A Marginal Maximum Likelihood Approach for Extended Quadratic Structural Equation Modeling with Ordinal Data

Shaobo Jin,Johan Vegelius,Fan Yang-Wallentin

doi:10.1080/10705511.2020.1712552

Shaobo Jin, Johan Vegelius + Show 1 more

Open Access

https://doi.org/10.1080/10705511.2020.1712552

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Abstract

ABSTRACT The literature on non-linear structural equation modeling is plentiful. Despite this fact, few studies consider interactions between exogenous and endogenous latent variables. Further, it is well known that treating ordinal data as continuous produces bias, a problem which is enhanced when non-linear relationships between latent variables are incorporated. A marginal maximum likelihood-based approach is proposed in order to fit a non-linear structural equation model including interactions between exogenous and endogenous latent variables in the presence of ordinal data. In this approach, the exact gradient of the approximated observed log-likelihood is calculated in order to attain the approximated maximum likelihood estimator. A simulation study shows that the proposed method provides estimates with low bias and accurate coverage probabilities.

Highlights

Non-linear structural equation modeling (SEM) has been of great interest in the past few decades
A marginal maximum likelihood-based approach is proposed in order to fit a non-linear structural equation model including interactions between exogenous and endogenous latent variables in the presence of ordinal data
Even though some methods can incorporate ordinal data into the model, they generally lack the interaction between endogenous latent variables and exogenous latent variables

Summary

Introduction

Non-linear structural equation modeling (SEM) has been of great interest in the past few decades. A marginal maximum likelihood-based approach is proposed in order to fit a non-linear structural equation model including interactions between exogenous and endogenous latent variables in the presence of ordinal data. Lee and Song (2008) and Song and Lee (2006a) considered Bayesian estimation and comparison of non-linear models with a mixture of continuous, dichotomous, and ordinal indicators.

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