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From |
Bert Lloyd <bert.lloyd.89@gmail.com> |

To |
statalist <statalist@hsphsun2.harvard.edu> |

Subject |
st: cholesky vs matpowersym for FGLS transformation in Mata |

Date |
Tue, 24 Apr 2012 21:50:22 -0400 |

Dear Statalist, I have an application for which I need to conduct FGLS estimation "by hand", that is, transform both the y and X variables so that their regression cross-products are weighted by an FGLS weighting matrix Omega^(-1). That is, my ultimate goal is a regression of the form (X'*(Omega^-1)*X)^-1*(X'*(Omega^-1)*y) but for various reasons I need to compute this as a regression of tilde_y on tilde_X, where either tilde_X = Omega^(-1/2)*X and tilde_y = Omega^(-1/2)*X or tilde_X = L'*X and tilde_y = L'*y where L*L' = Omega^(-1), i.e L is the cholesky decomposition of Omega^(-1). So, it seems that I could do either of the following tilde_X = matpowersym(invsym(Omega),0.5) or tilde_X = cholesky(invsym(Omega))'*X and similarly for y, and the ultimate result ought to be the same. Is there any reason to prefer one method over the other? Are there important tradeoffs between the two? Given that a google search for stata matpowersym returns 107 hits, while a search for stata cholesky returns 12,500 hits, I am inclined to use the Cholesky method, but would like to make a more informed choice if possible. Many thanks, BL PS - I am aware of the matrix glsaccum function in Stata, however this is not suitable for my context, essentially because the weighting matrix is not constant across groups. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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