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Maximum Likelihood Estimation in Multidimensional Scaling

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 Professor J. O. Ramsay, Department of Psychology, McGill University, Montreal, Quebec, Canada H3A 1B1
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Abstract

A variety of distributional assumptions for dissimilarity judgments are considered, with the lognormal distribution being favored for most situations. An implicit equation is discussed for the maximum likelihood estimation of the configuration with or without individual weighting of dimensions. A technique for solving this equation is described and a number of examples offered to indicate its performance in practice. The estimation of a power transformation of dissimilarity is also considered. A number of likelihood ratio hypothesis tests are discussed and a small Monte Carlo experiment described to illustrate the behavior of the test of dimensionality in small samples.

Keywords

lognormalhypothesis testingimplicit equation
Type
Original Paper
Information
Psychometrika , Volume 42 , Issue 2 , June 1977 , pp. 241 - 266
Copyright
Copyright © 1977 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.

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