Trait Correlation

Do you just mean the ordinary Pearson correlation between two phenotypes? That's pretty easy. Really, any model that fits a "saturated" covariance matrix can give you the correlation, because you can convert a covariance matrix to a correlation matrix with cov2cor(). Your best bet will be to analyze the raw data, because of the way full-information maximum-likelihood deals with missing data. As an example, you could search this website for BivariateSaturated_MatrixRawCholesky.R .

If this is in the context of a twin model, you could just apply cov2cor to whatever the model's expected covariance matrix works out to be, and look at the within-person, cross-trait correlation.