Can anyone direct me to a script indicating how to run a constraint model? I am combining two twin data sets and want to run a fully constrained and fully unconstrained model in order to know if the two samples can be combined. How can I tweak my multivariate Chlolesky to do this?
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It sounds like you're trying to fit a multiple group model to two separate datasets. Parameters may be constrained across groups/submodels by giving them the same label. Your general structure will probably look something like this:
Model 1: model contains two submodels, one for each dataset. The same matrices and algebras are in each model, and every free parameter in the first model has the same label as the same parameter in the second model. So if the first element in the Cholesky is labeled "a1" in the first group, it is labeled "a1" in the second group.
Model 2: model contains two submodels, one for each dataset. The same matrices and algebras are in each model, and every free parameter in the first model has a different label as the same parameter in the second model. So if the first element in the Cholesky is labeled "a1" in the first group, it is labeled "b1" in the second group.
Compare the two models with a likelihood ratio test.
One final nagging statistician critique: if you can't find a significant difference between the samples, that does not mean the two datasets are identical. It just means you don't have power to detect the ways that they differ. You can always run analyses on them as a multiple group model. Also, don't forget mean structure! Cholesky decompositions pertain to covariance structures only; mean differences in samples are important too!