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Psychometrika

, Volume 45, Issue 1, pp 139–144 | Cite as

Some small sample results for maximum likelihood estimation in multidimensional scaling

  • J. O. Ramsay
Notes And Comments

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.

Key words

test for dimensionality asymptotic chi-square test small sample correction 

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References

  1. Box, G.E.P. A general distribution theory for a class of likelihood criteria.Biometrika, 1949,36, 317–346.Google Scholar
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  5. Ramsay, J. O.MULTISCALE: Four programs for multidimensional scaling by the method of maximum likelihood. Chicago: International Education Services, 1978b.Google Scholar

Copyright information

© The Psychometric Society 1980

Authors and Affiliations

  • J. O. Ramsay
    • 1
  1. 1.Department of PsychologyMcGill UniversityMontrealCanada

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