# Equality of Covariances Matrices Test in R (varcomp)

October 9, 2011
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(This article was first published on fernandohrosa.com.br - en » R, and kindly contributed to R-bloggers)

This is a piece of code I implemented in 2004, which was supposed to be part of an R-package in multivariate testing (to be named, rather creatively, mvttests).

Time has flown, I haven’t still got around to implementing the said package, but people keep asking me for the varcomp function, so here it is, for posterity:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40  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) }