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I want to transform the results of a correlated-factor model into multivariate Cholesky form.

Loehlin (1996) [1] gives the formulae for a bivariate case, but I wonder if anyone has a reference or pseudo-code for the multivariate case?

My end goal is to set the correlations between factors in such a way as to be equivalent to dropping paths in a Cholesky.

[1] Loehlin, J. C. (1996). The Cholesky approach: A cautionary note. Behavior Genetics, 26(1), 65-69.