Estimating Latent Variable Interactions With Non-Normal Observed Data: A Comparison of Four Approaches

A Monte Carlo simulation was conducted to investigate the robustness of four latent variable interaction modeling approaches (Constrained Product Indicator [CPI], Generalized Appended Product Indicator [GAPI], Unconstrained Product Indicator [UPI], and Latent Moderated Structural Equations [LMS]) under high degrees of non-normality of the observed exogenous variables. Results showed that the CPI and LMS approaches yielded biased estimates of the interaction effect when the exogenous variables were highly non-normal. When the violation of non-normality was not severe (normal; symmetric with excess kurtosis < 1), the LMS approach yielded the most efficient estimates of the latent interaction effect with the highest statistical power. In highly non-normal conditions, the GAPI and UPI approaches with ML estimation yielded unbiased latent interaction effect estimates, with acceptable actual Type-I error rates for both the Wald and likelihood ratio tests of interaction effect at ≥ 500. An empirical example illustrated the use of the four approaches in testing a latent variable interaction between academic self-efficacy and positive family role models in the prediction of academic performance.