1d:T77a,# Correlation Matrix Correlation matrix of maximally selected rank statistics. ```r 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. ## Details The correlations between all two-sample rank statistics induced by all possible cutpoints in `X` are computed. ## Returns The correlation matrix with dimension depending on ties in `X` is returned. ## 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 ```r 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)) ```

corrmsrs function