R help - Apr 2007 - 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

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
greg.snow at intermountainmail.org
(801) 408-8111
 
 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Nguyen 
> Dinh Nguyen
> Sent: Sunday, April 01, 2007 7:47 PM
> To: r-help at 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
> 
>

Dear Greg,
Thanks million!
"As good as it gets" :)
All the best
Nguyen

-----Original Message-----
From: Greg Snow [mailto:Greg.Snow at intermountainmail.org] 
Sent: Wednesday, April 04, 2007 1:46 AM
To: Nguyen Dinh Nguyen; r-help at stat.math.ethz.ch
Subject: RE: [R] Generate a serie of new vars that correlate with existing
var

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
greg.snow at intermountainmail.org
(801) 408-8111
 
 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Nguyen 
> Dinh Nguyen
> Sent: Sunday, April 01, 2007 7:47 PM
> To: r-help at 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
> 
>