I am trying to run a two-level mixture model (non-parametric random effects LCA) with 897 participants in 11 clusters, testing 2 within classes and 2 between classes. I ran into the following message:
THE BEST LOGLIKELIHOOD VALUE HAS BEEN REPLICATED. RERUN WITH AT LEAST TWICE THE RANDOM STARTS TO CHECK THAT THE BEST LOGLIKELIHOOD IS STILL OBTAINED AND REPLICATED.
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 -0.518D-16. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 23, %WITHIN% %CB#1.CW#2%: [ DETAIL$1 ] (equality/label)
THE NONIDENTIFICATION IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER OF CLUSTERS. REDUCE THE NUMBER OF PARAMETERS.
I increased the number of clusters to 22 and ran into the same message. I then tried to reduce the number of parameters from 16 to 10 (= less parameters than clusters), but the message still showed up.
I was wondering if this could be a case of model nonidentification? All parameters are binary. I get the same warning message when using the parametric approach.
I have a similar problem - I am running a LPA and the warning about the non-positive definite matrix pops up.
I am trying to fit several profile solutions (1-6) of which the 2-profile solution runs without this error (entropy 0.774). The 3-profile solution does run and has excellent entropy (0.993). I have the feeling the sample size (approx n = 550) needs more discriminating power to define solutions with 3 profiles and up, but it does identifies a 2-profile because less discriminating power is ok.
Q1: This is just my interpretation of the error, but I want to check if this makes sense? Q2: is the error of the 3 profile solution to be ignored?