Hi all,
I am running CFA on Amos. My data violated multivariate normality, so I used Bollen-Stine (B-S) bootstrapping with ML.
However, the bootstrapping just changed the p-value of chi-square. As the limitations of X2, I reported "chi-square/df" instead of X2.
My question is, if I don't use chi-square as an model fit index, does that mean I don't really need to run bootstrapping because all the other indices are still the same with or without bootstrapping? Does that mean indices such as CFA, RMSEA are not affected by the assumption of multivariate normality??
TIA.
That is completely up to you, the χ2 is sensitive to normality, hence why you should do as you did, use for instance BS and report χ2/df, however, CFI, TLI and RMSEA are really robust against non-normality which is why you don't see them change, i.e., unlike χ2, the other fit indices are not really adjusted by the BS bootstrapping. You could, as you say, "skip" χ2 and the BS and report the other robust non-adjusted fit indices. But for extra rigor in your reporting, I'd include the BS with χ2/df as well as CFI, TLI, RMSEA etc. even though they really aren't affected by bootstrapping (don't forget confidence intervals!)
Oh sorry, in AMOS when using BS bootstrapping there should be an output for the bias corrected bootstrapped CIs for the parameter estimates, for instance a 95% CI of factor loadings (λs), error variances, latent variable correlations, regression βs if applicable, just note down everything as reviewers are likely to ask for these. These CIs are not for the fit estimates as they are point estimates really and CIs doesn't make any sense with them, sorry for creating confusion (well, apart from RMSEA which can be reported with CIs)
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