+++ /dev/null
-`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 / blobdiff