Hi--If I understand class membership in latent profile analysis, it is a posterior probability based on the similarity of the cases's response vector and the estimated means of each class, and the size of the class.
A collaborator is interested in a bit more detail--can you point me toward the equation Mplus uses for these posterior probabilities? Thanks in advance.
Many thanks. One more question: my collaborator and I are considering the differences betweeen LPA and K-means clustering. Just as multivariate outliers can strongly influence cluster centroids, would they affect, say, the estimated means of one or more classes? Would the impact on the mean estimates of each class be proportional to their posterior probability of membership in the class? Thanks.
I would say yes to the first question. Regarding the second question, it may be related to posterior probability to some extent, but a more direct way of assessing impact is to request the Mplus outlier statistics, for example "influence" which tells you how much each point influences the loglikelihood. You can then use Mplus to do a scatter plot of influence against some other key variable.