Correlated variables in LCA? PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Stephen C Messer posted on Thursday, December 14, 2006 - 5:34 pm
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?

Thanks for all the enlightenment you can provide :-)

 Linda K. Muthen posted on Thursday, December 14, 2006 - 5:59 pm
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.
 Stephen C Messer posted on Friday, December 15, 2006 - 7:50 am
Thanks Linda. Are there any scenarios where I might want to allow the variables to correlate within classes?
 Boliang Guo posted on Friday, December 15, 2006 - 8:12 am
if you correlated two residual in one class, this will violate the local independence assumption for LCA. I think.
 Stephen C Messer posted on Friday, December 15, 2006 - 9:14 am
thanks guo
 Bengt O. Muthen posted on Friday, December 15, 2006 - 9:56 am
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.
 Stephen C Messer posted on Friday, December 15, 2006 - 1:36 pm
Outstanding. Thanks!
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