On Identifying Anomaly Factor Scores Distribution in Estimating Structural Equation Model Using Bayesian Approach

The pattern of correlations between many latent components is tested using Structural Equation Modelling (SEM) analysis with Confirmatory Factor Analysis (CFA). This encompasses multiple model constructs that are assessed using a few observational indicators. Factor scores are the CFA results, which are “new data” for additional examination. It is vital to assess the factor score distribution before conducting additional analysis. This is due to research indicating that factor scores are typically not unimodal and can be bimodal or multimodal. A non-normal or skewed distribution of factor scores is another possibility. There has never been any research done on the distribution of factor scores. For this reason, the factor score distribution will be examined in this study. Before performing further analysis, the factor score distribution needs to be evaluated. The results of this study show that all factor scores from the 9 latent variables are not normally distributed and tend to be skewed. The p-value of the Kolmogorov-Smirnov test for all latent variables is less than 0.01, indicating a departure from normality. This suggests that there's a possibility that the factor scores' distribution is skewed. Several distributions can satisfy this requirement, including the skew-t distribution, skewed normal distribution, and Epsilon Skew Normal (ESN). However, more investigation is required to find the right distribution, which will improve the accuracy of the parameter estimate results.