maxstat (version 0.7-24)

corrmsrs: Correlation Matrix

Description

Correlation matrix of maximally selected rank statistics.

Usage

corrmsrs(X, minprop=0.1, maxprop=0.9)

Arguments

X

the vector, matrix or data.frame of prognostic factors under test.

minprop

at least minprop*100% of the observations in the first group.

maxprop

not more than minprop*100% of the observations in the first group.

Value

The correlation matrix with dimension depending on ties in X is returned.

Details

The correlations between all two-sample rank statistics induced by all possible cutpoints in X are computed.

References

Hothorn, T. and Lausen, B. (2003). On the Exact Distribution of Maximally Selected Rank Statistics. Computational Statistics & Data Analysis, 43, 121--137.

Lausen, B., Hothorn, T., Bretz, F. and Schmacher, M. (2004). Assessment of Optimally Selected Prognostic Factors. Biometrical Journal, 46(3), 364--374.

Examples

set.seed(29)

# matrix of hypothetical prognostic factors

X <- matrix(rnorm(30), ncol=3) 

# this function

a <- corrmsrs(X, minprop=0, maxprop=0.999)

# coded by just typing the definition of the correlation

testcorr <- function(X) {
  wh <- function(cut, x)
    which(x <= cut)
  index <- function(x) {
    ux <- unique(x)
    ux <- ux[ux < max(ux)]
    lapply(ux, wh, x = x)
  }
  a <- unlist(test <- apply(X, 2, index), recursive=FALSE)
  cnull <- rep(0, nrow(X))
  mycorr <- diag(length(a))
  for (i in 1:(length(a)-1)) {
    for (j in (i+1):length(a)) {
      cone <- cnull
      cone[a[[i]]] <- 1
      ctwo <- cnull
      ctwo[a[[j]]] <- 1
      sone <- sqrt(sum((cone - mean(cone))^2))
      stwo <- sqrt(sum((ctwo - mean(ctwo))^2))
      tcorr <- sum((cone - mean(cone))*(ctwo - mean(ctwo)))
      tcorr <- tcorr/(sone * stwo)
      mycorr[i,j] <- tcorr
    }
  }
  mycorr
}

tc <- testcorr(X)
tc <- tc + t(tc)
diag(tc) <- 1
stopifnot(all.equal(tc, a))