crossmatchtest {crossmatch}

The Cross-Match Test

Description

A test for comparing two multivariate distributions by using the distance between the observations.

Usage

crossmatchtest(z, D)

Arguments

z

A binary vector corresponding to observations class labels.

D

A distance matrix of dimensions NxN, where N is the total number of observations.

Details

Observations are divided into pairs to minimize the total distance within pairs, using a polynomial time algorithm made available in R by Lu, B., Greevy, R., Xu, X., and Beck, C in the R package "nbpMatching". The cross-match test takes as the test statistic the number of times a subject from one group was paired with a subject from another group, rejecting the hypothesis of equal distribution for small values of the statistic; see Rosenbaum (2005) for details.

Value

A list with the following

a1

The number of cross-matches

Ea1

The expected number of cross-matches under the null

Va1

The variance of number of cross-matches under the null

dev

The observed difference from expectation under null in SE units

pval

The p-value based on exact null distribution (NA for datasets with 340 observations or more)

approxpval

The approximate p-value based on normal approximation

Author(s)

Ruth Heller

References

Rosenbaum, P.R. (2005), An exact distribution-free test comparing two multivariate distributions based on adjacency, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67, 4, 515-530.

Examples

## The example in Section 2 of the article (see References)

#The data consists of 2 outcomes measured on 9 treated cases and 9 controls: 
dat <- rbind(c(0.47,0.39,0.47,0.78,1,1,0.54,1,0.38,1,0.27,0.63,0.22,0,-1,-0.42,-1,-1),
             c(0.03,0.11,0.16,-0.1,-0.05,0.16,0.12,0.4,0.04,0.71,0.01,0.21,-0.18,
               -0.08,-0.35,0.26,-0.6,-1.0))
z <- c(rep(0,9),rep(1,9))
X <- t(dat)

## Rank based Mahalanobis distance between each pair:
X <- as.matrix(X)
n <- dim(X)[1]
k <- dim(X)[2]
for (j in 1:k) X[,j] <- rank(X[,j])
cv <- cov(X)
vuntied <- var(1:n)
rat <- sqrt(vuntied/diag(cv))
cv <- diag(rat) %*% cv %*% diag(rat)
out <- matrix(NA,n,n)

library(MASS)

icov <- ginv(cv)
for (i in 1:n) out[i,] <- mahalanobis(X,X[i,],icov,inverted=TRUE)

dis <- out

## The cross-match test:

crossmatchtest(z,dis)