In the CFA analysis the x2/gl and the cfi-tli and rmsa-srmr comparison indices are taken into account.
Girum -
I am not familiar with this topic, but when you say that the "...statistic for the best model fit is sensitive to sample size, and always rejects the model..." that sounds like the situation always to be found that a model is never exactly correct, and with enough data that becomes apparent. Relatedly, you don't want to 'overfit' a model to sample data, as the sample will not perfectly 'represent' the population. With enough information you will 'reject' any hypothesis. This is why estimation and a standard error is often more easily interpretable for decision making than an hypothesis test, and an isolated p-value is not enough information. What you are doing sounds similar to me. But as I said ... not my area.
So, "...does a large sample size affect the model fit?" No, a larger sample can just show more about how close that fit may be.
The question is then "Is my model good enough ... as George Box noted ... to be useful?"
Cheers - Jim
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