pwSEM (version 1.0.0)

perm.generalized.covariance: perm.generalized.covariance

Description

This performs a permutation version of the generalized covariance test (see: generalized.covariance), which tests for conditional independence of two random variables (Y1, Y2) conditional of a common set of conditioning variables C; see Shah, R.D. & Peters, J. (2020). i.e. Y1 | Y2 |C. R1 and R2 are the response residuals from pairs of any type of appropriate regressions of two dependent variables (Y1 and Y2) on a set of conditioning variables.

Shah, R.D. & Peters, J. (2020). The hardness of conditional independence testing and the generalized covariance measure. The Annals of Statistics 48:1514-1538.

Usage

perm.generalized.covariance(R1, R2, nperm = 5000)

Value

A list containing the T statistic (T.stat), permutation.prob: the estimated null probability of independence of R1 and R2, based on the chosen number of permutations, lower.95.CI and upper.95.CI: the 95% confidence intervals of the estimated null probability

Arguments

R1

a numerical vector (typically residuals of the first regression)

R2

a numerical vector (typically residuals of the second regression)

nperm

the number of permutations (defaults to 5000)

Examples

R1<-residuals(mgcv::gam(X3~X2,data=sim_normal.no.nesting,family=gaussian),
type="response")
R2<-residuals(mgcv::gam(X1~X2,data=sim_normal.no.nesting,family=gaussian),
type="response")

#perm.generalized.covariance function
perm.generalized.covariance(R1,R2,nperm=5000)