A proposed method for cleaning data from outlier values using the robust RFCH method in structural equation modeling

The GLS and ML methods are the most common methods for estimating SEM but require multivariate normality. Therefore, methods robust to standard errors and quality of fit indexes to Chi-square have been proposed: MLR and they are considered superior to ML and GLS methods analyzing ordinal data. When we have a five-way Likert scale, the data is treated as continuous by calculating the covariance matrix as inputs for ML, GLS, and MLR. However, outliers are familiar because modeling requires a large sample size, either because of the input of data or answers more than is expressed within a particular category. Their presence affects even methods with robust corrections, where the accuracy of estimating parameters, standard errors, and fit indicators may be compromised the quality of fit indexes and inappropriate solutions, where a robust algorithm is proposed to clean the data from the outlier, as this proposed algorithm calculates the robust correlation matrix robust RFCH Reweighted Fast Consistent and High Breakdown, which consists of several steps and has been modified by taking the clean data before calculating the robust RFCH correlation matrix.  It was also suggested to make a comparison between the three methods before the treatment process with the presence of outlier values and note the extent of their impact on the methods and after using the robust RFCH method, and note the extent of improvement in estimations, standard errors and the overall quality of fit indexes for each of the Chi-square index, CFI, TLI, and RMSEA, SRMR and CRMR, with the robust corrections in the Chi-square index for each of the methods MLR. Through the simulation experiment, the researcher reached the power of the proposed method robust RFCH in improving the quality of parameter estimation, standard errors, and overall fit indexes quality.