Title: Estimation of nonlinear structural equation models with dichotomous indicator variables: a Monte Carlo comparison of methods

Authors: W. Holmes Finch

Addresses: Department of Educational Psychology, Ball State University, Muncie, IN 47304, USA

Abstract: Nonlinear structural equation models (SEMs), which include interactions among latent predictors, as well as quadratic or higher order terms, have been the focus of research over the last three decades, beginning with Kenny and Judd (1984). The great majority of that work has focused on the case where the indicator variables are continuous in nature. However, in practice many nonlinear SEMs will involve the use of responses to items on scales, which are categorical. The focus of the current simulation study was on comparing several methods for modelling nonlinear SEMs when indicator variables were dichotomous. Results of the study showed that a Bayesian approach, as well as a method based on 2-stage least squares, provided the most accurate parameter estimates, the highest power, and the best control over the Type I error rate for the interaction effect. Implications of these findings for practice are discussed.

Keywords: structural equation model; SEM; interaction; Bayesian estimation; 2-stage least squares.

DOI: 10.1504/IJQRE.2020.10028311

International Journal of Quantitative Research in Education, 2020 Vol.5 No.1, pp.39 - 66

Received: 15 May 2018
Accepted: 10 Apr 2019

Published online: 15 Apr 2020 *

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