| Type: | Package |
| Title: | Test for Conditional Independence Based on the Generalized Covariance Measure (GCM) |
| Version: | 0.2.0 |
| Author: | Jonas Peters and Rajen D. Shah |
| Maintainer: | Jonas Peters <jonas.peters@math.ku.dk> |
| Description: | A statistical hypothesis test for conditional independence. It performs nonlinear regressions on the conditioning variable and then tests for a vanishing covariance between the resulting residuals. It can be applied to both univariate random variables and multivariate random vectors. Details of the method can be found in Rajen D. Shah and Jonas Peters: The Hardness of Conditional Independence Testing and the Generalised Covariance Measure, Annals of Statistics 48(3), 1514–1538, 2020. |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| Imports: | CVST, graphics, kernlab, mgcv, stats, xgboost |
| RoxygenNote: | 6.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2022-03-23 11:23:10 UTC; jonas |
| Repository: | CRAN |
| Date/Publication: | 2022-03-24 08:10:05 UTC |
Package for testing conditional independence based on the Generalized Covariance Measure (GCM)
Description
Contains the function gcm.test that can be used for performing a conditional independence test based on the GCM.
Author(s)
Jonas Peters jonas.peters@math.ku.dk, Rajen D. Shah
References
Please cite the following paper. Rajen D. Shah, Jonas Peters: "The Hardness of Conditional Independence Testing and the Generalised Covariance Measure" https://arxiv.org/abs/1804.07203
Wrapper function to computing residuals from a regression method
Description
This function is used for the GCM test. Other methods can be added.
Usage
comp.resids(V, Z, regr.pars, regr.method)
Arguments
V |
A (nxp)-dimensional matrix (or data frame) with n observations of p variables. |
Z |
A (nxp)-dimensional matrix (or data frame) with n observations of p variables. |
regr.pars |
Some regression methods require a list of additional options. |
regr.method |
A string indicating the regression method that is used. Currently implemented are "gam", "xgboost", "kernel.ridge", "nystrom". The regression is performed only if not both resid.XonZ and resid.YonZ are set to NULL. |
Value
Vector of residuals.
References
Please cite the following paper. Rajen D. Shah, Jonas Peters: "The Hardness of Conditional Independence Testing and the Generalised Covariance Measure" https://arxiv.org/abs/1804.07203
Examples
set.seed(1)
n <- 250
Z <- 4*rnorm(n)
X <- 2*sin(Z) + rnorm(n)
res <- comp.resids(X, Z, regr.pars = list(), regr.method = "gam")
Test for Conditional Independence Based on the Generalized Covariance Measure (GCM)
Description
Test for Conditional Independence Based on the Generalized Covariance Measure (GCM)
Usage
gcm.test(X, Y, Z = NULL, alpha = 0.05, regr.method = "xgboost",
regr.pars = list(), plot.residuals = FALSE, nsim = 499L,
resid.XonZ = NULL, resid.YonZ = NULL)
Arguments
X |
A (nxp)-dimensional matrix (or data frame) with n observations of p variables. |
Y |
A (nxp)-dimensional matrix (or data frame) with n observations of p variables. |
Z |
A (nxp)-dimensional matrix (or data frame) with n observations of p variables. |
alpha |
Significance level of the test. |
regr.method |
A string indicating the regression method that is used. Currently implemented are "gam", "xgboost", "kernel.ridge". The regression is performed only if not both resid.XonZ and resid.YonZ are set to NULL. |
regr.pars |
Some regression methods require a list of additional options. |
plot.residuals |
A Boolean indicating whether some plots should be shown. |
nsim |
An integer indicating the number of bootstrap samples used to approximate the null distribution of the test statistic. |
resid.XonZ |
It is possible to directly provide the residuals instead of performing a regression. If set to NULL, the regression method specified in regr.method is used. |
resid.YonZ |
It is possible to directly provide the residuals instead of performing a regression. If set to NULL, the regression method specified in regr.method is used. |
Value
The function tests whether X is conditionally independent of Y given Z. The output is a list containing
-
p.value: P-value of the test. -
test.statistic: Test statistic of the test. -
reject: Boolean that is true iff p.value < alpha.
References
Please cite the following paper. Rajen D. Shah, Jonas Peters: "The Hardness of Conditional Independence Testing and the Generalised Covariance Measure" https://arxiv.org/abs/1804.07203
Examples
set.seed(1)
n <- 250
Z <- 4*rnorm(n)
X <- 2*sin(Z) + rnorm(n)
Y <- 2*sin(Z) + rnorm(n)
Y2 <- 2*sin(Z) + X + rnorm(n)
gcm.test(X, Y, Z, regr.method = "gam")
gcm.test(X, Y2, Z, regr.method = "gam")