At 10:04 AM 5/19/00 +0100, Prof Brian Ripley wrote:
On Fri, 19 May 2000, Prof Brian Ripley wrote: I thought that might be the reason. There is no mention of using n-1 rather than n in the denominator on the help page. Perhaps that might be added?
Um. What professional statistics package uses n, then? Are you suggesting that there is serious room for doubt?
S-PLUS, actually. Not in this context, of course, but princomp() when given a data matrix uses n as the divisor for the variance matrix. Amazing stuff. This in turn is translated into the eigenvalues (principal variances) of course. I was really puzzled about this while I was trying to explain to one of my colleagues what a simple generic calculation principal components really was and I was getting the same coefficients as princomp but slightly different variances. In a flash of inspiration I tried multiplying them by n/(n-1) and hey presto! Of course the case for an n-1 divisor is much less convincing in this context because even though it gives an unbiased (REML, maximum marginal likelihood, ...) estimator of the variance, the eigenvalues are certainly not unbiased estimators of the eigenvalues of the population variance matrix (but it can't hurt, either!). Bill. -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-devel mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-devel-request@stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._