[S] Followup on roundoff error and algorithms

Marc R. Feldesman (feldesmanm@pdx.edu)
Fri, 05 Jun 1998 08:16:05 -0700


Several people replied to my query about "roundoff" problems in extracting
the determinant of a pooled variance covariance matrix. I wasn't explicit
enough in providing a few pieces of information, which I provide now.

1. I'm forming the vcv matrices using a call to the function var().
2. I'm extracting the determinant using a call to det from the
library(Matrix), introduced in 1995, according to VR2.
3. The particular case in which I reported the inaccuracy at the second
decimal position involved a pooled matrix of 3 groups, a total N of 200,
and individual sample sizes of 59, 75, and 66.

Let me also stress that I do not know what specific algorithms SAS, SPSS,
or NCSS97 uses to form the covariance matrices or extract the determinant.
It is important to remember (I think) that my own function (involving var
and det) yields results substantially identical to SPSS, SAS and NCSS97 on
the determinants of the individual covariance matrices (out to decimal
position 6), but fails on the pooled matrix at the 2nd decimal position. I
don't think the issue is about what denominator (N (sum of n's), or N -
groups) is used to compute the matrix.

Bill Venables has suggested an alternative algorithm involving the qr
-decomposition. I haven't tried it yet.

But I wanted to share these other details with you since they may have a
bearing on the problem.

Thanks, as always, for your prompt, courteous, and helpful responses.

Dr. Marc R. Feldesman
email: feldesmanm@pdx.edu
email: feldesman@ibm.net
pager: 503-870-2515
fax: 503-725-3905

"If ignorance is bliss then why aren't there more happy people?" Lawrence
Peter

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