From: Mizanur Khondoker <Mizanur.Khondoker_at_ed.ac.uk>

Date: Thu, 26 Jun 2008 17:11:14 +0100

}

cov

}

*> ### Simualte multivarite gaussin data ( gives Error)
*

*> Sigma<-COV(p = 3, sd = 2, r= -0.6)
*

> mu<-1:3

> mvrnorm(5, mu=mu, Sigma=Sigma)

Error in mvrnorm(5, mu = mu, Sigma = Sigma) : 'Sigma' is not positive definite

Date: Thu, 26 Jun 2008 17:11:14 +0100

Dear list,

I am trying to use the 'mvrnorm' function from the MASS package for simulating multivariate Gaussian data with given covariance matrix. The diagonal elements of my covariance matrix should be the same, i.e., all variables have the same marginal variance. Also all correlations between all pair of variables should be identical, but could be any value in [-1,1]. The problem I am having is that the matrix I create is not always positive definite (and hence mvrnorm fails).

Is there any simple way of constructing covariance matrix of the above
structure (equal variance, same pairwise correlation from [-1, 1])
that will always be positive definite?

I have noticed that covraince matrices created using the following COV
function are positive definite for -0.5 < r <1. However, for r <
-0.5, the matrix is not positive definite.
Does anyone have any idea why this is the case? For my simualtion, I
need to generate multivariate data for the whole range of r, [-1, 1]
for a give value of sd.

Any help/ suggestion would be greatly appreciated.

Examples

########

COV<-function (p = 3, sd = 1, r= 0.5){

cov <- diag(sd^2, ncol=p, nrow=p)

for (i in 1:p) {

for (j in 1:p) { if (i != j) { cov[i, j] <- r * sd*sd } }

}

cov

}

*> library(MASS)
**> ### Simualte multivarite gaussin data (works OK)
**> Sigma<-COV(p = 3, sd = 2, r= 0.5)
*

> mu<-1:3

> mvrnorm(5, mu=mu, Sigma=Sigma)

[,1] [,2] [,3]

[1,] 1.2979984 1.843248 4.460891 [2,] 2.1061054 1.457201 3.774833 [3,] 2.1578538 2.761939 4.589977 [4,] 0.8775056 4.240710 2.203712 [5,] 0.2698180 2.075759 2.869573 >

> mu<-1:3

> mvrnorm(5, mu=mu, Sigma=Sigma)

Error in mvrnorm(5, mu = mu, Sigma = Sigma) : 'Sigma' is not positive definite

-- Mizanur Khondoker Division of Pathway Medicine (DPM) The University of Edinburgh Medical School The Chancellor's Building 49 Little France Crescent Edinburgh EH16 4SB United Kingdom Tel: +44 (0) 131 242 6287 Fax: +44 (0) 131 242 6244 http://www.pathwaymedicine.ed.ac.uk/ ______________________________________________ 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.Received on Thu 26 Jun 2008 - 16:15:46 GMT

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