# [R] how to generate a random correlation matrix with restrictions

Sat Aug 29 05:41:18 CEST 2009

```Hi Kingsford,

There is more structure to a correlation matrix than that meets the eye!  Your method will produce a matrix R that looks "like" a correlation matrix, but beware - it is an impostor!

You can obtain a valid correlation matrix, Q, from the impostor R by using the `nearPD' function in the "Matrix" package, which finds the positive definite matrix Q that is "nearest" to R.  However, note that when R is far from a positive-definite matrix, this step may give a Q that does not have the desired property.

require(Matrix)

R <- matrix(runif(16), ncol=4)

R <- (R * lower.tri(R)) + t(R * lower.tri(R))

diag(R) <- 1

eigen(R)\$val

Q <- nearPD(R, posd.tol=1.e-04)\$mat

eigen(Q)\$val

max(abs(Q - R))  # maximum discrepancy between R and Q

Another easy way to produce a valid correlation matrix is:

R <- matrix(runif(36), ncol=6)

RtR <- R %*% t(R)

Q <- cov2cor(RtR)

But this does not have the property that the correlations are uniformly distributed.

Hope this helps,
Ravi.

____________________________________________________________________

Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619

----- Original Message -----
From: Kingsford Jones <kingsfordjones at gmail.com>
Date: Friday, August 28, 2009 10:12 pm
Subject: Re: [R] how to generate a random correlation matrix with	restrictions
To: Ning Ma <pningma at gmail.com>
Cc: r-help at r-project.org

> Ahh -- Mark Leeds just pointed out off-list that it was supposed to be
> a correlation matrix.
>
> Perhaps
>
> R <- matrix(runif(10000), ncol=100)
> R <- (R * lower.tri(R)) + t(R * lower.tri(R))
> diag(R) <- 1
>
> These are of course uniformly distributed positive correlations.
>
> Kingsford
>
>
> On Fri, Aug 28, 2009 at 7:36 PM, Kingsford
> Jones<kingsfordjones at gmail.com> wrote:
> >  R <- matrix(runif(10000), ncol=100)
> >
> > hth,
> >
> > Kingsford Jones
> >
> > On Fri, Aug 28, 2009 at 7:26 PM, Ning Ma<pningma at gmail.com> wrote:
> >> Hi,
> >>
> >> How can I generate a random 100x100 correlation matrix, R={r_ij},
> >> where about 10% of r_ij are greater than 0.9
> >>
> >>
> >> ______________________________________________
> >> R-help at r-project.org mailing list
> >>
> >> and provide commented, minimal, self-contained, reproducible code.
> >>
> >
>
> ______________________________________________
> R-help at r-project.org mailing list
>