Hi, I've recently read an article by Imai and Tingley (2012) in which they use finite mixture modeling to compare several non-nested models. They use R to do so, and set up the competing models in the syntax. Their syntax allows researchers to evaluate which model best describes individual participants within the data set, and in turn allows for comparison of models (which is most accurate for most participants?)
Is it possible to implement something similar in Mplus. I was wondering whether the finite mixture regression command (7.1 in the examples within the manual) PLUS creating multiple models in the user defined starts section might enable model comparison?
Many thanks, Matt
Imai, Kosuke, and Dustin Tingley. (2012). A Statistical Method for Empirical Testing of Competing Theories.'' American Journal of Political Science, Vol. 56, No. 1 (January), pp. 218-236.
Seems like Mplus can be helpful here; although Mplus does not provide an option to analyze several models in one run, I wonder if you really need that here. A quick look at this suggests that Imai et al. consider a regression model where different theories correspond to using different sets of covariates. The different theories are represented by latent classes.
I haven't given this much thought, but why couldn't you then, for instance with 2 theories (2 sets of covariates), formulate a regression mixture model where you include both sets of variables in the model but fix coefficients to zero in the two classes corresponding to which covariates the theories specify? The mixture analysis then attempts to find who's in which latent class.
I would be a bit skeptical about this general idea, however - haven't seen it elsewhere. Seems like Bayesian model averaging is a more established approach for this (although possibly with somewhat different aims).