Re: sample variance-covariance matrices

["Alla Linetsky" <alinetsky@rogers.com>]

I did a bit of research into multivariate control charts a few years
ago, when I started PhD studies (which I later dropped). I found that
the extra effort in constructing a MV control chart did not provide
any new insight that univariate charts wouldn't offer. For one thing,
you cannot visualize a MV chart. The only thing you can do is take
univariate or bivariate projections. For something designed to be a
visual tool, this rather defeats the purpose.

A more serious problem was one of variable dependencies. By its
nature, a control chart is used to track processes in which stability
(i.e. nothing but random variation) is a desired feature. MV analysis,
on the other hand, works best when there are strong dependencies among
the variables, as well as strong cause-and-effect relationship between
the MV variables and some outcome. In my research, I used an iterative
technique (partial least squares) on real data to come up with the
var-cov matrix, and found that it simply didn't converge; most likely
due to an absense of a strong relationship with the outcome. The
paper, rather than being an illustration of the method, became a
critique.

While I've been too far removed from rigorous analysis to comment on
your var-cov matrix, all I can suggest is - try it, and see if it
gives you insight you can actually use. Test it first on a bivariate
situation, because then you can at least plot your results. But I
suspect that the chart will not find any more (or fewer) assignable
causes than a simultaneous examination of the univariate charts.

Alla Linetsky