Evaluating the Sensitivity ofGoodness-of-Fit Indices to Data Perturbation:An Integrated MC-SGR Approach

The issue of perturbations in real or simulated data has been substantially neglected in evaluating the adequacy of fit indices used to test covariance structure modeling. Nevertheless, it is certainly legitimate to wonder whether fit indices are reliably sensitive to data corruption. In particular, we would expect that a good index should approach its maximum under correct model specification and uncorrupted data, but also degrade substantially under massive data perturbation. In this paper we provide a possible methodological solution to the problem of evaluating the sensitivity of fit indices in structural equation modeling when perturbed data are considered. In particular, in our study the sensitivity of four different fit indices (two absolute fit-indices: GFI and AGFI, and two incremental fit-indices: CFI and NNFI) to perturbed data is examined in three different factorial models. The sensitivity evaluation is carried out by means of a new integrated approach which combines standard Monte Carlo (MC) simulations and a recent data generating procedure called Sample Generation by Replacements (SGR, [Lombardi et al., 2004]).