A comparison among robust estimation methods for structural equations modeling with ordinal categorical variables.

Categorical and ordered variables are commonly used in many scientific researches. Researchers often use the ML method, which assumes a multivariate normal distribution, and this is not true with categorical data because the normal state assumption is violated when a Likert scale is used which leads to shaded results.In this research, it has been suggested the robust MLR method with covariance matrix of the sample which deals with the data as it is a continuous data especially when the Likert scale is five or above. It has been suggested a method for reducing the error by linking error measurement, where a link was performed between three standard errors, and through the fit indices, it was obtained a good result in reducing the standard error of capabilities and improving the quality of fit indexes. It has been also used two of the robust methods, WLSMV method which known as RDWLS method, and ULSMV method which known as RULS method, use a polychoric correlation, each two methods deal with the data as it categorical. This research also included a comparison between the robust estimation methods ML , MLR , WLSMV and ULSMV and study its effects on the population corrected robust model fit indexes , and then select the best method for dealing with the categorical ordered data . The results showed a superiority of the robust methods in comparison with other methods, where it showed a robust corrections in the standard errors by using the polychoric correlation coefficient matrix, in addition to robust correction of the chi square. In addition of that, the fit indices is replaced by the robust fit indexes of chi- square robust, TLI, CFI and RMSIA.