u-Scores and Weights

Share:

Description

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

Usage

1
2
3
4
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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
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

1
2
3
4
5
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)")