Can Mplus estimate a 3-level growth mixture CACE model for data where the randomization and compliance occurs at level-3? The design in question involves a cluster randomized trial in which several hundred schools are randomized to either an intervention or control condition. Measures of student prosocial behavior are taken at 5 occasions. The research question focuses on whether the trajectory of prosocial development is different in the control and intervention conditions. Compliance with the intervention varied across schools, and was measured. In scouring the cluster randomized trials and growth mixture model publications by Muthen, Jo and colleagues, the Mplus manual, and examples, I could find no growth mixture CACE analysis with randomization and compliance at level-3 (school level). Yet it would seem to be feasible if there were good covariates at the student and school levels, and for compliance, based on Chapter 10 in the Mplus manual. Is such a model not possible in Mplus, or has no one tried it yet?
This should be possible. The 3-level modeling would be handled via Type = Mixture Twolevel, where the Within level is time and person and the Between level is school. The latent classes of compliers and noncompliers are then pertaining to a between-level latent class variable which is put on the Between = list. Let me know how it goes.
As I understand it, in that growth mixture CACE/ACE setup, unknown compliance status is handled as missing data. Is it possible for that growth mixture CACE/ACE model to accommodate missing data in either the outcome or the covariates? I noticed that the "auxiliary= (m) " command only works with "Type=General", so that option is out. Would a "Type =Mixture Twolevel Missing" be possible, assuming MAR missingness? Or would one have to do a multiple imputation prior to the mixture model?