Interpreting fit statistics based on the M2

[Danny Swan]

Hello Dr. Chalmers,

Before I begin let me just say that I appreciate all the work you've put into the mirt package.

At the moment I'm trying to compare a 2pl model with 21 items to a bifactor model with one general factor and three specific factors (7 items per specific factor). Based on Cai, L., & Hansen, M. (2013) I understand that I can use the difference in the M2 statistics like the standard chi-square model comparison. I was just curious if there is any guidance about how the CFI, TLI, RMSEA and SRMSR when computed from the M2 compare to the values calculated based on the chis-square? Do the same set of guidelines for cutoffs for "good" fit in SEM models apply here? (Taking into consideration that "general" guidelines about really broad classes of models need to be taken with a grain of salt).

Thanks,

Danny

[Phil Chalmers]

Hi Danny,

Thank you for your kind words. It sounds like you are interpreting CFI and friendly correctly (with a grain of salt). I would say that the guidelines in SEM are reasonable for IRT models as well in so far as they are both only approximations and should be hedged in the state of the empirical paradigm. 

That's a vague answer, I know, but I generally don't commend over-interpreting goodness-of-fit statistics; models can still be quite useful, even if the fit is only approximate for the data, so I would still find and IRT model with a CFI ~ .85-.90 useful but has room for improvement. HTH.

Phil

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[Danny Swan]

Hi Phil,

I'm a methodological PhD student myself (I just don't typically do IRT work, applied or otherwise), so I fully understand your vagueness. Your answer is quite helpful.

I am in quite the opposite position! CFI and TLI > .97 in the case of the 2PL and even better in the case of the bifactor, all other fit statistics in an equally desirable range. It seems like either model will work for my purposes, although the bifactor model is clearly the more ideal one. Thanks for your rely!