Class separation and entropy
Message/Author
 Jon Heron posted on Friday, March 14, 2014 - 10:17 am
Dear Bengt/Linda

this isn't strictly Mplus related but i'm at the end of my tether and would really appreciate any insight you may have.

I have in mind a 3-class mixture model, e.g. derived from a single tri-modal Y.

Whilst entropy would be a measure of the separation of those three classes, in theory one could also derive 3 additional measures of entropy, each from a different pairwise comparison, by working with the appropriate assignment probabilities.

Have you seen this done anywhere? I'm grappling with currently unanswerable questions regarding whether I discard the probabilities for the third class, perhaps rescale the two remaining probabilities so they sum to one within person and whether i also drop cases for which the modal class is neither of the two of interest.

many thanks, Jon
 Bengt O. Muthen posted on Friday, March 14, 2014 - 12:50 pm
Wouldn't you just consider the 3 x 3 classification table where you can see which classes are more clearly formed than others?
 Jon Heron posted on Friday, March 14, 2014 - 12:56 pm
thanks Bengt
that was where I started, and to be honest still looks like the best thing I have done.

For a class1/class2 fuzzyness I took the product of the first/second main diagonal element, or alternatively the sum of the [2,1] and [1,2] elements. I feel they both capture the same issue.

both have intuitive appeal but perhaps lack the statistical robustitude of a formula

best, Jon
 Jon Heron posted on Monday, March 17, 2014 - 7:52 am
No question, just an update.

Have stumbled across a paper which provides a formula for overlap between pairs of clusters in the case of a profile analysis

http://www.public.iastate.edu/~maitra/papers/SimMix.pdf

see equation in section 2.1, page 4.

Have calculated for a simulated example of one Y and 3-class mixture and the results are very close to the off-diagonal elements of Mplus' second classification matrix (the D-matrix).

Delighted to see that their recommendation - summing both off-diagonal elements - was just what I have been doing :-)