--- /dev/null
+`CADM.global` <-
+ function(Dmat, nmat, n, nperm=99, make.sym=TRUE, weights=NULL, silent=FALSE)
+{
+### Function to test the overall significance of the congruence among
+### a group of distance matrices using Kendall's coefficient of concordance W.
+###
+### copyleft - Pierre Legendre, December 2008
+###
+### Reference -
+### Legendre, P. and F.-J. Lapointe. 2004. Assessing congruence among distance
+### matrices: single malt Scotch whiskies revisited. Australian and New Zealand
+### Journal of Statistics 46: 615-629.
+###
+### Parameters of the function --
+###
+### Dmat = A text file listing the distance matrices one after the other, with
+### or without blank lines.
+### Each matrix is in the form of a square distance matrix with 0's
+### on the diagonal.
+###
+### nmat = number of distance matrices in file Dmat.
+###
+### n = number of objects in each distance matrix. All matrices have same n.
+###
+### nperm = number of permutations for the tests.
+###
+### make.sym = TRUE: turn asymmetric matrices into symmetric matrices by
+### averaging the two triangular portions.
+### = FALSE: analyse asymmetric matrices as they are.
+###
+### weights = a vector of positive weights for the distance matrices.
+### Example: weights = c(1,2,3)
+### = NULL (default): all matrices have same weight in calculation of W.
+###
+### silent = TRUE: informative messages will not be printed, except stopping
+### messages. Option useful for simulation work.
+### = FALSE: informative messages will be printed.
+###
+################################################################################
+
+ if(nmat < 2)
+ stop("Analysis requested for a single D matrix: CADM is useless")
+
+ a <- system.time({
+
+ ## Check the input file
+ if(ncol(Dmat) != n)
+ stop("Error in the value of 'n' or in the D matrices themselves")
+ nmat2 <- nrow(Dmat)/n
+ if(nmat2 < nmat) # OK if 'nmat' < number of matrices in the input file
+ stop("Number of input D matrices = ",nmat2,"; this value is < nmat")
+
+ nd <- n*(n-1)/2
+ if(is.null(weights)) {
+ w <- rep(1,nmat)
+ } else {
+ if(length(weights) != nmat)
+ stop("Incorrect number of values in vector 'weights'")
+ if(length(which(weights < 0)) > 0)
+ stop("Negative weights are not permitted")
+ w <- weights*nmat/sum(weights)
+ if(!silent) cat("Normalized weights =",w,'\n')
+ }
+
+ ## Are asymmetric D matrices present?
+ asy <- rep(FALSE, nmat)
+ asymm <- FALSE
+ end <- 0
+ for(k in 1:nmat) {
+ begin <- end+1
+ end <- end+n
+ D.temp <- Dmat[begin:end,]
+ if(sum(abs(diag(as.matrix(D.temp)))) > 0)
+ stop("Diagonal not 0: matrix #",k," is not a distance matrix")
+ vec1 <- as.vector(as.dist(D.temp))
+ vec2 <- as.vector(as.dist(t(D.temp)))
+ if(sum(abs((vec1-vec2))) > 0) {
+ if(!silent) cat("Matrix #",k," is asymmetric",'\n')
+ asy[k] <- TRUE
+ asymm <- TRUE
+ }
+ }
+ D1 <- as.list(1:nmat)
+ if(asymm) {
+ if(make.sym) {
+ if(!silent) cat("\nAsymmetric matrices were transformed to be symmetric",'\n')
+ } else {
+ nd <- nd*2
+ if(!silent) cat("\nAnalysis carried out on asymmetric matrices",'\n')
+ D2 <- as.list(1:nmat)
+ }
+ } else {
+ if(!silent) cat("Analysis of symmetric matrices",'\n')
+ }
+ Y <- rep(NA,nd)
+
+ ## String out the distance matrices (vec) and assemble them as columns into matrix 'Y'
+ ## Construct also matrices of ranked distances D1[[k]] and D2[[k]] for permutation test
+ end <- 0
+ for(k in 1:nmat) {
+ begin <- end+1
+ end <- end+n
+ D.temp <- as.matrix(Dmat[begin:end,])
+ vec <- as.vector(as.dist(D.temp))
+ if(asymm) {
+ if(!make.sym) {
+ ## Analysis carried out on asymmetric matrices:
+ ## The ranks are computed on the whole matrix except the diagonal values.
+ ## The two halves are stored as symmetric matrices in D1[[k]] and D2[[k]]
+ vec <- c(vec, as.vector(as.dist(t(D.temp))))
+ diag(D.temp) <- NA
+ D.temp2 <- rank(D.temp)
+ diag(D.temp2) <- 0
+ # cat("nrow =",nrow(D.temp2)," ncol =",ncol(D.temp2),'\n')
+ # cat("Matrix ",k," min =",min(D.temp2)," max =",max(D.temp2),'\n')
+ # cat("Matrix ",k," max values #",which(D.temp2 == max(D.temp2)),'\n')
+ D1[[k]] <- as.matrix(as.dist(D.temp2))
+ D2[[k]] <- as.matrix(as.dist(t(D.temp2)))
+ } else {
+ ## Asymmetric matrices transformed to be symmetric, stored in D1[[k]]
+ vec <- (vec + as.vector(as.dist(t(D.temp)))) / 2
+ D.temp2 <- (D.temp + t(D.temp)) / 2
+ D.temp2 <- as.dist(D.temp2)
+ D.temp2[] <- rank(D.temp2)
+ D.temp2 <- as.matrix(D.temp2)
+ D1[[k]] <- D.temp2
+ }
+ } else {
+ ## Symmetric matrices are stored in D1[[k]]
+ D.temp2 <- as.dist(D.temp)
+ D.temp2[] <- rank(D.temp2)
+ D1[[k]] <- as.matrix(D.temp2)
+ }
+ Y <- cbind(Y, vec)
+ }
+ Y <- as.matrix(Y[,-1])
+ colnames(Y) <- colnames(Y,do.NULL = FALSE, prefix = "Dmat.")
+
+ ## Begin calculations for global test
+
+ ## Compute the reference values of the statistics: W and Chi2
+ ## Transform the distances to ranks, by column
+ Rmat <- apply(Y,2,rank)
+
+ ## Correction factors for tied ranks (eq. 3.3)
+ t.ranks <- apply(Rmat, 2, function(x) summary(as.factor(x), maxsum=nd))
+ TT <- sum(unlist(lapply(t.ranks, function(x) sum((x^3)-x))))
+ # if(!silent) cat("TT = ",TT,'\n')
+
+ ## Compute the S = Sum-of-Squares of the row-marginal sums of ranks (eq. 1a)
+ ## The ranks are weighted during the sum by the vector of matrix weights 'w'
+ ## Eq. 1b cannot be used with weights; see formula for W below
+ sumRanks <- as.vector(Rmat%*%w)
+ S <- (nd-1)*var(sumRanks)
+
+ ## Compute Kendall's W (eq. 2a)
+ ## Eq. 2b cannot be used with weights
+ ## because the sum of all ranks is not equal to m*n*(n+1)/2 in that case
+ W <- (12*S)/(((nmat^2)*((nd^3)-nd))-(nmat*TT))
+
+ ## Calculate Friedman's Chi-square (Kendall W paper, 2005, eq. 3.4)
+ Chi2 <- nmat*(nd-1)*W
+
+ ## Test the Chi2 statistic by permutation
+ counter <- 1
+ for(j in 1:nperm) { # Each matrix is permuted independently
+ # There is no need to permute the last matrix
+ Rmat.perm <- rep(NA,nd)
+ ##
+ if(asymm & !make.sym) {
+ ## For asymmetric matrices: permute the values within each triangular
+ ## portion, stored as square matrices in D1[[]] and D2[[]]
+ for(k in 1:(nmat-1)) {
+ order <- sample(n)
+ vec <- as.vector(as.dist(D1[[k]][order,order]))
+ vec <- c(vec, as.vector(as.dist(D2[[k]][order,order])))
+ Rmat.perm <- cbind(Rmat.perm, vec)
+ }
+ vec <- as.vector(as.dist(D1[[nmat]]))
+ vec <- c(vec, as.vector(as.dist(D2[[nmat]])))
+ Rmat.perm <- cbind(Rmat.perm, vec)
+ } else {
+ for(k in 1:(nmat-1)) {
+ order <- sample(n)
+ vec <- as.vector(as.dist(D1[[k]][order,order]))
+ Rmat.perm <- cbind(Rmat.perm, vec)
+ }
+ vec <- as.vector(as.dist(D1[[nmat]]))
+ Rmat.perm <- cbind(Rmat.perm, vec)
+ }
+ # Remove the first column of Rmat.perm containing NA
+ # The test is based on the comparison of S and S.perm instead of the comparison of
+ # Chi2 and Chi2.perm: it is faster that way.
+ # S, W, and Chi2 are equivalent statistics for permutation tests.
+ Rmat.perm <- as.matrix(Rmat.perm[,-1])
+ S.perm <- (nd-1)*var(as.vector(Rmat.perm%*%w))
+ if(S.perm >= S) counter <- counter+1
+ }
+ prob.perm.gr <- counter/(nperm+1)
+
+ table <- rbind(W, Chi2, prob.perm.gr)
+ colnames(table) <- "Statistics"
+ rownames(table) <- c("W", "Chi2", "Prob.perm")
+ })
+ a[3] <- sprintf("%2f",a[3])
+ if(!silent) cat("\nTime to compute global test =",a[3]," sec",'\n')
+#
+ # if(asymm & !make.sym) { out <- list(congruence_analysis=table, D1=D1, D2=D2)
+ # } else {
+ out <- list(congruence_analysis=table)
+ # }
+#
+ out$nperm <- nperm
+ class(out) <- "CADM.global"
+ out
+}
projects / ape.git / blobdiff