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 Anouk van Dijk posted on Wednesday, January 15, 2020 - 6:38 am
I am conducting confirmatory LPA to compare 4 non-nested models. I use BIC and entropy to select the best-fitting model. However, these statistics do not converge. The lowest-BIC model has lower entropy (.74) than the second-lowest-BIC model (.79). As such, I am not clear which model to select as the best-fitting model.

I wonder:
1. Should I attach more weight to either BIC or entropy?
2. Would it be helpful to look at additional indices, such as aBIC or AIC?

Thanks in advance!
 Bengt O. Muthen posted on Wednesday, January 15, 2020 - 10:53 am
You should go with BIC. Only if 2 models have very similar BIC would I go with entropy. I think of entropy as R-square in SEM while BIC is closer to a model fit index - R-square has nothing to do with model fit but only the model's usefulness (which you wouldn't benefit from if the model doesn't fit well).
 Anouk van Dijk posted on Wednesday, January 15, 2020 - 11:37 pm
Thank you! Could I ask: what would be "very similar BIC?" In my case, the BICs were 602.69 and 607.28.

And, if I may: Did I understand correctly that there would be no use looking at other fit indices?

Thanks again!
 Bengt O. Muthen posted on Thursday, January 16, 2020 - 1:49 pm
That's less than 1% difference which isn't much.

You can always work with what I call neighboring models - that is, for a given H0 model, you can specify a more general model (e.g. residual covariances) and see if those extra parameters are significant.
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