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Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients

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Abstract

The method of finding the maximum likelihood estimates of the parameters in a multivariate normal model with some of the component variables observable only in polytomous form is developed. The main stratagem used is a reparameterization which converts the corresponding log likelihood function to an easily handled one. The maximum likelihood estimates are found by a Fletcher-Powell algorithm, and their standard error estimates are obtained from the information matrix. When the dimension of the random vector observable only in polytomous form is large, obtaining the maximum likelihood estimates is computationally rather labor expensive. Therefore, a more efficient method, the partition maximum likelihood method, is proposed. These estimation methods are demonstrated by real and simulated data, and are compared by means of a simulation study.

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Authors and Affiliations

  1. University of California, Los Angeles

    Wai-Yin Poon

  2. Department of Statistics, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong

    Sik-Yum Lee

Authors
  1. Wai-Yin Poon
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  2. Sik-Yum Lee
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Additional information

This research was supported in part by a research grant (DA01070) from the U.S. Public Health Service. The authors are indebted to the editor and anonymous reviewers for some very valuable comments and suggestions. The assistance of K. W. Ling and K. Y. Leung in manuscript production is also gratefully acknowledged.

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Poon, WY., Lee, SY. Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients. Psychometrika 52, 409–430 (1987). https://doi.org/10.1007/BF02294364

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  • DOI: https://doi.org/10.1007/BF02294364

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