Use the robust RFCH method with a polychoric correlation matrix in structural equation modeling When you are ordinal data

Structural Equation Modeling is a statistical methodology commonly used in the social and administrative sciences and all other. In this research, the researcher made a comparison between methods of estimation Unweighted Least Squares with Mean and Variance Adjusted( ULSMV) and weighted Least Squares with Mean and Variance Adjusted (WLSMV). When we have a five-way Likert scale, the data is treated as ordinal using the polychoric matrix as inputs for the weighted methods with robust corrections. With robust standard errors ULSMV and WLSMV.No study compared these methods and the impact of outliers on them. where a robust algorithm is proposed to clean the data from the outlier, as this proposed algorithm calculates the robust correlation matrix Reweighted Fast Consistent and High Breakdown (RFCH), which consists of several steps and has been modified by taking the clean data before calculating the RFCH correlation matrix, where these data are data clean from outlier to add in the methods and to calculate a correlation matrix for each method where the purpose is to keep the ordinal data to calculate the polychoric matrix, which is robust to the violation of the assumption of normal distribution.By conducting a simulation experiment on different sample sizes and the degree of distribution to observe the accuracy of the proposed method for obtaining clean data. On methods ULSMV and WLSMV before and after the treatment process by calculating the absolute bias rate For the standard errors and the estimated parameters, in addition to studying the extent of their effect on the quality of fit indicators for each of the chi-square index, Comparative fit index (CFI), Tucker-Lewis Index (TLI), and Root-Mean-Squared-Error-of Approximation( RMSEA), Standardized Root Mean square Residual (SRMR), , with the robust corrections in the chi-square index for each of the methods WLSMV and ULSMV the accuracy of the proposed.