Abstract
A Monte Carlo simulation was performed for estimating and testing hypotheses of three-way interaction effect in latent variable regression models. A considerable amount of research has been done on estimation of simple interaction and quadratic effect in nonlinear structural equation. 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 different 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 effect and type I error control were also manipulated showing that power increased as interaction effect size, sample size and latent covariance increased.
Highlights
Structural Equation Modeling (SEM) is a statistical method used for building models, making inference and quantify the relationship among latent variables that are not observable or cannot be measured precisely
The present study extended to three-way continuous latent interaction in structural equation model
With small sample size(i.e, n=50)and moderate reliability, this bias was very high.The resulting overestimation decreased as reliability of the indicators and sample size increased, but kept increasing as the interaction effect size for the three-way interaction term ((R2γ7)) and co-variance between latent exogenous variables increased
Summary
Structural Equation Modeling (SEM) is a statistical method used for building models, making inference and quantify the relationship among latent variables that are not observable or cannot be measured precisely. Measurement on the indicator variable related to those unobservable variables are available This relationship began its bases as a method for modeling linear relationship. (Kenny & Judd, 1984) introduced the first statistical method aimed at producing estimates of parameters in a nonlinear structural equation model ( a quadratic or cross-product structural model with a linear measurement model). Their method attracted methodological discussions and alterations by a number of papers. (Hayduck, 1987) demonstrated how the Kenny-Judd model could be implemented in LISREL
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