Multivariate test of independence based on spatial signs or ranks

Description

Test of independence between two sets of variables. Inference is based on the spatial signs of the observations, symmetrized signs of the observations or spatial signed ranks of the observations.

Usage

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 sr.indep.test(X, Y = NULL, g = NULL, score = c("sign", 
"symmsign", "rank"), regexp = FALSE, cond = FALSE, cond.n = 1000, 
na.action = na.fail) 

Arguments

X

a matrix or a data frame

Y

an optional matrix or a data frame

g

a factor giving the two sets of variables, or numeric vector or vector of column names giving the first set of variables. See details

score

a character string indicating which transformation of the observations should be used

regexp

logical. Is g a regular expression?

cond

logical. Should the conditionally distribution free test be used?

cond.n

Number of permutations to use in the conditionally distribution free test

na.action

a function which indicates what should happen when the data contain 'NA's. Default is to fail.

Details

X should contain the first set of variables and Y the second with matching rows. Alternatively, X should contain both sets and g should be a factor of length equal to number of columns of X, or, g should be a numeric or character vector naming the variables in the first set. If g is a character vector it is assumed to name all wanted columns exactly, unless regexp is TRUE.

Value

A list with class 'htest' containing the following components:

statistic

the value of the statistic

parameter

the degrees of freedom for the statistic or the number of replications if conditionally distribution free p-value was used

p.value

the p-value for the test

null.value

the specified hypothesized value of the measure of dependence (always 0)

alternative

a character string with the value 'two.sided'.

method

a character string indicating what type of test was performed

data.name

a character string giving the name of the data (and grouping vector)

Author(s)

Seija Sirkia, seija.sirkia@iki.fi

References

Taskinen, S., Oja, H., Randles R. (2004) Multivariate Nonparametric Tests of Independence. JASA, 100, 916-925

See Also

Spatial signs and ranks

Examples

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A<-matrix(c(1,2,-3,4,3,-2,-1,0,4),ncol=3)
X<-matrix(rnorm(3000),ncol=3)%*%t(A)
Y<-cbind(X+runif(3000,-1,1),runif(1000))
sr.indep.test(X,Y)
#alternative calls:
Z<-cbind(X,Y)
colnames(Z)<-c("a1","a2","a3","b1","b2","b3","b4")
g<-factor(c(rep(1,3),rep(2,4)))
sr.indep.test(Z,g=g)
sr.indep.test(Z,g=c("b"),regexp=TRUE)
sr.indep.test(Z,g=1:3)