Folks: Please help me understand why I get a WARNING :"variable is uncorrelated with other variables within class" when conducting my LCA.
It's not that I don't know that I could set the covariances free... the question is SHOULD I?
In CFA for example, the tradition is to leave the observed variable variances set to uncorrelated.
So here is my naive question: Is there something I am missing in LCA where I SHOULD be allowing the vars within classes to be correlated? Regardless of theory? If I allow all the vars to be correlated within classes (but constrained to be equal across classes), of course the model will fit the data "better" but what are the implications?
It's just a warning in case you had variables that you didn't realize you were using in the analysis. For example, if you forgot to include a USEVARIABLES statement when you were not analyzing all variables in a data set.
Note, however, that the local independence assumption of conventional LCA is not a sacred assumption - other, more flexible models than LCA could be very useful in many applications. So, yes, I would think there are scenarios where you might want to correlate variables within classes. We have one such example in the UG ex 7.16 with a reference. And of course factor mixture modeling is built on within-class correlation modeling - see for example the Muthen-Asparouhov (2006) article on tobacco dependence on our web site under Papers, Factor Mixture Analysis.