I want to do a SEM by simultaneously analyzing data from two studies. The goal is to get combined structural parameter estimates (like in a mini meta-analysis of individual participant data). Both studies have an identical instrumentation, but differ in the sampling (both have complex survey samples; study two has more clusters).
In the literature on integrative data analysis/meta-analysis I found two methods for this purpose: * Cooper and Patall (2009) mention that study can be used as a stratification variable. * Curran & Hussong (2009) suggest including study membership as a categorical predictor as well as its interactions with other predictors in the model. This seems impractical in SEM because - to my knowledge - interactions between manifest and latent variables can only be modeled in multi-group SEM which would not provide pooled estimates over both groups.
So my questions are: (1) Is it sufficient/defensible to use the stratification approach for the discussed purpose? (2) Is there a better way to get the pooled estimates?