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Re: st: Re: hessian condition number


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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