The reccommedndations of Hu and Bentler and others like them on cut-off criteria of GOF indices for assessing model fits in structural equation modeling are well known. However, these criteria have come under criticism and even considered unrealistic especially when data invloved categorical variables. This is because in the simulation studies of Hu and Bentler and others continuous variables were used coupled with maximum likelihood estimator. In the case of categorical variables and especially using WLSMV estimator little or no such studies are readily available within my reach. I will appreaciate your reccommedation on these criteria backed with appropriate literature.

Best wishes.