+`CADM.post` <-
+ function(Dmat, nmat, n, nperm=99, make.sym=TRUE, weights=NULL, mult="holm", mantel=FALSE, silent=FALSE)
+{
+### Function to carry out a posteriori tests of the contribution of individual
+### matrices to the congruence of a group of distance matrices.
+###
+### 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.
+###
+### mult = method for correcting P-values due to multiple testing. The methods
+### are "holm" (default), "sidak", and "bonferroni". The Bonferroni
+### correction is overly conservative; it is not recommended. It is
+### included to allow comparisons with the other methods.
+###
+### mantel = TRUE: Mantel statistics are computed from ranked distances,
+### as well as permutational P-values.
+### = FALSE (default): Mantel statistics and tests are not computed.
+###
+### silent = TRUE: informative messages will not be printed, except stopping
+### messages. Option useful for simulation work.
+### = FALSE: informative messages will be printed.
+###
+################################################################################
+
+ mult <- match.arg(mult, c("sidak", "holm", "bonferroni"))
+ 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: compute reference value of S
+
+ ## Transform the distances to ranks, by column
+ Rmat <- apply(Y,2,rank)
+
+ ## 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'
+ sumRanks <- as.vector(Rmat%*%w)
+ S <- (nd-1)*var(sumRanks)
+
+ ## Begin a posteriori tests of individual matrices
+
+ ## Statistics displayed for each matrix: "Mantel.mean" and "W.per.matrix"
+ ## Calculate the mean of the Mantel correlations on ranks for each matrix
+ Mantel.cor <- cor(Rmat)
+ diag(Mantel.cor) <- 0
+ spear.mean <- as.vector(Mantel.cor%*%w)/(nmat-1)
+ ## Calculate Kendall's W for each variable
+ ## W.var <- ((nmat-1)*spear.mean+1)/nmat
+
+ ## P-value for each matrix: test of S, permuting values in matrix[[k]] only
+ ## as in program CADM.f (2004)
+ ## Initialize the counters
+ counter <- rep(1,nmat)
+
+ ## Test each matrix 'k' in turn
+ for(k in 1:nmat) {
+ ## Create a new Rmat table where the permuted column has been removed
+ Rmat.mod <- Rmat[,-k]
+
+ ## Permutation loop: string out permuted matrix 'k' only
+ for(j in 1:nperm) {
+ order <- sample(n)
+ if(asymm & !make.sym) {
+ ## For asymmetric matrices: permute the values within each triangular
+ ## portion, stored as square matrices in D1[[]] and D2[[]]
+ vec <- as.vector(as.dist(D1[[k]][order,order]))
+ vec <- c(vec, as.vector(as.dist(D2[[k]][order,order])))
+ } else {
+ vec <- as.vector(as.dist(D1[[k]][order,order]))
+ }
+ Rmat.perm <- cbind(Rmat.mod, vec)
+ S.perm <- (nd-1)*var(as.vector(Rmat.perm%*%w))
+ if(S.perm >= S) counter[k] <- counter[k]+1
+ }
+ }
+
+ ## Calculate P-values
+ counter <- counter/(nperm+1)
+
+ ## Correction to P-values for multiple testing
+ if(mult == "sidak") {
+ vec.corr = NA
+ for(i in 1:p) vec.corr = c(vec.corr, (1-(1-counter[i])^p))
+ vec.corr <- vec.corr[-1]
+ }
+ if(mult == "holm") vec.corr <- p.adjust(counter, method="holm")
+ if(mult == "bonferroni") vec.corr <- p.adjust(counter, method="bonferroni")
+
+ ## Create a data frame containing the results
+ # table <- rbind(spear.mean, W.var, counter, vec.corr)
+ # rownames(table) <- c("Mantel.mean", "W.per.matrix", "Prob", "Corrected prob")
+ table <- rbind(spear.mean, counter, vec.corr)
+ rownames(table) <- c("Mantel.mean", "Prob", "Corrected.prob")
+ colnames(table) <- colnames(table,do.NULL = FALSE, prefix = "Dmat.")
+
+ ## Mantel tests
+ if(mantel) {
+ diag(Mantel.cor) <- 1
+ rownames(Mantel.cor) <- colnames(table)
+ colnames(Mantel.cor) <- colnames(table)
+ Mantel.prob <- matrix(1,nmat,nmat)
+ rownames(Mantel.prob) <- colnames(table)
+ colnames(Mantel.prob) <- colnames(table)
+
+ 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
+ Rmat.perm <- as.matrix(Rmat.perm[,-1])
+ # Compute Mantel correlations on ranks under permutation
+ Mantel.cor.perm <- cor(Rmat.perm)
+ for(j2 in 1:(nmat-1)) { # Compute prob in the upper tail
+ for(j1 in (j2+1):nmat) {
+ if(Mantel.cor.perm[j1,j2] >= Mantel.cor[j1,j2]) Mantel.prob[j1,j2] <- Mantel.prob[j1,j2]+1
+ }
+ }
+ }
+ Mantel.prob <- as.matrix(as.dist(Mantel.prob/(nperm+1)))
+ diag(Mantel.prob) <- NA # Corrected 08feb13
+ }
+
+ })
+ a[3] <- sprintf("%2f",a[3])
+ if(!silent) cat("Time to compute a posteriori tests (per matrix) =",a[3]," sec",'\n')
+
+ out <- list(A_posteriori_tests=table, Correction.type=mult)
+
+ if(mantel) {
+ out$Mantel.cor <- Mantel.cor
+ out$Mantel.prob <- Mantel.prob
+ }
+ out$nperm <- nperm
+ class(out) <- "CADM.post"
+ out
+}
projects / ape.git / commitdiff