Apologies if this is answered elsewhere, but I was wondering if OpenMx allows estimation of random factor loadings at the within-level in a multilevel confirmatory factor analysis.
A less important aside: has anyone been able to successfully include a nonlinear constraint in a two level CFA or SEM with latent variables?
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Right now, OpenMx does not allow random factor loadings in a multilevel CFA. You can have definition variables deterministically change the factor loadings (including algebraic expressions involving free parameters and definition variables), and you can estimate a different factor loading for each level 1 unit. However, in both these cases, the factor loadings are fixed effects, not random.
As for using nonlinear constraints,
mxConstraint()works regardless of the kind of model, so there should be no issues. In many cases, it's computationally better to usemxAlgebra()to set parameters to be the result of the algebra instead of usingmxConstraint(), but it should work either way.