Petrie: Multisample Crossmatch (MCM) Test

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

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 = NULL, 
       shuffle = FALSE)

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: NULL). A random seed will only be set if one is provided.
shuffle	Logical indicator specifying whether the pooled sample should be randomly permuted before matching in the presence of ties (default: FALSE).

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.

Note that due to the specific implementation of the non-bipartite matching algorithm, inflated cross-counts in case of high numbers of ties in the distance matrix were observed in simulations under the null scenario, see note below. Therefore, the option to shuffle the dataset before the matching algorithm was introduce to circumvent this inflated cross-counts. A warning is thrown in case any ties in the distance matrix are detected.

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

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. For this reason, a warning is issued whenever ties are detected. As a workaround, users can set shuffle = TRUE in the function call, which randomly permutes the pooled sample before matching. When using this option, it is strongly recommended to set a random seed to ensure reproducibility.

Because this method cannot handle missing data, any missing values are removed automatically and a warning is issued.

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")}

Stolte, M., Rahnenführer, J., Bommert, A. (2026). An Empirical Comparison of Methods for Quantifying the Similarity of Numeric Datasets. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.2604.12327")}

Stolte, M., Rahnenführer, J., Bommert, A. (2026). An Empirical Comparison of Methods for Quantifying the Similarity of Categorical Datasets. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.2604.11458")}

See Also

MMCM, Rosenbaum

Examples

set.seed(1234)
# 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)
}

DataSimilarity documentation built on May 15, 2026, 9:07 a.m.