On Structural Equation Model Equivalence

Tenko Raykov · Spiridon I. Penev

68 citations0/0 files storedMultivariate Behavioral Research

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Psychometric Methodologies and Testing Statistical Methods and Applications Statistical Methods and Bayesian Inference

Abstract

A necessary and sufficient condition for equivalence of structural equation models is presented. Compared to existing rules for equivalent model generation (Stelzl, 1986; Lee & Hershberger, 1990; Hershberger, 1994), it is applicable to a more general class including models with parameter restrictions and models that may or may not fulfil assumptions of the rules, to show that two models are nonequivalent, or to nonidentified models. The validity of the replacement rule by Lee and Hershberger, Stelzl's rules, and Hershberger's inverse indicator rule is implied from the present method. Its application for studying model equivalence or lack thereof is demonstrated on a series of empirical examples.

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References

1989Structural Equations with Latent Variables 1991Structural Equations with Latent Variables.1989EQS : structural equations program manual 1993The problem of equivalent models in applications of covariance structure analysis.1990Applications of covariance structure modeling in psychology: Cause for concern?1990A Simple Rule for Generating Equivalent Models in Covariance Structure Modeling 1986Changing a Causal Hypothesis without Changing the Fit: some Rules for Generating Equivalent Path Models

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2011Mind the Gap: A Psychometric Approach to the Reduction Problem 2006The Presence of Equivalent Models in Strategic Management Research Using Structural Equation Modeling 2019Model-Based Manifest and Latent Composite Scores in Structural Equation Models 2007A Framework of Statistical Tests For Comparing Mean and Covariance Structure Models 2008A proposed framework for conducting data-based test analysis.2022Fifty years of structural equation modeling: A history of generalization, unification, and diffusion

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