

Multilevel Mixture Modeling 

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I would appreciate your guidance for a crosssectional LCA I am running on data for 1200 adolescents. I identified a 4class solution with 6 binary substance use indicators and regressed class membership on risk/protective factors of interest. I have one class fixed as a "no use" class. Fit indices, etc. all appeared to be OK. The 1200 youth are nested within 10 schools, so I modified my analyses to incorporate this structure based on ex. 10.3. My problem is that I am getting a fairly extensive warning indiating: 1) standard errors for the parameter estimates may not be trustworthy due to a nonpositive definite firstorder derivative product matrix and potential model nonidentification relating to a particular parameter (11); and 2) An indication that nonidentification may be due to having more parameters than the number of clusters and a suggestion to reduce parameters. How do I resolve the problems related to a particular parameter (since my starting values are based on a successful model where the nested structure was ignored). Also, does reducing parameters mean dropping risk/protection factors from my regression model b/c I don't have enough schools to test the nesting effect? Is there a more appropriate way to address the nesting, given that I really just want to correct my estimates but am not examining Level2 effects on the model directly? 


The error message refers to parameter 11 because you have only 10 clusters  the standard errors are evaluated based on the number of independent observations which are the 10 clusters. With only 10 clusters, the standard error calculations are not trustworthy  as in regular multilevel modeling you need at least 20 and preferrably 3050. This is true for both TYPE=TWOLEVEL and TYPE=COMPLEX. It's hard to say what to do in such situations  you might instead use school as a fixed effect, using 9 dummy variables as IVs. 


Thank you for the response  another question related to these analyses. I am using the classes as DVs in a logit regression model (to assess predictors of membership). Is it also possible to use the classes as IVs for another set of variables in the same set of analyses (i.e., some variables predict class membership and class membership predicts another set of continuous variables). An alterative is to export the class membership probabilities and then run an ANOVA to see if groups differ on current frequency of use, but I'm thinking it would be more efficient to estimate these relationships simultaneously, if possible. Thank you, 


Yes, you can have the class variable both being influenced by and influencing other variables. For the latter (distal outcome case), note that you don't say e.g. "y on c#", but c influencing a continuous y is handled by the y means changing over the c classes (by default). See the UG ex8.6 where the distal is categorical (u). 


A couple of brief followups: 1) I'm not sure I see the regression of class membership on u in examine 8.6  is there something I am missing in the code? 2) I added the following statement to my model: "daysalc on c#1c#3;" in an effort to model membership on the continous outcome (in this case days using alcohol), but get a number of warnings including "Variable is uncorrelated with all other variables within class" and "One or more MODEL statements were ignored. These statements may be incorrect or are only supported by ALGORITHM=INTEGRATION." Introducing integration did not produce any better results. Also, since class 4 is a "zerouse" group  is it possible to exclude them from this subsequent step (since I know their use frequency is 0)? 


Sorry  I just reread your post and the example, again, more closely. Basically, it looks like these continuous indicators would be treated as variables in the LCA, and I would assess mean differences across classes. Of course, this changes the "meaning" of the classes, since they now incorporate a continous indicator (i.e., there may be heterogeneity in the way the continous indicator operates within classes  and different class structures may be required). 

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