R help - Nov 2009 - simulated correlated vectors

Hi,
Having a vector x of float type without any assumption of its distribution
(mean, variance etc), how to generate another vector that is correlated with x?
Extensibility: how to simulate more than two correlated vectors (again float
type and no preference for their distribution and without having vector x)?

Cheers,

Carol

On Thu, 12 Nov 2009 08:10:12 -0800 (PST) carol white <wht_crl at
yahoo.com>
wrote:
> Having a vector x of float type without any assumption of its distribution 
> (mean, variance etc), how to generate another vector that is 
> correlated with x?
Define an arbitrary function 'f', where 'f' may have a random
component,
and calculate f(x).
> Extensibility: how to simulate more than two correlated vectors (again 
> float type and no preference for their distribution and without having 
> vector x)?
Repeat step 1 several times. If you don't have 'x', define an
arbitrary
vector 'x' first ...

HTH. HAND.

-- 
Karl Ove Hufthammer

Try this:

x <- rexp(100, 1/3)

xp <- scale(x)

cor.mat <- rbind( c(1, 0.8, 0.7), c(0.8, 1, 0.3), c(0.7, 0.3, 1) )

x23 <- matrix( rnorm( 100 * 2, 1/3 ), ncol=2 )

x23 <- cbind(xp, scale(x23)) 

x23 <- x23 %*% solve(chol(var(x23))) ## skip if you don't want exact
cor's

x.new <- x23 %*% chol(cor.mat) 
x.new[,1] <- x.new[,1]*attr(xp, 'scaled:scale') + attr(xp,
'scaled:center')

all.equal( x.new[,1], x )

cor(x.new)
pairs(x.new)


you can generate the data from other distributions than the normal, and you can
add and multiply constants in the columns of x.new to give different
means/sd's.  This will set the correlations, but the exact distributions of
the columns is not guaranteed.

Hope this helps,

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of carol white
> Sent: Thursday, November 12, 2009 9:10 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] simulated correlated vectors
> 
> Hi,
> Having a vector x of float type without any assumption of its
> distribution (mean, variance etc), how to generate another vector that
> is correlated with x? Extensibility: how to simulate more than two
> correlated vectors (again float type and no preference for their
> distribution and without having vector x)?
> 
> Cheers,
> 
> Carol
> 
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