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Profile Likelihood-Based Confidence Intervals and Regions for Structural Equation Models

Published online by Cambridge University Press:  01 January 2025

Jolynn Pek  and
Hao Wu
Jolynn Pek*
Affiliation:
York University
Hao Wu
Affiliation:
Boston College
*
Correspondence should be made to Jolynn Pek, Department of Psychology, York University, 322 Behavioural Science Building, 4700 Keele Street, Toronto, ON M3J 1P3 Canada. Email: pek@yorku.ca
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Abstract

Structural equation models (SEM) are widely used for modeling complex multivariate relationships among measured and latent variables. Although several analytical approaches to interval estimation in SEM have been developed, there lacks a comprehensive review of these methods. We review the popular Wald-type and lesser known likelihood-based methods in linear SEM, emphasizing profile likelihood-based confidence intervals (CIs). Existing algorithms for computing profile likelihood-based CIs are described, including two newer algorithms which are extended to construct profile likelihood-based confidence regions (CRs). Finally, we illustrate the use of these CIs and CRs with two empirical examples, and provide practical recommendations on when to use Wald-type CIs and CRs versus profile likelihood-based CIs and CRs. OpenMx example code is provided in an Online Appendix for constructing profile likelihood-based CIs and CRs for SEM.

Keywords

confidence intervalsconfidence regionsprofile likelihoodWaldmulti-parameter

Information

Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 4 , December 2015 , pp. 1123 - 1145
Copyright
Copyright © 2015 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-015-9461-1) contains supplementary material, which is available to authorized users.

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