MMCM: Multisample Mahalanobis Crossmatch (MMCM) Test

In DataSimilarity: Quantifying Similarity of Datasets and Multivariate Two- And k-Sample Testing

Multisample Mahalanobis Crossmatch (MMCM) Test

Description

Performs the multisample Mahalanobis crossmatch (MMCM) test (Mukherjee et al., 2022).

Usage

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

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)

Details

The test is an extension of the Rosenbaum (2005) crossmatch test to multiple samples. Its test statistic is the Mahalanobis distance of the observed cross-counts of all pairs of datasets.

It aims to improve the power for large dimensions or numbers of groups compared to another extension, the multisample crossmatch (MCM) test (Petrie, 2016).

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

Small values of the test statistic indicate similarity of the datasets, therefore the test rejects the null hypothesis of equal distributions for large values of the test statistic.

Value

An object of class htest with the following components:

statistic	Observed value of the test statistic
p.value	Asymptotic p value
alternative	The alternative hypothesis
method	Description of the test
data.name	The dataset names

Applicability

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

Note

In case of ties in the distance matrix, the optimal non-bipartite matching might not be defined uniquely. Here, the observations are matched in the order in which the samples are supplied. When searching for a match, the implementation starts at the end of the pooled sample. Therefore, with many ties (e.g. for categorical data), observations from the first dataset are often matched with ones from the last dataset and so on. This might affect the validity of the test negatively.

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, \Sexpr[results=rd]{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, \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/24-SS149")}

See Also

Petrie, Rosenbaum

Examples

# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
X3 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform MMCM test 
if(requireNamespace("nbpMatching", quietly = TRUE)) {
   MMCM(X1, X2, X3)
}

DataSimilarity documentation built on April 3, 2025, 9:39 p.m.