In a confirmatory study, researchers are expected to employ the covariance-based structural equation modeling (CB-SEM). One of the key presumptions when utilizing CB-SEM is that the data is multivariate normal. Nevertheless, a perfect normal distribution is rarely observed in real-life data. To resolve this, the unweighted least square (ULS) is designed to specifically deal with non-normal data in SEM. However, ULS often yields improper solutions like negative, or boundary estimates of unique variances since it considers measurement errors in observed variables. The disturbance in SEM is reflected in unique variance, which is random error due to unreliability or measurement error and reliable variation in the item that indicates unknown latent causes. Consequently, this can generate bias in indicator loadings estimates. As an action to disentangle this issue, the present study proposes the implementation of regularization parameters by adding small positive values to the variance-covariance matrix. The ratio of bias to variance in a model can be improved to obtain the best estimation performance. Pro-Active Monte Carlo simulation was used to produce multivariate non-normal data with designated sample sizes and population characteristics. The data were analyzed using R Programming Environment by employing “psych”, “MASS”, “foreign”, “mvrnonnorm”, “purr”, and “semTools” packages with 1000 replications to produce multivariate non-normal data. Next, the “lavaan” package was used for SEM and regularized SEM analyses. The outcome of this study proves the capability of regularized ULS to improve parameter estimation.

Structural equation modeling offers various estimation methods for estimating parameters. The most used method in covariance-based structural equation modeling (CB-SEM) is the maximum likelihood (ML) estimator. The ML estimator is typically used when fitting models with normally distributed data. The growth of partial least squares path modeling (PLS-PM), including consistent partial least squares (PLSc), has also been noticed by researchers in the SEM fields. The PLSc has elevated interest in the scholastic setting in measuring the performance of various estimation methods in structural equation modeling. The choice of estimation methods has substantial impact in yielding parameter estimates. There could be a trade-off among the estimation methods’ ability to deal with different types of data based on the model tested. Accordingly, this study aims to compare the performance of ML, generalized least squares (GLS), and scale-free least squares (SFLS) for CB-SEM as well as partial least squares (PLS) and consistent partial least squares (PLSc). Multivariate normal data were generated using Monte Carlo simulation with pre-determined population parameters and sample sizes using R Programming packages. To produce the estimated values, data analysis was performed using AMOS and SmartPLS for CB-SEM and PLS-SEM, respectively. The findings illustrate notable similarities between CB-SEM (ML) and PLS-SEM results when the true indicator loading is certainly high.

Structural Equation Modeling (SEM) includes measurement and structural model for hypothesis testing. The results yielded from structural model is unlikely to be valid if a poor loading of an indicator is selected. The impact of these erroneous result on standardized loading is disregard. Thus, knowing how poor loading can affect the validity of measurement model is a crucial issue. This paper attempts to compare the standardized loadings result between two prominent SEM methods (CBSEM and PLS-SEM) using three varied of simulation models (TRA, Loyalty and UTAUT model) to investigate their effects on reliability and validity of measurement model. The data for each model were generated using R software by setting the value of standardized loading and the construct correlations (N=50, 100, 200 and 500). The value of standardized loadings was set to 0.60 for each construct in the model while the construct correlations were set in the range between 0.45 to 0.65. Then, the AMOS 21.0 and ADANCO 2.0 were used to perform the statistical analysis. It shows that good standardized loading can increase the reliability and validity of construct representation. CBSEM is particularly yielded valid and unbiased estimation under confirmatory condition (established theory) compared with PLS-SEM. The results are illustrated with empirical examples. This paper provides updated evidence about CBSEM and PLS-SEM when assessing the measurement model.