Using covariates to improve entropy PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Kim Betts posted on Monday, October 03, 2016 - 4:52 pm
Hi Bengt and Linda,

I have read somewhere on the discussion boards before that regressing covariates on the class variable in LCA/FMA is an appropriate way to improve entropy. Can you point out any reference materials where the rationale for this statement is explained and/or tested?

Thank you.

Kim Betts.
 Bengt O. Muthen posted on Tuesday, October 04, 2016 - 1:37 pm
Here is what a colleague of mine thinks and I agree:

There isnít a particular paper that jumps to mind but I feel like there might be something out there. In my experience, bringing in covariates can actually drop the entropy some. It doesnít necessarily seem like the best strategy to me--if the class separation is bad, I donít know that including covariates is the answer. If the covariate effect on the class indicators is misspecified and the classes shift from the unconditional model, then the entropy could appear to improve when in fact the classes themselves have shifted to accommodate the misspecification of the joint distribution of the covariate and indicators. Also, Iím not sure that I would advocate chasing a higher entropy value to begin with. In my experience sometimes high entropy values actually mask classification problems with the smaller latent classes.
 Kim Betts posted on Tuesday, October 04, 2016 - 6:20 pm
Thank you Bengt,

I take your point that I have been placing too much emphasis on the entropy.

One last question if I may.

From a different perspective (forgetting the improvement in entropy), would you say it is a good strategy to introduce a covariate if:
(i) the covariate introduced is theoretically closely related to the indicator variables in the LCA/FMA;
(ii) introduction results in a better class discrimination (i.e., the two classes are now more distinct - with a high and a low class);
(iii) introduction makes the resulting LCA/FMA perform much better in subsequent validation analyses.

Lastly, if the above is true, are you aware of any references material that support this strategy? I have found some papers which seem to allude to this (at least as far as I interpret them), but none which say it or test it directly.

Thanks again.

Kim Betts.
 Bengt O. Muthen posted on Wednesday, October 05, 2016 - 4:17 pm
I would say yes to (i) - (iii).

Will let you know if I think of a reference.
 Kim Betts posted on Wednesday, October 05, 2016 - 6:59 pm
Great, thanks again Bengt.
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