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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 k1 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)? Thank you very much in advance. 


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, 169177, DOI: 10.1080/10705511.2014.935844. (Download scripts). 


Thank you very much for your answer. 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? Thank you and kind regards, Luisa 


That message refers to the model that you specify, not how well your model fits. You may still have big residuals comparing your fitted model to the data. 


Thank you for this explanation! what would be the easiest way to find out which associations should be included in the model? I have nine continuous indicators. I already tried including all possible associations to see which ones are significant, but I could not yet find a stable solution without local maxima. Kind regards, Luisa 


No easy way beyond what you've done. Try adding a single factor (see our FMA literature and UG examples) and see which items have large loadings  suggesting residual correlation. 


Sorry to keep bothering you. 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. Thank you so much for your advice. 


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. 


Would it be correct to do a LCFA model for this where only the factor mean is allowed to vary across classes? Or should I use a less restrictive model? And sorry if this is obvious, but I'm not quite sure where I see the factor loadings in the output file? Are they the estimates under model results? And how would I decide which ones are large enough to be included? Many thanks!! 


Q1: The problem of no minimum BIC would remain, wouldn't it? Q2: They are listed under factor loadings in the output. Q3: Significant ones. You may want to watch our video of Short Course Topic 5 on our web site. 

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