DataSimilarity (version 0.1.1)

Petrie: Multisample Crossmatch (MCM) Test

Description

Performs the multisample crossmatch (MCM) test (Petrie, 2016).

Usage

Petrie(X1, X2, ..., dist.fun = stats::dist, dist.args = NULL, seed = 42)

Value

An object of class htest with the following components:

statistic

Observed value of the test statistic

p.value

Asymptotic p value

estimate

Observed multisample edge-count

alternative

The alternative hypothesis

method

Description of the test

data.name

The dataset names

stderr

Standard deviation under the null

mu0

Expectation under the null

Arguments

X1

First dataset as matrix or data.frame

X2

Second dataset as matrix or data.frame

...

Optionally more datasets as matrices or data.frames

dist.fun

Function for calculating a distance matrix on the pooled dataset (default: stats::dist, Euclidean distance).

dist.args

Named list of further arguments passed to dist.fun (default: NULL).

seed

Random seed (default: 42)

Applicability

Target variable?	Numeric?	Categorical?	K-sample?
No	Yes	Yes	Yes

Details

The test is an extension of the Rosenbaum (2005) crossmatch test to multiple samples that uses the crossmatch count of all pairs of samples.

The observed cross-counts are calculated using the functions distancematrix and nonbimatch from the nbpMatching package.

High values of the multisample crossmatch statistic indicate similarity between the datasets. Thus, the test rejects the null hypothesis of equal distributions for low values of the test statistic.

References

Mukherjee, S., Agarwal, D., Zhang, N. R. and Bhattacharya, B. B. (2022). Distribution-Free Multisample Tests Based on Optimal Matchings With Applications to Single Cell Genomics, Journal of the American Statistical Association, 117(538), 627-638, tools:::Rd_expr_doi("10.1080/01621459.2020.1791131")

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.

Petrie, A. (2016). Graph-theoretic multisample tests of equality in distribution for high dimensional data. Computational Statistics & Data Analysis, 96, 145-158, tools:::Rd_expr_doi("10.1016/j.csda.2015.11.003")

Stolte, M., Kappenberg, F., Rahnenführer, J., Bommert, A. (2024). Methods for quantifying dataset similarity: a review, taxonomy and comparison. Statist. Surv. 18, 163 - 298. tools:::Rd_expr_doi("10.1214/24-SS149")

See Also

MMCM, Rosenbaum

Examples

# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform MCM test 
if(requireNamespace("nbpMatching", quietly = TRUE)) {
   Petrie(X1, X2)
}