Multidimensional scaling of derived dissimilarities

Fritz Drasgow, Lawrence E. Jones

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)227-244
Number of pages18
JournalMultivariate Behavioral Research
Volume14
Issue number2
DOIs
StatePublished - Jan 4 1979

ASJC Scopus subject areas

  • Statistics and Probability
  • Experimental and Cognitive Psychology
  • Arts and Humanities (miscellaneous)

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