mu.Sums {muStat}R Documentation

u-Scores and Weights

Description

mu.Sums computes u-scores and weights from a partial ordering.

Usage

mu.Sums(GE, dsgn=1, wght=TRUE)
mu.wScr  (x, y=NULL, frml=NULL, dsgn=1, wght=TRUE) 
mu.score (x, y=NULL, frml=NULL, dsgn=1, wght=FALSE) 
mu.weight(x, y=NULL, frml=NULL, dsgn=1, wght=TRUE)

Arguments

GE partial ordering
x data matrix, variables as columns
y data matrix, variables as columns
frml see mu.AND,
dsgn design of the experiment.
wght logical flag, if weights should be calculated.

Value

score u-scores
weight weights
nBelow number of observations that are inferior
nAbove number of observations that are superior
nEqual number of observations that are equivalent

Algorithm

mu.Sums <- function(GE, dsgn=1, wght=TRUE) {
    ICW <- function(GE,dsgn) {
        wgt <- colSums(GE|t(GE))        # 0: orig NA, 1: like NA, >1: no NA
        sqrt(wgt*(wgt>1)/if (dsgn!=1) colSums(dsgn) else nrow(GE))
    }
    GE <- sq.matrix(GE)
    nE <- colSums(GE*t(GE)) 
    nA <- colSums(GE) - nE
    nB <- rowSums(GE) - nE
        weight <- ifelse1(wght, ICW(GE,dsgn), rep(1, length(nE)))
        list(score  = (nB-nA) * ifelse(weight==0,NA,1),
                weight = weight,
                nBelow = nB,
                nAbove = nA,
                nEqual = nE)       
}

mu.wScr <- function(x, y=NULL, frml=NULL, dsgn=1, wght=TRUE) 
        mu.Sums(mu.AND(mu.GE(x, y), frml), dsgn=dsgn, wght=wght)

mu.score  <- function(x, y=NULL, frml=NULL, dsgn=1, wght=FALSE) 
        mu.Sums(mu.AND(mu.GE(x, y), frml), dsgn=dsgn, wght=wght)$score

mu.weight <- function(x, y=NULL, frml=NULL, dsgn=1, wght=TRUE) 
        mu.Sums(mu.AND(mu.GE(x, y), frml), dsgn=dsgn, wght=wght)$weight

Author(s)

Knut M. Wittkowski kmw@rockefeller.edu, Tingting Song ttsong@gmail.com

Examples

mu.Sums(mu.GE(1:100))
a.1 <- 1:10
a.2 <- 3:12
b <- c(1:5,2:6)
mu.wScr(cbind(a.1,a.2,b), frml="((1,2),3)")

[Package muStat version 1.5.0 Index]