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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

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

Subject |
st: RE: -estimates post- question |

Date |
Tue, 19 Aug 2003 23:41:33 +0100 |

Mark Schaffer > I've just discovered that -estimates post- > in version 7 > seems to behave inconsistently when the covariance matrix > being posted is > not positive definite. Sometimes it posts the matrix > without complaint; > other times it bombs out with error 506, "matrix not > positive definite". A > demonsration is below. > > Any ideas about why -est post- might accept some non-pd > matrices and not > others? > > --Mark > > * This covariance matrix is not positive definite, > * and -est post- will refuse to post it. > > . mat list Vsave > > symmetric Vsave[4,4] > L. > p w p _cons > p .00649023 > w -.00412379 .001033 > L.p -.00480518 .00311278 .00541914 > _cons .15565638 -.03696101 -.14100874 1.592022 > > . mat list bsave > > bsave[1,4] > L. > p w p _cons > y1 .19293435 .79621877 .08988469 16.236603 > > . matsqrt Vsave > matrix is not poisitive definite > r(504); > > . est post bsave Vsave > matrix not positive definite > r(506); > > * This matrix covariance matrix is also not positive definite, > * but -estimates post- will post it anyway. > > . mat list Vsave2 > > symmetric Vsave2[4,4] > L. > p w p _cons > p .02953177 > w -.0035374 .00122606 > L.p -.02182449 .00140922 .01935147 > _cons -.01117901 -.02100185 .0169305 1.0082315 > > . mat list bsave2 > > bsave2[1,4] > L. > p w p _cons > y1 .01730217 .81018271 .21623384 16.554759 > > . matsqrt Vsave > matrix is not poisitive definite > r(504); > > . est post bsave2 Vsave2 > > . mat list e(V) > > symmetric e(V)[4,4] > L. > p w p _cons > p .02953177 > w -.0035374 .00122606 > L.p -.02182449 .00140922 .01935147 > _cons -.01117901 -.02100185 .0169305 1.0082315 > Here's a guess: this is a replay, with details changed, of the "when is a matrix (deemed to be) symmetric?" debate (see e.g. Vince Wiggins' 10 June posting on that, also to Mark). In principle, a matrix is positive definite or not, period, as every pure mathematician will (presumably) insist. Write a program to do it, using finite precision arithmetic etc., and things are not quite so straightforward, as every numerical analyst will (presumably) insist. Mark is using -matsqrt-, as a test, but is this doing ___exactly____ the same thing? Nick n.j.cox@durham.ac.uk * * 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/

**References**:**st: -estimates post- question***From:*Mark Schaffer <M.E.Schaffer@hw.ac.uk>

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