[Rd] Additional output in cancor

[Prof Brian Ripley]

Oh, great timing!   R went into feature-freeze last night for 1.3.0.
No new features until 1.4.0 in December or whatever comes next.

On Mon, 11 Jun 2001, Jonathan Rougier wrote:

> Can I suggest an additional output component in cancor, from package
> mva?  It would be useful to have the number of canonical correlation
> vectors, equivalently the rank of the covariance between x and y (label
> "rank").  This would usually be min(dx, dy), where dx and dy have
> already been computed for the svd function, but there might be
> situations where it was less than this, so I guess the safe option would
> be to include
>
> 	rank = qr(t(x) %*% y)$rank
>
> among the outputs.  Then the last four lines of the help might be
> amended to
>
>      rk <- cxy$rank
>      all.equal(cor(x %*% cxy$xcoef[, 1:rk, drop=FALSE],
>        y %*% cxy$ycoef[, 1:rk, drop=FALSE]), diag(cxy$cor))
>      all.equal(cor(x %*% cxy$xcoef[, 1:rk, drop=FALSE]), diag(1, rk))
>      all.equal(cor(y %*% cxy$ycoef[, 1:rk, drop=FALSE]), diag(1, rk))
>
> which I think is more intuitive.
>
> More radically, the xcoef and ycoef components of cancor might
> themselves be restricted to the appropriate columns (1:rank).  This
> might affect some existing code, although any code that uses the
> non-informative columns has got to be broken, hasn't it?!

Nope.  It's rare, but needing to span the orthocomplement can happen.

> Can I also suggest an extra reference for the help page:
>
> 	Mardia, K. V., J. T. Kent and J. M. Bibby (1979).  Multivariate
> Analysis, London, Academic Press Ltd, ch. 10.

I'd say that was inferior to Seber (and I find it rather confusing).
Your mileage may vary....

-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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