Abstract
In a confirmatory investigation, researchers are mandated to employ covariance-based structural equation modeling (CB-SEM). A crucial assumption inherent in CB-SEM is the multivariate normality of the data. However, real-world data rarely conforms to a perfectly normal distribution. To address this, unweighted least squares (ULS) is specifically tailored for handling non-normally distributed data in SEM. Nonetheless, ULS often yields unsatisfactory outcomes, such as negative or boundary estimates of unique variances, as it accounts for measurement errors in observed variables. In the realm of SEM, unique variance manifests as disturbance, arising from unreliability or measurement error and reliable variation in items indicating latent causes that are not explicitly known. One common cause of improper solutions in SEM is non-convergence, wherein the estimation fails to reach a minimum fit function. To address this challenge, the present study proposes the regularization of the ULS estimator to rectify inadequacies in model fit. Multivariate non-normally distributed data, with predetermined population parameters and sample sizes, were generated through Pro-Active Monte Carlo simulation and subsequently analyzed using the R Programming Environment. The results reveal the effectiveness of the regularized ULS in enhancing model fit indices such as the Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), Root Mean Square Error of Approximation (RMSEA), and Standardized Root Mean Square Residual (SRMR).
Keywords: Fitness Indexes, Monte Carlo, Regularization, SEM, ULS.