I am performing latent class analysis on different measures of political attitudes. I have run the analysis with up to 10 classes, yet the BIC keeps getting smaller and the BLRT still yiels significant results when comparing k-1 models. What other statistical indices should I consider in order to determine the number of classes? Or should I look primarily at interpretability (which ends at about 7 classes)?
It may be the you need some residual correlations. Have a look at the paper on our website:
Asparouhov, T. & Muthen, B. (2015). Residual associations in latent class and latent transition analysis. Structural Equation Modeling: A Multidisciplinary Journal, 22:2, 169-177, DOI: 10.1080/10705511.2014.935844. (Download scripts).
However, I do get the message in the output file that all variables are uncorrelated within class. Should this not mean that the assumption of local independence is fulfilled and residual associations aren't necessary?
My situation is now as follows: I have tried several variations of the Factor Mixture Models, with up to six classes and three factors. However, the BIC still kept getting smaller and smaller. I also had many problems with finding stable solutions without local maxima. Furthermore, I got warnings such as this:
ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT DISTRIBUTION OF THE CATEGORICAL VARIABLES IN THE MODEL. THE FOLLOWING PARAMETERS WERE FIXED:
Should I continue this approach? Is there anything else I can try? I also noticed that the classes resulting from the FMA look mostly similar to the ones I had from the initial LCA without factors or residual associations.
My idea was to use FMM as a tool to see which variables might need a residual correlation and then add those correlations - not to keep the FMM. Just adding the correlations would use fewer parameters than the FMM and therefore have a better chance of getting a small BIC.