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#' Mantel test for association of two distance matirces
#'
#' This function performs Mantel test for correlation between two distance matrices. It
#' computes P value by randomly permuting rows and columns of the second matrix.
#'
#' @param Dx A numeric matrix of pairwise distances.
#' @param Dy A second numeric matrix of pairwise distances.
#' @param nperm The number of times to permute the rows and columns of \code{Dy}.
#'
#' @return A list contains Mantel statistic and permutation P value.
#'
#' @references Mantel, N. (1967) The detection of disease clustering and a generalized
#' regression approach. Cancer Research, 27, 209 - 220.
#'
#' @export
#'
#' @examples
#'
#' x <- runif(8)
#' y <- runif(8)
#' # Distance matrices
#' distX = as.matrix(dist(x, upper = TRUE, diag = TRUE))
#' distY = as.matrix(dist(y, upper = TRUE, diag = TRUE))
#'
#' MantelTest(Dx = distX, Dy = distY, nperm = 1000)
#'
#'
MantelTest <- function(Dx, Dy, nperm){
MTObs <- mantelStat(Dx, Dy)
if(nperm != 0 ){
permStats <- rep(NA, nperm)
# P-value by permuting the rows and columns (haplotypes) of the original distance matrix, Dy
# instead of permuting the rows of hapMat matrix(rows of original haplotype matrix).
s <-lapply(1:nperm, function(x) c(sample(nrow(Dy))))
for(i in 1:nperm){
permStats[i] <- mantelStat(Dx = Dx, Dy = Dy[s[[i]], s[[i]]])
}
pVal <- (sum(permStats > MTObs) + 1)/(nperm + 1)
return(list(Stat = MTObs, pValue = pVal, permStats = permStats))
}
else{
return(list(Stat = MTObs))
}
}
#' This function performs Mantel test for correlation between two matrices.
#'
#' @param Dx A numeric matrix of pairwise distances.
#' @param Dy A second numeric matrix of pairwise distances.
#'
#' @return A matrix of numeric values.
#'
#' @keywords internal
#'
#'
mantelStat = function(Dx, Dy){
v1 = as.numeric(Dx[lower.tri(Dx)])
v2 = as.numeric(Dy[lower.tri(Dy)])
return(cor(v1,v2))
}
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