R-squared of a Latent Interaction in Structural Equation Model: A Tutorial of Using R

Lu Qin,Jihong Zhang,Qianqian Pan,Xinya Liang

doi:10.5539/ijsp.v10n3p69

Abstract

Mplus (Muth&eacute;n &amp; Muth&eacute;n, 1998 - 2017) is one popular statistical software to estimate the latent interaction effects using the latent moderated structural equation approach (LMS). However, the variance explained by a latent interaction that supports the interpretation of estimation results is not currently available from the Mplus output. To relieve human computations and to facilitate interpretations of latent interaction effects in social science research, we developed two functions (LIR &amp; LOIR) in the R package IRmplus to calculate the R-squared of a latent interaction above and beyond the first-order simple main effects in Structural Equation Modeling. This tutorial provides a step-by-step guide for applied researchers to estimating a latent interaction effect in Mplus, and to obtaining the R-squared of a latent interaction effect using the LIR &amp; LOIR functions. Example data and syntax are available online.

Highlights

Mplus (Muthén & Muthén, 1998 - 2017) is one popular statistical software to estimate the latent interaction effects using the latent moderated structural equation approach (LMS)
To relieve human computations and to facilitate interpretations of latent interaction effects in social science research, we developed two functions (LIR & LOIR) in the R package IRmplus to calculate the R-squared of a latent interaction above and beyond the first-order simple main effects in Structural Equation Modeling
This tutorial provides a step-by-step guide for applied researchers to estimating a latent interaction effect in Mplus, and to obtaining the R-squared of a latent interaction effect using the LIR & LOIR functions

Summary

A Brief Overview of the R-squared of Latent Interaction

Interactions between two latent variables are often estimated in structural equation models (SEM). The LIR and LOIR functions in the IRmplus package were developed to compute the R-squared of a single two-way latent interaction in the SEM given the Mplus output, following Equations (1) through (7). It is to note that the R script is case-sensitive so that the IRmplus arguments (e.g., “INTER”) need to be the same as that shown on the Mplus output In this example, the LIR function returns the R-squared of a latent interaction as 0.127, which indicates that the two-way latent interaction explains around 13% additional variances above and beyond the simple main effects of exogenous latent factors. To use the LOIR function in the IRmplus package for the computation of the R-squared of the latent interaction between a latent factor and an observed covariate using the second simulated dataset “Example2.dat”.

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Discussion

Conclusions