topic Re: Covariance and Correlation in SAS/IML Software and Matrix Computations

Covariance and Correlation

bhfield — Tue, 27 Jan 2015 16:26:04 GMT

I am replicating Rick's Covariance / Correlation Cholesky transformation within Proc IML as follows:

proc iml;

D = { 1 2 3,

2 4 3,

3 3 9};

X = root(D)`*root(D);

print D;

print X;

run;

Interestingly, X does not equal D. I am wondering if this is due to D not being Positive Definite or, in other words, Det(D) <0. The code runs without any indication of a problem.....had I not printed X, I would have never known that that Root(D)`*Root(D) would not equal D.

Any thoughts on why this is the case?

Re: Covariance and Correlation

Rick_SAS — Tue, 27 Jan 2015 17:49:18 GMT

Interesting. I've never seen this behavior before. The correct behavior would be for the ROOT function to report an error in the log:

ERROR: (execution) Matrix should be positive definite

If I were to guess, I'd say that the exact integer values are causing a numerical problem in the ROOT function such that the ROOT function does not report the error. In the following code I perturb an element by a tiny amount and the ROOT function correctly reports that the matrix is not PD:

D[1] = D[1] + 1e-8;

G = root(D);

I will enter a bug report at SAS so that someone can look into this situation further.

Re: Covariance and Correlation

bhfield — Tue, 27 Jan 2015 17:54:02 GMT

Thanks Dr. Wicklin.