R help - Dec 2004 - R code for var-cov matrix given variances and correlations

Dear list members,

Where can I find code for computing the p*p variance-covariance 
matrix given a vector of p variances (ordered varA, varB, ..., 
varp) and a vector of all possible correlations (ordered corAB, 
corAC, ..., corp-1,p)?

I know that the covariance between 2 variables is equal to the 
product of their correlation and their standard deviations: 
corAB * varA^.5 * varB^.5
and so:
covAB <- function(corAB, varA, varB) {
    corAB * varA^.5 * varB^.5
    }

If the vector of variances were
var.vec <- c(14, 12, 7) 
and the vector of correlations were 
cor.vec <- c(.4, .2, .5), 
then the vector of covariances would be:
> covAB(c(.4, .2, .5),c(14, 14, 12), c(12, 7, 7))
[1] 5.184593 1.979899 4.582576
>
and the variance-covariance matrix with covariances rounded to 
the first decimal place would be:
> vmat <- matrix(c(14, 5.2, 2.0, 5.2, 12, 4.6, 2.0, 4.6, 7),
+ nrow=3)
> vmat
     [,1] [,2] [,3]
[1,] 14.0  5.2  2.0
[2,]  5.2 12.0  4.6
[3,]  2.0  4.6  7.0
> 
So the question is: How can I generate a p*p variance-covariance
matrix from a vector of variances and a vector of correlations
without resorting to a construction like:
    vmat <- matrix(rep(0, p*p), nrow=p)
    if (p == 2) {
        vmat[1,1] <- var[1]
        vmat[1,2] <- cor[1] * (var[1]^.5 * var[2]^.5)
        vmat[2,1] <- cor[1] * (var[2]^.5 * var[1]^.5)
        vmat[2,2] <- var[2]
        }
    if (p == 3) {
        vmat[1,1] <- var[1]
        vmat[1,2] <- cor[1] * (var[1]^.5 * var[2]^.5)
        vmat[1,3] <- cor[2] * (var[1]^.5 * var[3]^.5)
        vmat[2,1] <- cor[1] * (var[2]^.5 * var[1]^.5)
        vmat[2,2] <- var[2]
        vmat[2,3] <- cor[3] * (var[2]^.5 * var[3]^.5)
        vmat[3,1] <- cor[2] * (var[3]^.5 * var[1]^.5)
        vmat[3,2] <- cor[3] * (var[3]^.5 * var[2]^.5)
        vmat[3,3] <- var[3]
        }
and so forth?

Thanks,

Maurice Haynes
National Institute of Child Health and Human Development
Child and Family Research Section
6705 Rockledge Drive, Suite 8030
Bethesda, MD  20892
Voice: 301-496-8180
Fax: 301-496-2766
E-mail: mh192j at nih.gov

"Haynes, Maurice (NIH/NICHD)" <haynesm at cfr.nichd.nih.gov>
writes:
> If the vector of variances were
> var.vec <- c(14, 12, 7) 
> and the vector of correlations were 
> cor.vec <- c(.4, .2, .5), 
> then the vector of covariances would be:
> > covAB(c(.4, .2, .5),c(14, 14, 12), c(12, 7, 7))
> [1] 5.184593 1.979899 4.582576
> >
> and the variance-covariance matrix with covariances rounded to 
> the first decimal place would be:
> > vmat <- matrix(c(14, 5.2, 2.0, 5.2, 12, 4.6, 2.0, 4.6, 7),
> + nrow=3)
> > vmat
>      [,1] [,2] [,3]
> [1,] 14.0  5.2  2.0
> [2,]  5.2 12.0  4.6
> [3,]  2.0  4.6  7.0
> > 

# First fill in the correlation matrix:

V <- matrix(NA,3,3)
diag(V) <- 1
V[lower.tri(V)] <-  c(.4, .2, .5)
V[upper.tri(V)] <- t(V)[upper.tri(V)]

# then scale rows and columns

D <- diag(sqrt( c(14, 12, 7)))
D %*% V %*% D

# or, more efficiently

s <- sqrt( c(14, 12, 7))
sweep(sweep(V,1,s,"*"),2,s,"*")




-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

On 21 Dec, 2004, at 13:09, Haynes, Maurice (NIH/NICHD) wrote:
> Dear list members,
>
> Where can I find code for computing the p*p variance-covariance
> matrix given a vector of p variances (ordered varA, varB, ...,
> varp) and a vector of all possible correlations (ordered corAB,
> corAC, ..., corp-1,p)?
Something like this (not tested):

         sd.vec <- sqrt(var.vec)
         n <- length(sd.vec)
         cor.mat <- matrix(1, n, n)
         for (i in 2:n){
             for (j in 1:i-1){
                 cor.mat[i,j] <- cor.vec[(i-1)*(i-2)/2 + j]
                 cor.mat[j,i] <- cor.mat[i,j]}}
         cov.mat <- cor.mat * outer(sd.vec, sd.vec)

I hope that helps.

David

>
> I know that the covariance between 2 variables is equal to the
> product of their correlation and their standard deviations:
> corAB * varA^.5 * varB^.5
> and so:
> covAB <- function(corAB, varA, varB) {
>     corAB * varA^.5 * varB^.5
>     }
>
> If the vector of variances were
> var.vec <- c(14, 12, 7)
> and the vector of correlations were
> cor.vec <- c(.4, .2, .5),
> then the vector of covariances would be:
>> covAB(c(.4, .2, .5),c(14, 14, 12), c(12, 7, 7))
> [1] 5.184593 1.979899 4.582576
>>
> and the variance-covariance matrix with covariances rounded to
> the first decimal place would be:
>> vmat <- matrix(c(14, 5.2, 2.0, 5.2, 12, 4.6, 2.0, 4.6, 7),
> + nrow=3)
>> vmat
>      [,1] [,2] [,3]
> [1,] 14.0  5.2  2.0
> [2,]  5.2 12.0  4.6
> [3,]  2.0  4.6  7.0
>>
>
> So the question is: How can I generate a p*p variance-covariance
> matrix from a vector of variances and a vector of correlations
> without resorting to a construction like:
>     vmat <- matrix(rep(0, p*p), nrow=p)
>     if (p == 2) {
>         vmat[1,1] <- var[1]
>         vmat[1,2] <- cor[1] * (var[1]^.5 * var[2]^.5)
>         vmat[2,1] <- cor[1] * (var[2]^.5 * var[1]^.5)
>         vmat[2,2] <- var[2]
>         }
>     if (p == 3) {
>         vmat[1,1] <- var[1]
>         vmat[1,2] <- cor[1] * (var[1]^.5 * var[2]^.5)
>         vmat[1,3] <- cor[2] * (var[1]^.5 * var[3]^.5)
>         vmat[2,1] <- cor[1] * (var[2]^.5 * var[1]^.5)
>         vmat[2,2] <- var[2]
>         vmat[2,3] <- cor[3] * (var[2]^.5 * var[3]^.5)
>         vmat[3,1] <- cor[2] * (var[3]^.5 * var[1]^.5)
>         vmat[3,2] <- cor[3] * (var[3]^.5 * var[2]^.5)
>         vmat[3,3] <- var[3]
>         }
> and so forth?
>
> Thanks,
>
> Maurice Haynes
> National Institute of Child Health and Human Development
> Child and Family Research Section
> 6705 Rockledge Drive, Suite 8030
> Bethesda, MD  20892
> Voice: 301-496-8180
> Fax: 301-496-2766
> E-mail: mh192j at nih.gov
>
> ______________________________________________
> R-help at 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

On 21-Dec-04 Haynes, Maurice (NIH/NICHD) wrote:
> Dear list members,
> 
> Where can I find code for computing the p*p variance-covariance 
> matrix given a vector of p variances (ordered varA, varB, ..., 
> varp) and a vector of all possible correlations (ordered corAB, 
> corAC, ..., corp-1,p)?
> [...]
example:
> X<-cbind(rnorm(10),rnorm(10))
> cov(X)
           [,1]       [,2]
[1,] 0.90141614 0.09364018
[2,] 0.09364018 0.88476825
> cor(X)
          [,1]      [,2]
[1,] 1.0000000 0.1048540
[2,] 0.1048540 1.0000000
> vars<-apply(X,2,var)
> vars
[1] 0.9014161 0.8847682
> diag(sqrt(vars))%*%cor(X)%*%diag(sqrt(vars))
           [,1]       [,2]
[1,] 0.90141614 0.09364018
[2,] 0.09364018 0.88476825

Ted.


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Date: 21-Dec-04                                       Time: 13:54:45
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