Well, if you think about the geometry, all correlations equal usually won't work. Think of the SDs as the sides of a simplex and the correlations as the cosines of the angles between the sides (pick one variable as the 'origin'.) Only certain values will give a valid covariance or correlation matrix. HTH, David L. Reiner, PhD Head Quant Rho Trading Securities, LLC -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Mizanur Khondoker Sent: Thursday, June 26, 2008 11:11 AM To: r-help@r-project.org Subject: [SPAM] - [R] constructing arbitrary (positive definite) covariance matrix - Found word(s) list error in the Text body
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 > > ### 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 -- 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@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. ______________________________________________ R-help@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.