Performs the nonparametric graph-based LP (GLP) multisample test proposed by Mokhopadhyay and Wang (2020). The implementation here uses the GLP implementation from the LPKsample package.
MW(X1, X2, ..., sum.all = FALSE, m.max = 4, components = NULL, alpha = 0.05,
c.poly = 0.5, clust.alg = "kmeans", n.perm = 0, combine.criterion = "kernel",
multiple.comparison = TRUE, compress.algorithm = FALSE, nbasis = 8, seed = 42)An object of class htest with the following components:
Observed value of the GLP test statistic
Asymptotic or permutation overall p value
Needed for pretty printing of results
Needed for pretty printing of results
Description of the test
The dataset names
The alternative hypothesis
First dataset as matrix or data.frame
Second dataset as matrix or data.frame
Optionally more datasets as matrices or data.frames
Should all components be summed up for calculating the test statistic? (default: FALSE, only significant components are summed up)
Maximum order of LP components to investigate (default: 4)
Vector specifying which components to test. If components is not NULL (default), only the specified components are examined and m.max is ignored.
Significance level \(\alpha\) (default: 0.05)
Parameter for polynomial kernel (default: 0.5)
Character specifying the cluster algorithm used in graph community detection. possible options are "kmeans" (default) and "mclust".
Number of permutations for permutation test (default: 0, asymptotic test is performed).
Character specifying how to obtain the overall test result based on the component-wise results. Possible options are "kernel" meaning that an overall kernel \(W\) is computed based on the significant components and the LP graph test is run on \(W\), and "pvalue" which uses Fisher's method to combine the p values from each component.
Should an adjustment for multiple comparisons be used when determining which components are significant? (default: TRUE)
Should smooth compression of Laplacian spectra be used for testing? (default: FALSE). It is recommended to set this to TRUE for large sample sizes.
Number of bases used for approximation when compress.algorithm = TRUE (default: 8)
Random seed (default: 42)
| Target variable? | Numeric? | Categorical? | K-sample? |
| No | Yes | No | Yes |
The GLP statistic is based on learning an LP graph kernel using a pre-specified number of LP components and performing clustering on the eigenvectors of the Laplacian matrix for this learned kernel. The cluster assignment is tested for association with the true dataset memberships for each component of the LP graph kernel. The results are combined by either constructing a super-kernel using specific components and performing the cluster and test step again or by using the combination of the significant components after adjustment for multiple testing.
Small values of the GLP statistic indicate dataset similarity. Therefore, the test rejects for large values.
Mukhopadhyay, S. and Wang, K. (2020). A nonparametric approach to high-dimensional k-sample comparison problems, Biometrika, 107(3), 555-572, tools:::Rd_expr_doi("10.1093/biomet/asaa015")
Mukhopadhyay, S. and Wang, K. (2019). Towards a unified statistical theory of spectralgraph analysis, tools:::Rd_expr_doi("10.48550/arXiv.1901.07090")
Mukhopadhyay, S., Wang, K. (2020). LPKsample: LP Nonparametric High Dimensional K-Sample Comparison. R package version 2.1, https://CRAN.R-project.org/package=LPKsample
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")
# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform GLP test
if(requireNamespace("LPKsample", quietly = TRUE)) {
MW(X1, X2, n.perm = 100)
}
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