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Some Small Sample Results for 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 J. O. Ramsay, McGill University, Department of Psychology, 1205 Docteur Penfield Avenue, Montreal, Quebec, Canada H3A 1B1.
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Abstract

Some aspects of the small sample behavior of maximum likelihood estimates in multidimensional scaling are investigated by Monte Carlo. An investigation of Model M2 in the MULTISCALE program package shows that the chi-square test of dimensionality requires a correction of tabled chi-square values to be unbiased. A formula for this correction in the case of two dimensions is estimated. The power of the test of dimensionality is acceptable with as few as two replications for 15 stimuli and as few as five replications for 10 stimuli. The biases in the exponent and standard error estimates in this model are also investigated.

Keywords

test for dimensionalityasymptotic chi-square testsmall sample correction
Type
Notes and Comments
Information
Psychometrika , Volume 45 , Issue 1 , March 1980 , pp. 139 - 144
Copyright
Copyright © 1980 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 Science and Engineering Research Council of Canada.

References

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Ramsay, J. O. MULTISCALE: Four programs for multidimensional scaling by the method of maximum likelihood, 1978, Chicago: International Education Services.Google Scholar