Creating Misspecified Models in Moment Structure Analysis

  • Keke LaiEmail author


To understand how SEM methods perform in practice where models always have misfit, simulation studies often involve incorrect models. To create a wrong model, traditionally one specifies a perfect model first and then removes some paths. This approach becomes difficult or even impossible to implement in moment structure analysis and fails to control the amounts of misfit separately and precisely for the mean and covariance parts. Most importantly, this approach assumes a perfect model exists and wrong models can eventually be made perfect, whereas in practice models are all implausible if taken literally and at best provide approximations of the real world. To improve the traditional approach, we propose a more realistic and flexible way to create model misfit for multiple group moment structure analysis. Given (a) the model \(\varvec{{{\upmu }}} (\cdot ) \) and \(\varvec{{\Sigma }} (\cdot ) \), (b) population model parameters \(\varvec{{{\uptheta }}} _0\), and (c) \(F_1\) and \(F_2\) specified by the researcher, our method creates \(\varvec{{{\upmu }}} ^*\) and \(\varvec{{\Sigma }} ^*\) to simultaneously satisfy (a) \(\varvec{{{\uptheta }}} _0 = \arg \min F[\varvec{{{\upmu }}} ^*, \varvec{{\Sigma }} ^*; \varvec{{{\upmu }}} (\cdot ), \varvec{{\Sigma }} (\cdot )]\), (b) the mean structure’s misfit equals \(F_1\), and (c) the covariance structure’s misfit equals \(F_2\).


Monte Carlo experiments model misspecification moment structure analysis multiple group analysis 


Supplementary material

11336_2018_9655_MOESM1_ESM.r (7 kb)
Supplementary material 1 (R 7 KB)


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Copyright information

© The Psychometric Society 2019

Authors and Affiliations

  1. 1.Psychological SciencesUniversity of CaliforniaMercedUSA

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