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Efficient Likelihood Estimation of Generalized Structural Equation Models with a Mix of Normal and Nonnormal Responses

Published online by Cambridge University Press:  01 January 2025

Nicholas J. Rockwood Open the ORCID record for Nicholas J. Rockwood [Opens in a new window]
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, CA92350, USA. Email: [email protected]; URL: https://www.njrockwood.com
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Abstract

A maximum likelihood estimation routine is presented for a generalized structural equation model that permits a combination of response variables from various distributions (e.g., normal, Poisson, binomial, etc.). The likelihood function does not have a closed-form solution and so must be numerically approximated, which can be computationally demanding for models with several latent variables. However, the dimension of numerical integration can be reduced if one or more of the latent variables do not directly affect any nonnormal endogenous variables. The method is demonstrated using an empirical example, and the full estimation details, including first-order derivatives of the likelihood function, are provided.

Keywords

structural equation modelinglatent variable modelinggeneralized linear modelsmaximum likelihood estimation
Type
Theory and Methods
Information
Psychometrika , Volume 86 , Issue 2 , June 2021 , pp. 642 - 667
Copyright
Copyright © 2021 The Psychometric Society

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