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Maximum Likelihood Estimation of Latent Interaction Effects with the LMS Method

Published online by Cambridge University Press:  01 January 2025

Andreas Klein  and
Helfried Moosbrugger
Andreas Klein*
Affiliation:
Johann Wolfgang Goethe-University, Frankfurt Am Main, Germany
Helfried Moosbrugger
Affiliation:
Johann Wolfgang Goethe-University, Frankfurt Am Main, Germany
*
Requests for reprints should be sent to Andreas Klein, Department of Psychology, Mertonstrasse 17, D-60054 Frankfurt am Main, Germany. E-Mail: a.klein@psych.uni-frankfurt.de
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Abstract

In the context of structural equation modeling, a general interaction model with multiple latent interaction effects is introduced. A stochastic analysis represents the nonnormal distribution of the joint indicator vector as a finite mixture of normal distributions. The Latent Moderated Structural Equations (LMS) approach is a new method developed for the analysis of the general interaction model that utilizes the mixture distribution and provides a ML estimation of model parameters by adapting the EM algorithm. The finite sample properties and the robustness of LMS are discussed. Finally, the applicability of the new method is illustrated by an empirical example.

Keywords

latent interaction effectsmixture distributionML estimationstructural equation modeling (SEM)EM algorithm
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 4 , December 2000 , pp. 457 - 474
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

This research has been supported by a grant from the Deutsche Forschungsgemeinschaft, Germany, No. Mo 474/1 and Mo 474/2. The data for the empirical example have been provided by Andreas Thiele of the University of Frankfurt, Germany. The authors are indebted to an associate editor and to three anonymous reviewers of Psychometrika whose comments and suggestions have been very helpful.

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