# Comparing structural equation models with multivariate non-normality

I am aware that multivariate non-normality in SEM can inflate the chi-square statistic and deflate standard errors of parameter estimates. I can deal with the latter (in AMOS) using bootstrapping procedures. But here's my specific question: while I can't correct for chi-square inflation in AMOS (as far as I am aware), does this inflation matter if I am mostly interested in comparing several models using the chi-square change, each of which will presumably be inflated in the same manner, rather than simply testing whether a single model is well-fitting? Moreover, my best fitting model fits well by all sensible criteria, so the chi-square inflation per se is not a major concern.

As this query implies, I use AMOS and haven't currently got access to M-Plus or another similar package to apply the correction to chi-square inflation they provide.

-

This won't work, the models rarely get inflated in the same way. The proper analysis should involve Satorra-Benter scaled difference. I am not sure as to what the bootstrap analogues would be, although I am sure something can be constructed along the lines of the Bollen-Stine bootstrap (which should have become known as Beran-Srivastava bootstrap). I don't know if AMOS allows enough flexibility to construct the appropriate bootstrap scheme for the nested model testing, although I am sure it can run the bootstrap for the overall test.

-
Hi @StasK: Thanks for those comments. I didn’t realize that a Bollen-Stine bootstrap could be produced by AMOS (good to learn that). So, can one use the mean chi-square value produced by the bootstrapping for each model to then compare the models? For instance, one could then calculate the probability of the chi-square change in R to distinguish models? And is the mean chi-square value from the bootstrapping - along with the corresponding p-value - the figure to report in a manuscript (i.e. in the same way one would for a regular chi-square)? –  Gary Sep 12 '12 at 17:33
I am afraid you are all mixed up about what the Bollen-Stine bootstrap does. Did you read the actual paper? –  StasK Sep 12 '12 at 20:34