rg.test {rgTest}

Robust graph-based two sample test

Description

Performs robust graph-based two sample test.

Usage

rg.test(data.X, data.Y, dis = NULL, E = NULL, n1, n2, k = 5, weigh.fun, perm.num = 0, 
test.type = list("ori", "gen", "wei", "max"), progress_bar = FALSE)

Arguments

data.X

a numeric matrix for observations in sample 1.

data.Y

a numeric matrix for observations in sample 2.

dis

a distance matrix of the pooled dataset of sample 1 and sample 2. The indices of observations in sample 1 are from 1 to n1 and indices of observations in sample 2 are from 1+n1 to n1+n2 in the pooled dataset.

E

an edge matrix representing a similarity graph. Each row represents an edge and records the indices of two ends of an edge in two columns. The indices of observations in sample 1 are from 1 to n1 and indices of observations in sample 2 are from 1+n1 to n1+n2.

n1

number of observations in sample 1.

n2

number of observations in sample 2.

k

parameter in K-MST, with default 5.

weigh.fun

weighted function which returns weights of each edge and is a function of node degrees.

perm.num

number of permutations used to calculate the p-value (default=1000). Use 0 for getting only the approximate p-value based on asymptotic theory.

test.type

type of graph-based test. This must be a list containing elements chosen from "ori", "gen", "wei", and "max", with default 'list("ori", "gen", "wei", "max")'. "ori" refers to robust orignial edge-count test, "gen" refers to robust generalized edge-count test, "wei" refers to robust weighted edge-count test and "max" refers to robust max-type edge-count tests.

progress_bar

a logical evaluating to TRUE or FALSE indicating whether a progress bar of the permutation should be printed.

Details

The input should be one of the following:

1. datasets of the two samples;

2. the distance matrix of the pooled dataset;

3. the edge matrix generated from a similarity graph.

Typical usages are:

rg.test(data.X, data.Y, n1, n2, weigh.fun, ...)

rg.test(dis, n1, n2, weigh.fun, ...)

rg.test(E, n1, n2, weigh.fun, ...)

If the data matrices or the distance matrix are used, the similarity graph is generated using K-MST.

Value

A list containing the following components:

asy.ori.statistic

the asymptotic test statistic using robust original graph-based test.

asy.ori.pval

the asymptotic p-value using robust original graph-based test.

asy.gen.statistic

the asymptotic test statistic using robust generalized graph-based test.

asy.gen.pval

the asymptotic p-value using robust generalized graph-based test.

asy.wei.statistic

the asymptotic test statistic using robust weighted graph-based test.

asy.wei.pval

the asymptotic p-value using robust weighted graph-based test.

asy.max.statistic

the asymptotic test statistic using robust max-type graph-based test.

asy.max.pval

the asymptotic p-value using robust max-type graph-based test.

perm.ori.pval

the p-value based on permutation using robust original graph-based test.

perm.gen.pval

the p-value based on permutation using robust generalized graph-based test.

perm.wei.pval

the p-value based on permutation using robust weighted graph-based test.

perm.max.pval

the p-value based on permutation using robust max-type graph-based test.

Examples

## Simulated from Student's t-distribution. 
## Observations for the two samples are from different distributions.
data(example0)
data = as.matrix(example0$data)     # pooled dataset
label = example0$label              # label of observations
s1 = data[label == 'sample 1', ]    # sample 1
s2 = data[label == 'sample 2', ]    # sample 2
num1 = nrow(s1)                     # number of observations in sample 1
num2 = nrow(s2)                     # number of observations in sample 2

## Graph-based two sample test using data as input
rg.test(data.X = s1, data.Y = s2, n1 = num1, n2 = num2, k = 5, weigh.fun = weiMax, perm.num = 0)

## Graph-based two sample test using distance matrix as input
dist = example0$distance
rg.test(dis = dist, n1 = num1, n2 = num2, k = 5, weigh.fun = weiMax, perm.num = 0)

## Graph-based two sample test using edge matrix of the similarity graph as input
E = example0$edge
rg.test(E = E, n1 = num1, n2 = num2, weigh.fun = weiMax, perm.num = 0)