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Interval Estimation for the Intraclass Correlation in Dirichlet-Multinomial Data

Published online by Cambridge University Press:  01 January 2025

Kung-Jong Lui ,
William G. Cumberland ,
Joni A. Mayer  and
Laura Eckhardt
Kung-Jong Lui*
Affiliation:
Department of Mathematical and Computer Sciences, San Diego State University
William G. Cumberland
Affiliation:
Department of Biostatistics, University of California, Los Angeles
Joni A. Mayer
Affiliation:
Graduate School of Public Health, San Diego State University
Laura Eckhardt
Affiliation:
Graduate School of Public Health, San Diego State University
*
Requests for reprints should be sent to Kung-Jong Lui, Department of Mathematical and Computer Sciences, San Diego State University, San Diego CA 92182-7720.
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Abstract

When the underlying distribution is discrete with a limited number of categories, methods for interval estimation of the intraclass correlation which assume normality are theoretically inadequate for use. On the basis of large sample theory, this paper develops an asymptotic closed-form interval estimate of the intraclass correlation for the case where there is a natural score associated with each category. This paper employs Monte Carlo simulation to demonstrate that when the underlying intraclass correlation is large, the traditional interval estimator which assumes normality can be misleading. We find that when the number of classes is ≥ 20, the interval estimator proposed here can generally perform reasonably well in a variety of situations. This paper further notes that the proposed interval estimator is invariant with respect to a linear transformation. When the data are on a nominal scale, an extension of the proposed method to account for this case, as well as a discussion on the relationship between the intraclass correlation and a kappa-type measure defined here and on the limitation of the corresponding kappa-type estimator are given.

Keywords

confidence limitsFieller's theoremcoverage probabilityintraclass correlationDirichlet-multinomial.
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 3 , September 1999 , pp. 355 - 369
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

The authors wish to thank the Editor, the Associate Editor, and the three referees for many valuable comments and suggestions to improve the clarity of this paper. The works for the first, the third, and the fourth authors were partially supported by grant #R01AR43025-01 from the National Institute of Arthritis and Musculoskeletal and Skin Diseases.

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