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On Muthén’s Maximum Likelihood for Two-Level Covariance Structure Models

Published online by Cambridge University Press:  01 January 2025

Ke-Hai Yuan  and
Kentaro Hayashi
Ke-Hai Yuan*
Affiliation:
University of Notre Dame
Kentaro Hayashi
Affiliation:
University of Hawaii at Manoa
*
Request for reprints should be sent to Ke-Hai Yuan, University of Notre Dame, In 46556, USA. E-mail: [email protected]
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Abstract

Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures that take into account the dependence of such observations have been developed. Among procedures for 2-level covariance structure analysis, Muthén’s maximum likelihood (MUML) has the advantage of easier computation and faster convergence. When data are balanced, MUML is equivalent to the maximum likelihood procedure. Simulation results in the literature endorse the MUML procedure also for unbalanced data. This paper studies the analytical properties of the MUML procedure in general. The results indicate that the MUML procedure leads to correct model inference asymptotically when level-2 sample size goes to infinity and the coefficient of variation of the level-1 sample sizes goes to zero. The study clearly identifies the impact of level-1 and level-2 sample sizes on the standard errors and test statistic of the MUML procedure. Analytical results explain previous simulation results and will guide the design or data collection for the future applications of MUML.

Keywords

asymptoticslikelihood ratio statisticmultilevel covariance structurestandard error estimates
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 1 , March 2005 , pp. 147 - 167
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

This research was supported by NSF Grant DMS04-37167.

We thank Dr. Bengt Muthén for providing key references. We are also grateful to three expert reviewers for their constructive comments that have led the paper to an improvement over the previous version.

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