Here is one way to do it: # create the initial x variable x1 <- rnorm(100, 15, 5)
# x2, x3, and x4 in a matrix, these will be modified to meet the criteria x234 <- scale(matrix( rnorm(300), ncol=3 )) # put all into 1 matrix for simplicity x1234 <- cbind(scale(x1),x234) # find the current correlation matrix c1 <- var(x1234) # cholesky decomposition to get independence chol1 <- solve(chol(c1)) newx <- x1234 %*% chol1 # check that we have independence and x1 unchanged zapsmall(cor(newx)) all.equal( x1234[,1], newx[,1] ) # create new correlation structure (zeros can be replaced with other r vals) newc <- matrix( c(1 , 0.4, 0.5, 0.6, 0.4, 1 , 0 , 0 , 0.5, 0 , 1 , 0 , 0.6, 0 , 0 , 1 ), ncol=4 ) # check that it is positive definite eigen(newc) chol2 <- chol(newc) finalx <- newx %*% chol2 * sd(x1) + mean(x1) # verify success mean(x1) colMeans(finalx) sd(x1) apply(finalx, 2, sd) zapsmall(cor(finalx)) pairs(finalx) all.equal(x1, finalx[,1]) Hope this helps, -- Gregory (Greg) L. Snow Ph.D. Statistical Data Center Intermountain Healthcare [EMAIL PROTECTED] (801) 408-8111 > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Nguyen > Dinh Nguyen > Sent: Sunday, April 01, 2007 7:47 PM > To: r-help@stat.math.ethz.ch > Subject: [R] Generate a serie of new vars that correlate with > existing var > > Dear R helpers, > I have a var (let call X1) with approximately Normal > distribution (say, mean=15, SD=5). > I want to generate a series of additional vars X2, X3, > X4...such that the correlation between X2 and X1 is o.4, X3 and > X1 is 0.5, X4 and X1 is 0.6 and so on with the condition all > variables X2, X3, X4....have the same mean and SD with X1. > Any help should be appreciated > Regards > Nguyen > > ______________________________________________ R-help@stat.math.ethz.ch 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.
