Create correlated variables from existing variable [closed] - r

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Let's say I have a vector:
Q<-rnorm(10,mean=0,sd=20)
From this vector I would like to:
1. create 10 variables (a1...a10) that each have a correlation above .5 (i.e. between .5 and 1) with Q.
the first part can be done with:
t1<-sapply(1:10, function(x) jitter(t, factor=100))
2. each of these variables (a1...a10) should have a pre-specified correlation with each other. For example some should be correlated .8 and some -.2.
Can these two things be done?
I create a correlation matrix:
cor.table <- matrix( sample( c(0.9,-0.9) , 2500 , prob = c( 0.8 , 0.2 ) , repl = TRUE ) , 50 , 50 )
k=1
while (k<=length(cor.table[1,])){
cor.table[1,k]<-0.55
k=k+1
}
k=1
while (k<=length(cor.table[,1])){
cor.table[k,1]<-0.55
k=k+1
}
diag(cor.table) <- 1
However, when I apply the excellent solution by #SprengMeister I get the error:
Error in eigen(cor.table)$values > 0 :
invalid comparison with complex values
continued here: Eigenvalue decomposition of correlation matrix

Answer 1

As a pointer to solution use noise function jitter in R:
set.seed(100)
t = rnorm(10,mean=0,sd=20)
t1 = jitter(t, factor = 100)
cor(t,t1)
[1] 0.8719447

Answer 2

To generate data with a prescribed correlation (or variance),
you can start with random data,
and rescale it using the Cholesky decomposition of the desired correlation matrix.
# Sample data
Q <- rnorm(10, mean=0, sd=20)
desired_correlations <- matrix(c(
1, .5, .6, .5,
.5, 1, .2, .8,
.6, .2, 1, .5,
.5, .8, .5, 1 ), 4, 4 )
stopifnot( eigen( desired_correlations )$values > 0 )
# Random data, with Q in the first column
n <- length(Q)
k <- ncol(desired_correlations)
x <- matrix( rnorm(n*k), nc=k )
x[,1] <- Q
# Rescale, first to make the variance equal to the identity matrix,
# then to get the desired correlation matrix.
y <- x %*% solve(chol(var(x))) %*% chol(desired_correlations)
var(y)
y[,1] <- Q # The first column was only rescaled: that does not affect the correlation
cor(y) # Desired correlation matrix

Answer 3

I answered a very similar question a little while ago
R: Constructing correlated variables
I am not familiar with jitter so maybe my solutions is more verbose but it would allow you determining exactly what the intercorrelations of each of your variables and q is supposed to be.
The F matrix referenced in that answer describes the intercorrelations that you want to impose on your data.
EDIT to answer question in comment:
If i am not mistaken, you are trying to create a multivariate correlated data set. So all the variables in the set are correlated to varying degrees. I assume Q is your criterion or DV, and a1-a10 are predictors or IVs.
In the F matrix you would reflect the relationships between these variables. For example
cor_Matrix <- matrix(c(1.00, 0.90, 0.20 ,
0.90, 1.00, 0.40 ,
0.20, 0.40, 1.00),
nrow=3,ncol=3,byrow=TRUE)
describes the relationships between three variables. The first one could be Q, the second a1 and the third a2. So in this scenario, q is correlated with a1 (.90) and a2 (.20).
a1 is correlated with a2 (.40)
The rest of the matrix is redundant.
In the remainder of the code, you are simply creating your raw, uncorrelated variables and then impose the loadings that you have previously pulled from the F matrix.
I hope this helps. If there is a package in R that does all that, please let me know. I build this to help me understand how multivariate data sets are actually generated.
To generalize this to 10 variables plus q, just set the parameters that are set to 3 now to 11 and create an 11x11 F matrix.