gTests_cat {DataSimilarity} | R Documentation |
Graph-Based Tests for Discrete Data
Description
Performs the edge-count two-sample tests for multivariate categorical data implementated in g.tests
from the gTests package. This function is inteded to be used e.g. in comparison studies where all four graph-based tests need to be calculated at the same time. Since large parts of the calculation coincide, using this function should be faster than computing all four statistics individually.
Usage
gTests_cat(X1, X2, dist.fun = function(x, y) sum(x != y), graph.type = "mstree",
K = 1, n.perm = 0, maxtype.kappa = 1.14, seed = NULL)
Arguments
X1 |
First dataset as matrix or data.frame |
X2 |
Second dataset as matrix or data.frame |
dist.fun |
Function for calculating the distance of two observations. Should take two vectors as its input and return their distance as a scalar value (default: Number of unequal components). |
graph.type |
Character specifying which similarity graph to use. Possible options are |
K |
Parameter for graph (default: 1). If |
n.perm |
Number of permutations for permutation test (default: 0, asymptotic test is performed). |
maxtype.kappa |
Parameter |
seed |
Random seed (default: NULL). A random seed will only be set if one is provided. |
Details
The original, weighted, generalized and maxtype edge-count test are performed.
For discrete data, the similarity graph used in the test is not necessarily unique. This can be solved by either taking a union ("u") of all optimal similarity graphs or averaging ("a") the test statistics over all optimal similarity graphs. For details, see Zhang and Chen (2022). Both options are performed here.
For n.perm = 0
, an asymptotic test using the asymptotic normal approximation of the null distribution is performed. For n.perm > 0
, a permutation test is performed.
This implementation is a wrapper function around the function g.tests
that modifies the in- and output of that function to match the other functions provided in this package. For more details see the g.tests
.
Value
A list with the following components:
statistic |
Observed values of the test statistics |
p.value |
Asymptotic or permutation p values |
alternative |
The alternative hypothesis |
method |
Description of the test |
data.name |
The dataset names |
Applicability
Target variable? | Numeric? | Categorical? | K-sample? |
No | No | Yes | No |
References
Friedman, J. H., and Rafsky, L. C. (1979). Multivariate Generalizations of the Wald-Wolfowitz and Smirnov Two-Sample Tests. The Annals of Statistics, 7(4), 697-717.
Chen, H. and Friedman, J.H. (2017). A New Graph-Based Two-Sample Test for Multivariate and Object Data. Journal of the American Statistical Association, 112(517), 397-409. doi:10.1080/01621459.2016.1147356
Chen, H., Chen, X. and Su, Y. (2018). A Weighted Edge-Count Two-Sample Test for Multivariate and Object Data. Journal of the American Statistical Association, 113(523), 1146-1155, doi:10.1080/01621459.2017.1307757
Zhang, J. and Chen, H. (2022). Graph-Based Two-Sample Tests for Data with Repeated Observations. Statistica Sinica 32, 391-415, doi:10.5705/ss.202019.0116.
Chen, H., and Zhang, J. (2017). gTests: Graph-Based Two-Sample Tests. R package version 0.2, https://CRAN.R-project.org/package=gTests.
Stolte, M., Kappenberg, F., Rahnenführer, J., Bommert, A. (2024). Methods for quantifying dataset similarity: a review, taxonomy and comparison. Statist. Surv. 18, 163 - 298. doi:10.1214/24-SS149
See Also
FR_cat
for the original edge-count test, CF_cat
for the generalized edge-count test, CCS_cat
for the weighted edge-count test, and ZC_cat
for the maxtype edge-count test,
gTests
, FR
, CF
, CCS
, and ZC
for versions of the test for continuous data
Examples
set.seed(1234)
# Draw some data
X1cat <- matrix(sample(1:4, 300, replace = TRUE), ncol = 3)
X2cat <- matrix(sample(1:4, 300, replace = TRUE, prob = 1:4), ncol = 3)
# Perform edge-count tests
if(requireNamespace("gTests", quietly = TRUE)) {
gTests_cat(X1cat, X2cat)
}