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Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Published online by Cambridge University Press:  01 January 2025

Myrsini Katsikatsou  and
Irini Moustaki
Myrsini Katsikatsou*
Affiliation:
London School of Economics
Irini Moustaki
Affiliation:
London School of Economics
*
Correspondence should be made to Myrsini Katsikatsou, Department of Statistics, London School of Economics, Houghton Street, London, WC2A 2AE UK. Email: m.katsikatsou@lse.ac.uk
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Abstract

Correlated multivariate ordinal data can be analysed with structural equation models. Parameter estimation has been tackled in the literature using limited-information methods including three-stage least squares and pseudo-likelihood estimation methods such as pairwise maximum likelihood estimation. In this paper, two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness-of-fit and nested models, respectively, under the estimation framework of pairwise maximum likelihood estimation. Simulation results show a satisfactory performance of type I error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three-stage diagonally weighted and unweighted least squares. Furthermore, the corresponding, under the pairwise framework, model selection criteria, AIC and BIC, show satisfactory results in selecting the right model in our simulation examples. The derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data. The test statistics derived and the model selection criteria are used on data on ‘trust in the police’ selected from the 2010 European Social Survey. The proposed test statistics and the model selection criteria have been implemented in the R package lavaan.

Keywords

latent variable modellingcomposite likelihoodunderlying variable approach
Type
Article
Information
Psychometrika , Volume 81 , Issue 4 , December 2016 , pp. 1046 - 1068
Copyright
Copyright © 2016 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi: 10.1007/s11336-016-9523-z) contains supplementary material, which is available to authorized users.

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