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Random Effects Diagonal Metric Multidimensional Scaling Models

Published online by Cambridge University Press:  01 January 2025

Douglas B. Clarkson  and
Richard Gonzalez
Douglas B. Clarkson*
Affiliation:
Data Analysis Products Division, MathSoft, Inc.
Richard Gonzalez
Affiliation:
University of Michigan
*
Requests for reprints should be sent to Douglas Clarkson, Dala Analysis Products Division, MathSoft, Inc., 1700 Westlake Ave. N., Suite 500, Seattle, WA, 98109-3044. E-Mail: [email protected]
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Abstract

By assuming a distribution for the subject weights in a diagonal metric (INDSCAL) multidimensional scaling model, the subject weights become random effects. Including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the INDSCAL, ALSCAL, and other multidimensional scaling programs. Unlike traditional models, the number of parameters does not increase with the number of subjects, and, because the distribution of the subject weights is modeled, the construction of linear models of the subject weights and the testing of those models is immediate. Here we define a random effects diagonal metric multidimensional scaling model, give computational algorithms, describe our experiences with these algorithms, and provide an example illustrating the use of the model and algorithms.

Keywords

multidimensional scalingrandom coefficients
Type
Articles
Information
Psychometrika , Volume 66 , Issue 1 , March 2001 , pp. 25 - 43
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

We would like to thank J. Douglas Carroll for early consultation of this research, and Robert I. Jennrich for commenting on an earlier draft of this paper and for help on the computational algorithms. James O. Ramsay and Forrest W. Young were instrumental in providing the example data. This work was supported in part by National Institute of Mental Health grant 1 R43 MH57559-01. We would also like to thank the anonymous referees for comments that helped to clarify our work.

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