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Maximum Likelihood Estimation of Multilevel Structural Equation Models with Random Slopes for Latent Covariates

Published online by Cambridge University Press:  01 January 2025

Nicholas J. Rockwood
Nicholas J. Rockwood*
Affiliation:
Loma Linda University
*
Correspondence should be made to Nicholas J. Rockwood, Division of Interdisciplinary Studies, School of Behavioral Health, Loma Linda University, 11065 Campus St., Loma Linda, CA 92350, USA. Email: [email protected]; URL: https://njrockwood.com
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Abstract

A maximum likelihood estimation routine for two-level structural equation models with random slopes for latent covariates is presented. Because the likelihood function does not typically have a closed-form solution, numerical integration over the random effects is required. The routine relies upon a method proposed by du Toit and Cudeck (Psychometrika 74(1):65–82, 2009) for reformulating the likelihood function so that an often large subset of the random effects can be integrated analytically, reducing the computational burden of high-dimensional numerical integration. The method is demonstrated and assessed using a small-scale simulation study and an empirical example.

Keywords

multilevel SEMrandom effectsrandom slopesmaximum likelihood estimation
Type
Theory and Methods
Information
Psychometrika , Volume 85 , Issue 2 , June 2020 , pp. 275 - 300
Copyright
Copyright © 2020 The Psychometric Society

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