past research, a matrix of squared profile distances, 3, has sometimes been multidimensionally scaled rather than the matrix of original dissimilarities, D. It is thought that scaling solutions derived from 5 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 S 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) solutions 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.
AB - In past research, a matrix of squared profile distances, 3, has sometimes been multidimensionally scaled rather than the matrix of original dissimilarities, D. It is thought that scaling solutions derived from 5 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 S 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) solutions 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.
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U2 - 10.1207/s15327906mbr1402_7
DO - 10.1207/s15327906mbr1402_7
M3 - Article
AN - SCOPUS:0011362409
SN - 0027-3171
VL - 14
SP - 227
EP - 244
JO - Multivariate Behavioral Research
JF - Multivariate Behavioral Research
IS - 2
ER -