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Re: st: cmp and condition numbers
From
David Hoaglin <[email protected]>
To
[email protected]
Subject
Re: st: cmp and condition numbers
Date
Fri, 4 May 2012 08:30:24 -0400
In a least-squares regression problem, the condition number is the
ratio of the largest and smallest singular values of the matrix of
regressors (X). The singular values are the eigenvalues of
(X-transpose)X. For a nonsingular square matrix A, the eigenvalues of
A-inverse are the reciprocals of the eigenvalues of A. Centering and
rescaling the regressors changes the condition number, usually making
it smaller. The correlation matrix should have a smaller condition
number than (X-transpose)X, but that need not be smaller than the
condition number of X. As condition numbers go, 1000 is not terribly
high.
David Hoaglin
On Fri, May 4, 2012 at 7:45 AM, David Roodman ([email protected])
<[email protected]> wrote:
> Philip the two issues you raise may be unrelated.
>
> cmp is not designed for true simultaneous systems, by which I mean ones in the matrix of coefficients of the dependent variables in each other's equations is not triangular.
>
> As for the condition number, there is more than one way to compute this. For each equation, cmp applies Mata's built-in cond() function to the correlation matrix of the non-constant regressors, taking cond()'s defaults. This amounts to computing the product of the maximum eigenvalues of the correlation matrix and its inverse. I think I got this formulation from Greene, but I can't check today because I am travelling.
>
> --David
>
> ---------------
> From "Bromiley, Philip" <[email protected]>
> To "[email protected]" <[email protected]>
> Subject st: cmp and condition numbers
> Date Mon, 30 Apr 2012 23:30:28 +0000
> I'm trying to estimate a simultaneous system with three continuous and one discrete variable using cmp. I have been unable to get it to estimate properly - lots of not concave and backed up messages and then it crashes saying it has hit a discontinuous or flat region.
>
> Cmp warns me that I have an ill-conditioned regressor matrix and reports high condition numbers for each of the equations (40 to 1000). However, when I run the equation with regress, I don't get high VIF's, and get a much lower condition number.
>
> Would someone know the reason for such a discrepancy? Any suggestions would be welcome.
>
> Phil
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