I have two quick questions about LCA output in Mplus that I hope you can help me with.
(1) Does the following message always point to model underidentification (i.e., should replications with such a message, for example, be deleted from a simulation study?)? Or can there be other reasons for this (other than underidentification)?
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.982D-11. PROBLEM INVOLVING PARAMETER 4.
(2) What does it mean to get logit threshold estimates > 15 or < -15 in Mplus? I always thought that 15 and -15 were the boundary values in Mplus, but it seems that even more "extreme" values are sometimes output by the program. In particular, I would like to know if such values should be categorized as boundary estimates or not? Or are they a sign of a more serious problem like underidentification?
1. No, this could simply mean that a logit estimate goes large, corresponding to a probability being almost zero or one. With large estimates the ML information matrix can get numerically too close to singular and Mplus automatically fixes such estimates to eliminate them from the information matrix. So check if parameter 4 is large before condemning the model.
2. That is related to 1, where in many cases Mplus automatically doesn't push the estimate beyond 15 - the logit then translates almost exactly to a probability of zero or one. This in turn helps the interpretation of the model.