pwSEM (version 1.0.0)

generalized.covariance: Generalized covariance function

Description

This function calculates the generalized covariance statistic of Shah, R.D. & Peters, J. (2020); i.e. Y1 | Y2 |C, where C is a set of common conditioning variables. R1 and R2 are the response residuals from pairs of 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

generalized.covariance(R1, R2)

Value

A list containing T.stat (the test statistic) and prob (asymptotic null probability of the T statistic).

Arguments

R1

a numerical vector of residuals

R2

a second numerical vector of residuals

Examples

#generalized.covariance function: X1_|_X3|{X2}
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")
generalized.covariance(R1,R2)