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From |
Marcello Pagano <pagano@hsph.harvard.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Re: hessian condition number |

Date |
Mon, 29 Mar 2004 07:45:34 -0500 |

The log is a measure of how many digits of accuracy are lost in the calculations with floating point arithmetic. Been around a long time.

m.p.

Kit Baum wrote:

On Mar 28, 2004, at 2:33 AM, Clive wrote:]OK, I think I've solved my own question of finding log10(hessian) in Stata. Please alert me if I've gone wrong somewhere. (1) Get -ereturn list-; (2) get -matrix list e(V)-; (3) calculate the hessian condition number = [max root/min root]^1/2 (as given in Greene, 2000: 40) (can you calculate the hessian directly in Stata?); (4) -display log10([hcn])-. In step (3), I can only assume 'roots' means covariances. If so, I find that the interchanging of these terms is a bit confusing! Is all this correct?

The condition number of a p.d. matrix is related to the ratio of its largest to smallest eigenvalues. They are the roots of the characteristic polynomial of the matrix. "findit condition number". I have never heard of taking the log10 of the condition number; well-conditioned regressor matrices are usually condition<20 (with condition being the positive sqrt of the ratio). See Belsley et al. as referenced under [r] regression diagnostics.

Kit

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**Follow-Ups**:**Re: st: Re: hessian condition number***From:*"Clive Nicholas" <Clive.Nicholas@newcastle.ac.uk>

**References**:**st: Re: hessian condition number***From:*Kit Baum <kitbaum@mac.com>

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