I was wondering if anyone has considered placing confidence intervals around fit indices other than rmsea to explore sem model fit, E. G. Srmr, cfi.. . Recent packages such as lavaan can create nice bootstraped distributions around each fit indicie and this seems like a logical progression for model fit. Similarly to test statistics in wider inferential statistics, treating the estimates as a defined point may be misleading, while a ci is a better estimation of plausible values. Is this a line of statistics others consider valid, or published papers/theoretical papers which have employed this technique. I'm happy to post the r code for these calculations if people are interested in pursuing this approach.
Dear Conal,
I agree with your approach and proposal. But you know the most difficult task is to determine what known statistical distribution underliess each index. Bootstrapping could be a good approach but it is the plan B. Anyway, it is always better than a point-estimation. All the best. I will follow your findings.
Dear Conal,
Agreeing with Albert, I must say that CIs are calculated around RMSEA (in LISREL) because its probabilty distribution has been established. I will try to find a reference for this and share it.
Dear Manual and Albert,
It's very useful to have RMSEA as an established CI which draws from a known underlying distribution. I agree with Albert that it would be best to determine underlying distributions to identify CIs. As a result, bootstrapping would be more of an estimate of precision based on a standard normal distribution.
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