Estimating Three-Way Latent Interaction E ects in Structural Equations Modeling

Abstract

A Monte Carlo simulation was performed for estimating and testing hypotheses of three-way interaction e ect in latent variable regression models. A considerable amount of research has been done on estimation of simple interaction and quadratic e ect in nonlinear structural equation. However no work has been done in estimating three-way continuous latent interaction. The present study extended to three-way continuous latent interaction in structural equation model. The latent moderated structural equation (LMS)approach was used to estimate the parameters of the three-way interaction in structural equation model and investigate the properties of the method under di erent conditions though simulations. The approach showed least bias, standard error,and root mean square error as indicator reliability and sample size increased. The power to detect interaction e ect and type I error control were also manipulated showing that power increased as interaction e ect size, sample size and latent covariance increased.