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An EM Algorithm for Fitting Two-Level Structural Equation Models

Published online by Cambridge University Press:  01 January 2025

Jiajuan Liang  and
Peter M. Bentler
Jiajuan Liang
Affiliation:
University of New Haven, School of Business
Peter M. Bentler*
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to Peter M. Bentler, University of California, Los Angeles, Department of Psychology, Box 951563, Los Angeles, CA 90095-1563. E-mail: bentler@ucla.edu
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Abstract

Maximum likelihood is an important approach to analysis of two-level structural equation models. Different algorithms for this purpose have been available in the literature. In this paper, we present a new formulation of two-level structural equation models and develop an EM algorithm for fitting this formulation. This new formulation covers a variety of two-level structural equation models. As a result, the proposed EM algorithm is widely applicable in practice. A practical example illustrates the performance of the EM algorithm and the maximum likelihood statistic.

Keywords

Chi-square statisticmean and covariance structuresEM algorithmmaximum likelihoodmultivariate normal distributiontwo-level structural equation models
Type
Theory And Methods
Information
Psychometrika , Volume 69 , Issue 1 , March 2004 , pp. 101 - 122
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

We are thankful to the reviewers for their constructive comments that have led to significant improvement on the first version of this paper. Special thanks are due to the reviewer who suggested a comparison with the LISREL program in the saturated means model, and provided its setup and output. This work was supported by National Institute on Drug Abuse grants DA01070, DA00017, and a UNH 2002 Summer Faculty Fellowship.

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