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From: Steven on 16 Jun 2010 16:16
Hi,

Right now, I'm trying to calculate the confidence intervals for some regressed parameters. Thus, I'm trying to obtain the covariance matrix (Cov), where Cov = s2*inv(J'*J), where s2 is the error variance.

Right now, I'm just using the inv() function, but I tend to get warnings about ill-conditioned matrices and lots of NaN and Inf answers. I know you aren't supposed to use inv() usually, so is there another way to perform this calculation without using the inv() function, or would that not really help?

Thanks,
From: esozo on 16 Jun 2010 16:43
> Cov = s2*inv(J'*J), where s2 is the error variance.

What are the dimension of your particular J? It could eventually be Cov = s2 * inv( J * J' )
From: Peter Perkins on 16 Jun 2010 17:21
On 6/16/2010 4:16 PM, Steven wrote:

> Right now, I'm trying to calculate the confidence intervals for some
> regressed parameters. Thus, I'm trying to obtain the covariance matrix
> (Cov), where Cov = s2*inv(J'*J), where s2 is the error variance.
> Right now, I'm just using the inv() function, but I tend to get warnings
> about ill-conditioned matrices and lots of NaN and Inf answers. I know
> you aren't supposed to use inv() usually, so is there another way to
> perform this calculation without using the inv() function, or would that
> not really help?

This is a case where you really do need the diagonal elements of the
inverse. It's possible to QR your Jacobian, invert R, and then get the
diagonal elements by summing squares along rows. This will be better
conditioned than when using J'*J. Your J may be so badly conditioned
that this won't help, but it might.

But first make sure you have the right orientation for J, as esozo
points out. Hope this helps.
From: Steven on 16 Jun 2010 17:40
Thanks for the help esozo and Peter. I tried doing the QR factorization and finding the diagonal elements that way. It did help somewhat--I actually got some numbers, although they are very high--I guess the rest of my problem lies with the function itself.

Thanks again!
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