Some small sample results for maximum likelihood estimation in multidimensional scaling |
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Authors: | J. O. Ramsay |
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Affiliation: | (1) Department of Psychology, McGill University, 1205 Docteur Penfield Avenue, H3A 1B1 Montreal, Quebec, Canada |
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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.The research reported here was supported by grant number APA 320 to the author by the National Science and Engineering Research Council of Canada. |
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Keywords: | test for dimensionality asymptotic chi-square test small sample correction |
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