Robust nonlinear structural equation modeling with interaction between exogenous and endogenous latent variables

ABSTRACT

A handful of studies have been devoted to nonlinear structural equation modeling (SEM) in the literature. However, they generally overlooked the interactions among exogenous and endogenous latent variables and the interactions among endogenous latent variables. In this study, we propose a maximum likelihood approach for a nonlinear SEM model that incorporates such overlooked interactions. We also propose a two-stage pseudo maximum likelihood approach under the assumption of normal mixture, being computational efficient and robust against distributional misspecification. The simulation study shows that both approaches accurately estimate the unknown parameters if the distribution is correctly specified. However, only the pseudo maximum likelihood approach is robust against distributional misspecification.

KEYWORDS:

• Normal mixture
• factor mixture analysis
• Gauss-Hermite quadrature
• pseudo-maximum likelihood

Acknowledgments

We are grateful to the reviewers for their comments to improve the study.

Notes

¹ We are grateful to Cajsa Bartusch for sharing the data set.

Additional information

Funding

This study was supported by the National Research Foundation of Korea Grants [NRF-2019R1A2C1002408] and Vetenskapsrådet [Swedish Research Council 2017-01175].