R help - Aug 2009 - how to generate a random correlation matrix with restrictions

Hi,

How can I generate a random 100x100 correlation matrix, R={r_ij},
where about 10% of r_ij are greater than 0.9

Thanks in advance.

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
>
> Thanks in advance.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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
>>
>> Thanks in advance.
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>

So, you want about 10% of the correlations to be greater than 0.9. And
what about the others? It would be helpful to know why you need this
kind of matrix and what you are going to do with it. 

Here is an attempt, based on generating a random variance matrix from
a Wishart distribution and transforming it to a correlation matrix.
(Package dlm contains a Wishart generator).

This will generate all the correlations to be around 0.9.
 
> require(dlm)
> n <- 100
> df <- n + 5
> S <- matrix(0.9, n, n)
> diag(S) <- 1
> S <- S / df
> set.seed(125)
> x <- cov2cor(rwishart(df, Sigma = S))
> summary(x[x!=1]) # off-diagonal elements
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.8576  0.9025  0.9116  0.9108  0.9196  0.9525 
> 
This is one possibility to obtain just about 10% of the correlations
to be around 0.9.
> N <- n * (n - 1) / 2 # number of correlations
> k <- 0.1 * N # want this number close to 0.9
> n1 <- round(max(Re(polyroot(c(-2*k, -1, 1)))))
> S[row(S) > n1 | col(S) > n1] <- 0
> diag(S) <- S[1, 1]
> y <- cov2cor(rwishart(df, Sigma = S))
> mean(y[y != 1] > 0.8) # about 10%
[1] 0.1002020
> summary(y[y != 1 & y > 0.8]) 
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.8630  0.8976  0.9051  0.9045  0.9126  0.9424 
> 
Again, with more background info we may be able to give you more
meaningful advice. 

HTH
Giovanni
> Date: Sat, 29 Aug 2009 09:26:34 +0800
> From: Ning Ma <pningma at gmail.com>
> Sender: r-help-bounces at r-project.org
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> 
> Hi,
> 
> How can I generate a random 100x100 correlation matrix, R={r_ij},
> where about 10% of r_ij are greater than 0.9
> 
> Thanks in advance.
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 
> 

-- 

Giovanni Petris  <GPetris at uark.edu>
Associate Professor
Department of Mathematical Sciences
University of Arkansas - Fayetteville, AR 72701
Ph: (479) 575-6324, 575-8630 (fax)
http://definetti.uark.edu/~gpetris/