michael watson (IAH-C)
2004-Nov-16 14:49 UTC
[R] Difference between two correlation matrices
Hi Now a more theoretical question. I have two correlation matrices - one of a set of variables under a particular condition, the other of the same set of variables under a different condition. Is there a statistical test I can use to see if these correlation matrices are "different"? Thanks Mick
Hello, I don't know if it is applicable in your case, but have you tried Mantel test? You can use it to determine significant correlation between two matrices, using Pearsion, Spearman or Kendal correlation indices. Hope it helps, All the best, Marta ----- Original Message ----- From: "michael watson (IAH-C)" <michael.watson at bbsrc.ac.uk> To: <r-help at stat.math.ethz.ch> Sent: Tuesday, November 16, 2004 2:49 PM Subject: [R] Difference between two correlation matrices> Hi > > Now a more theoretical question. I have two correlation matrices - one > of a set of variables under a particular condition, the other of the > same set of variables under a different condition. Is there a > statistical test I can use to see if these correlation matrices are > "different"? > > Thanks > Mick > > ______________________________________________ > 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
One solution is to use procruste analysis.
Perform a principal coordinate analysis on your data (cmdscale) to obtain
two individuals by variables tables.
Then, you can perform procruste rotation and test to know if the two
matrice tell the same thing. It is more powerful than mantel test.
As you have correlations, I suppose than you can consider your original
variables rather than correlation and cmdscale
Functions are available in the ade4 package:
procuste(ade4) Simple Procruste Rotation between two sets of
points
procuste.randtest(ade4)
Monte-Carlo Test on the sum of the singular
values of a procustean rotation (in C).
procuste.rtest(ade4) Monte-Carlo Test on the sum of the singular
values of a procustean rotation (in R).
A reference on the analysis:
<http://www.steph280.freesurf.fr/files/articles/Ecosci2003.pdf>S. Dray, D.
Chessel, J. Thioulouse : Procrustean co-inertia analysis for the linking of
ecological tables.
Ecoscience<http://www.steph280.freesurf.fr/files/articles/Ecosci2003.pdf>,
2003, vol. 10, 110-119.
available at :
http://www.steph280.freesurf.fr/files/articles/Ecosci2003.pdf
Hope this helps !
At 10:31 16/11/2004, Marta Rufino wrote:>Hello,
>
>I don't know if it is applicable in your case, but have you tried Mantel
>test?
>You can use it to determine significant correlation between two matrices,
>using Pearsion, Spearman or Kendal correlation indices.
>
>Hope it helps,
>All the best,
>Marta
>
>
>----- Original Message -----
>From: "michael watson (IAH-C)" <michael.watson at
bbsrc.ac.uk>
>To: <r-help at stat.math.ethz.ch>
>Sent: Tuesday, November 16, 2004 2:49 PM
>Subject: [R] Difference between two correlation matrices
>
>
> > Hi
> >
> > Now a more theoretical question. I have two correlation matrices -
one
> > of a set of variables under a particular condition, the other of the
> > same set of variables under a different condition. Is there a
> > statistical test I can use to see if these correlation matrices are
> > "different"?
> >
> > Thanks
> > Mick
> >
> > ______________________________________________
> > 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
>
>______________________________________________
>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
St??phane DRAY
--------------------------------------------------------------------------------------------------
D??partement des Sciences Biologiques
Universit?? de Montr??al, C.P. 6128, succursale centre-ville
Montr??al, Qu??bec H3C 3J7, Canada
Tel : (514) 343-6111 poste 1233 Fax : (514) 343-2293
E-mail : stephane.dray at umontreal.ca
--------------------------------------------------------------------------------------------------
Web http://www.steph280.freesurf.fr/
If you have the data that created the correlation matrices, then you can do a permutation test. The first question to ask is, "What does 'different' mean?" Some choices include: max(abs(cor1 - cor2)) max(abs(eigen(cor1 - cor2)$values)) Once you have decided what metric makes most sense, you can perform the test. First pool all of the data (if you think that there are different means in the two conditions, then remove the means within each group before pooling). Then perform a number of random allocations of the pooled data into two groups with the number in each group equal to the original numbers. The test compares your statistic using the original correlation matrices to the distribution of statistics of the correlations from the random allocations. Patrick Burns Burns Statistics patrick at burns-stat.com +44 (0)20 8525 0696 http://www.burns-stat.com (home of S Poetry and "A Guide for the Unwilling S User") michael watson (IAH-C) wrote:>Hi > >Now a more theoretical question. I have two correlation matrices - one >of a set of variables under a particular condition, the other of the >same set of variables under a different condition. Is there a >statistical test I can use to see if these correlation matrices are >"different"? > >Thanks >Mick > >______________________________________________ >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 > > > >
Fernando Henrique Ferraz P. da Rosa
2004-Nov-19 22:17 UTC
[R] Difference between two correlation matrices
michael watson (IAH-C) writes:> Hi > > Now a more theoretical question. I have two correlation matrices - one > of a set of variables under a particular condition, the other of the > same set of variables under a different condition. Is there a > statistical test I can use to see if these correlation matrices are > "different"? > > Thanks > Mick >If you can assume multivariate normality, you can use a test of hypothesis to test if the covariance+ matrices are equal. Such a test is described for example in Anderson (1958)*. I am currently working on implementing some multivariate tests on R (sphericity test, equality of covariance matrices, etc). Attached follows a preliminary version of varcomp(): this function implements the test for equality of covariance matrices under multivare normality aforementioned. It takes as first argument a list with the covariance matrices and a vector n indicating the sample size used to calculate each of them. Example of use: Suppose you have 3 estimated covariance matrices S1, S2, S3, from a sample of 3 bivariate normal populations with unkown covariance matrices. The sample size for each Si, was 11,12,11. S1 <- matrix(c(7.17,19.47,19.47,113.38),byrow=T,ncol=2) S2 <- matrix(c(20.33,59.78,59.78,229.02),byrow=T,ncol=2) S3 <- matrix(c(5.22,17.33,17.33,112.88),byrow=T,ncol=2) varcomp(list(S1,S2,S3),n=c(11,12,11)) Will test H0: Sigma1 = Sigma2 = Sigma3, vs. H1: at least two of them are different from each other. Beware though that it's still work in progress, I've tested it for a few examples and it gave sensible results, but it still needs some polishing. * An Introduction to Multivariate Analysis, Wiley. + note that a correlation matrix is a special type of a covariance matrix, so you can use a test of hypothesis designed for covariance matrices. -- Fernando Henrique Ferraz P. da Rosa http://www.ime.usp.br/~feferraz
Fernando Henrique Ferraz P. da Rosa
2004-Nov-19 22:18 UTC
[R] Difference between two correlation matrices
er.. forgot to attach the file. there it goes. (sorry) michael watson (IAH-C) writes:> Hi > > Now a more theoretical question. I have two correlation matrices - one > of a set of variables under a particular condition, the other of the > same set of variables under a different condition. Is there a > statistical test I can use to see if these correlation matrices are > "different"? > > Thanks > Mick > > ______________________________________________ > 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 > >-- Fernando Henrique Ferraz P. da Rosa http://www.ime.usp.br/~feferraz -------------- next part -------------- varcomp <- function(covmat,n) { if (is.list(covmat)) { if (length(covmat) < 2) stop("covmat must be a list with at least 2 elements") ps <- as.vector(sapply(covmat,dim)) if (sum(ps[1] == ps) != length(ps)) stop("all covariance matrices must have the same dimension") p <- ps[1] q <- length(covmat) if (length(n) == 1) Ng <- rep(n,q) else if (length(n) == q) Ng <- n else stop("n must be equal length(covmat) or 1") DNAME <- deparse(substitute(covmat)) } else stop("covmat must be a list") ng <- Ng - 1 Ag <- lapply(1:length(covmat),function(i,mat,n) { n[i] * mat[[i]] },mat=covmat,n=ng) A <- matrix(colSums(matrix(unlist(Ag),ncol=p^2,byrow=T)),ncol=p) detAg <- sapply(Ag,det) detA <- det(A) V1 <- prod(detAg^(ng/2))/(detA^(sum(ng)/2)) kg <- ng/sum(ng) l1 <- prod((1/kg)^kg)^(p*sum(ng)/2) * V1 rho <- 1 - (sum(1/ng) - 1/sum(ng))*(2*p^2+3*p-1)/(6*(p+1)*(q-1)) w2 <- p*(p+1) * ((p-1)*(p+2) * (sum(1/ng^2) - 1/(sum(ng)^2)) - 6*(q-1)*(1-rho)^2) / (48*rho^2) f <- 0.5 * (q-1)*p*(p+1) STATISTIC <- -2*rho*log(l1) PVAL <- 1 - (pchisq(STATISTIC,f) + w2*(pchisq(STATISTIC,f+4) - pchisq(STATISTIC,f))) names(STATISTIC) <- "corrected lambda*" names(f) <- "df" RVAL <- structure(list(statistic = STATISTIC, parameter = f,p.value = PVAL, data.name = DNAME, method = "Equality of Covariances Matrices Test"),class="htest") return(RVAL) }