Estimating Latent Variable Interactions With Nonnormal Observed Data: A Comparison of Four Approaches

Abstract

A Monte Carlo simulation was conducted to investigate the robustness of 4 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 nonnormality 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 nonnormal. When the violation of nonnormality 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 nonnormal conditions, the GAPI and UPI approaches with maximum likelihood (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 N ≥ 500. An empirical example illustrated the use of the 4 approaches in testing a latent variable interaction between academic self-efficacy and positive family role models in the prediction of academic performance.

Notes

¹Throughout this article, kurtosis is defined as excess kurtosis having a value of 0 for a normally distributed variable.

Note. ^aTheoretical values calculated based on Mattson (1997).

^bSimulation values calculated using 100 randomly generated data sets of size 1,000,000.

*Relative bias ≤ |10%| criterion met.

*(0.9 ≤ SE ratio ≤ 1.1) criterion met.

*(Coverage Rate > 0.9) criterion met.

+p < .10.

*p < .05.

**p < .01.