Robust evaluation of fit indices to fake-good perturbation of ordinal data

This study extended the findings of a former simulation study (Multivar Behav Res 47:519–546, 2012) to evaluate the sensitivity of a large set of SEM-based fit indices to fake-good ordinal data. In the new simulation study we manipulated a comprehensive set of factors (including 3 robust estimation procedures and 3 different faking good models) that could influence the performance of 8 widely used fit indices. The simulation study conditions were chosen to highlight the differences among the fit indices, as well as to cover a wide variety of conditions. Our results demonstrated empirically that the normed fit index (NFI) turned out to be the most reliable fit index with a high sensitivity to fake perturbations. This result was evident in all the simulation design conditions except for those characterized by slight faking levels of perturbations. Interestingly, unlike NFI, the comparative fit index seemed to be highly insensitive to fake data when robust estimation conditions were considered. On the basis of the results of the simulation study we proposed a simple qualitative criterion to evaluate the impact of faking on statistical results.