

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 3class mixture model, e.g. derived from a single trimodal 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 


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 3class mixture and the results are very close to the offdiagonal elements of Mplus' second classification matrix (the Dmatrix). Delighted to see that their recommendation  summing both offdiagonal elements  was just what I have been doing :) 

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