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Tests of Homogeneity of Means and Covariance Matrices for Multivariate Incomplete Data

Published online by Cambridge University Press:  01 January 2025

Kevin H. Kim  and
Peter M. Bentler
Kevin H. Kim*
Affiliation:
University of California, Los Angeles
Peter M. Bentler
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to Kevin H. Kim, Department of Psychology, UCLA, Box 951563, Los Angeles, CA 90095-1563. E-Mail: kevinkim@ucla.edu.
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Abstract

Existing test statistics for assessing whether incomplete data represent a missing completely at random sample from a single population are based on a normal likelihood rationale and effectively test for homogeneity of means and covariances across missing data patterns. The likelihood approach cannot be implemented adequately if a pattern of missing data contains very few subjects. A generalized least squares rationale is used to develop parallel tests that are expected to be more stable in small samples. Three factors were varied for a simulation: number of variables, percent missing completely at random, and sample size. One thousand data sets were simulated for each condition. The generalized least squares test of homogeneity of means performed close to an ideal Type I error rate for most of the conditions. The generalized least squares test of homogeneity of covariance matrices and a combined test performed quite well also.

Keywords

missing datalikelihood ratiogeneralized least squaresmultivariate normal distribution
Type
Articles
Information
Psychometrika , Volume 67 , Issue 4 , December 2002 , pp. 609 - 623
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

Preliminary results on this research were presented at the 1999 Western Psychological Association convention, Irvine, CA, and in the UCLA Statistics Preprint No. 265 (http://www.stat.ucla.edu). The assistance of Ke-Hai Yuan and several anonymous reviewers is gratefully acknowledged.

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