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Re: st: eigenvector after manovatest |

Date |
Tue, 20 May 2003 09:20:18 -0500 |

Ricardo Ovaldia <[email protected]> asks > The -manovatest- command after manova saves the > eigenvalues of the (H^-1)(E) matrix in r(eigvals). How > can get the eigenvectors? [I assume you mean (E^-1)(H).] And in another message asks > One more question about -manova- (if you don't mind): > is there a way to get the 1st canonical variate for a > given null hypothesis. For example Ho: > foreign=domestic? > > This is computed as V_1'Y_j, where v_1 is the > eigenvector corresponding to the largest eigenvalue, > and Y_j is the vector of dependent variables for the j > subject. Can predict do this? Since the MANOVA test statistics are functions of the eigenvalues and do not directly make use of the eigenvectors, -manova- and -manovatest- do not save off the eigenvectors. Actually, -manova- and -manovatest- internally compute the eigenvalues of KHK' where K is inv(cholesky(E)). This has the same eigenvalues as inv(E)*H. So internally, Stata does not compute the eigenvectors of inv(E)*H at all, and hence does not have them sitting around to return to the user. After -manova- and -manovatest- you can grab the eigenvalues and the H and E matrices of interest. You can take the H and E matrices and try to compute the eigenvectors. Realize that inv(E)*H is not symmetric. The -matrix symeigen- command give eigenvalues and vectors, but only for symmetric matrices, while -matrix eigenvalues- gives only eigenvalues, but allows nonsymmetric matrices. Just today I read on statalist where Mark Schaffer <[email protected]> responded to Kaleb Michauds inquiry concerning obtaining eigenvectors from a square non-symmetric matrix. > > PS. I still would LOVE to see a program in Stata for determining > > eigenvectors from a square non-symmetric matrix. You've got one for > > eigenvalues, just one more not-quite-simple step. :) > > finidit eigenvalues => Kit Baum's GENEIGEN. Does exactly what you > want, I think. I have no experience with -geneigen-, but you might want to explore that possibility for obtaining the eigenvectors of inv(E)*H Ken Higbee [email protected] StataCorp 1-800-STATAPC * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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