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Confidence Regions for Multidimensional Scaling Analysis

Published online by Cambridge University Press:  01 January 2025

J. O. Ramsay
J. O. Ramsay*
Affiliation:
McGill University
*
Requests for reprints should be sent to J. O. Ramsay, Department of Psychology, McGill University, 1205 McGregor Avenue, Montreal, Quebec, Canada H3A 1B1.
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Abstract

Techniques are developed for surrounding each of the points in a multidimensional scaling solution with a region which will contain the population point with some level of confidence. Bayesian credibility regions are also discussed. A general theorem is proven which describes the asymptotic distribution of maximum likelihood estimates subject to identifiability constraints. This theorem is applied to a number of models to display asymptotic variance-covariance matrices for coordinate estimates under different rotational constraints. A technique is described for displaying Bayesian conditional credibility regions for any sample size.

Keywords

conditional credibility regionsBayesian analysisasymptotic distributionmaximum likelihood estimationvariance-covariance of configuration

Information

Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 2 , June 1978, pp. 145 - 160
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

The research reported here was supported by grant number APA 320 to the author by the National Research Council of Canada.

References

Reference Notes

Ramsay, J. O. Further developments in maximum likelihood multidimensional scaling. Paper submitted for publication, 1977.CrossRefGoogle Scholar
Ramsay, J. O. Asymptotic results for singular information matrices with internal and external identifiability constraints. Paper submitted for publication, 1977.Google Scholar

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