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Statistical Evaluation of Measures of Fit in the Lingoes-Borg Procrustean Individual Differences Scaling

Published online by Cambridge University Press:  01 January 2025

Rolf Langeheine
Rolf Langeheine*
Affiliation:
Institute for Science Education at the University of Kiel
*
Requests for reprints and/or the volume of the simulation norms should be sent to: Rolf Langeheine, IPN at the University of Kiel, Olshausenstr. 40-60, D-2300 Kiel 1, Federal Republic of Germany.
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Abstract

PINDIS, as recently presented by Lingoes and Borg [1978] not only marks the latest development within the scope of individual differences scaling, but, may be of benefit in some closely related topics, such as target analysis. Decisions on whether the various models available from PINDIS fit fallible data are relatively arbitrary, however, since a statistical theory of the fit measures is lacking. Using Monte Carlo simulation, expected fit measures as well as some related statistics were therefore obtained by scaling sets of 4(4)24 random configurations of 5(5)30 objects in 2, 3, and 4 dimensions (individual differences case) and by fitting one random configuration to a fixed random target for 5(5)30 objects in 2, 3, and 4 dimensions (target analysis case). Applications are presented.

Keywords

individual differences scalingprocrustean transformationsmatrix fittingtarget analysisconfiguration similarityMonte Carlo evaluation
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 4 , December 1982 , pp. 427 - 442
Copyright
Copyright © 1982 The Psychometric Society

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Footnotes

The author wishes to thank Ingwer Borg and Peter Schönemann, along with several anonymous reviewers, for a number of suggestions concerning this paper.

References

Reference Note

Langeheine, R. Approximate norms and significance tests for the Lingoes-Borg procrustean individual differences scaling (PINDIS), 1980, Kiel: Institute for Science Education.Google Scholar

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