# SV: [R] Correlation matrices

Patrik Waldmann Patrik.Waldmann at sysbot.lu.se
Wed Jul 26 18:16:05 CEST 2000

```Tests of covariance matrices are best performed with the hierarchical common principal component (CPC) approach (Flury 1988,1997), as the matrices can be equal, proportional, have CPC structure, partial CPC or be unrelated. This approach assumes multivariate normality, and that the covariance matrices are estimated in the same way. There are already programs written for this, for example http://www.uta.edu/biology/phillips/ . I'm sure this approach would be useful also for R users, but I don't have time writing it (one of the reasons for asking was to see if someone had implemented it in R). The problem with correlation matrices is that the assumption of multivariate normality doesn't hold. Some kind of resampling approach could be a solution. My problem is that I estimate two kinds of correlation matrices from the same sample, with two different methods. So in a way I'm testing if the methods give the same result (some kind of a Monte-Carlo test but with a given sample), and a permutation test would therefore not be meaningful (I think). The test of equal matrices is of most interest, and therefore the Mantel test is not appropriate (as it only tests for structure). The main problem seems to be how to relate a relevant test statistic of equality to a relevant resampling scheme (or whatever). Sorry for bothering you about this not-so-much-of-an-R-issue.

Patrik Waldmann
Patrik.Waldmann at sysbot.lu.se

>
>   Do you have any leads on statistical methods for solving this problem
> (independent of implementation in a particular system)? This doesn't seem
> like an R problem as much as a more general statistical problem.  Also,
> what do you mean by "better"?  More powerful?  Incorporating more
> admittedly pretty ignorant) of any really good general alternatives to
> Mantel's test, given the breadth of possible applications. You could try
> asking in sci.stat.math or sci.stat.consult (?).
>
>   I guess the only R-specific issue is that if you did have an alternative
> in mind it would quite probably be a permutation test of some sort, which
> would mean that either efficient R-coding or coding the test in C or
> FORTRAN and interfacing to R would be a good idea.
>
> On Wed, 26 Jul 2000, Patrik Waldmann wrote:
>
> > Hello,
> >
> > are there any good methods in R that will test if two correlation
> > matrices (obtained in different ways) are equal? Something better than
> > the Mantel test would be preferable.
> >
> > Regards,
> >
> > Patrik Waldmann
> >
> >
> >
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>
>

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