Partial coefficient of correlation

Let have 3 variables, x, y and a:
x <- rnorm(100, mean=10, sd=2)
y <- x+rnorm(100, mean=20, sd=5)
a <- rnorm(100, mean=10, sd=2)

df <- data.frame(x=x, y=y, a=a)

The partial coefficient correlation between x and y relative to a is the correlation coefficient of the residuals of the linear regression of x and y over a:

pcor <- function(df) {

  ax <- lm(x ~ a, data=df)

  ay <- lm(y ~ a, data=df)

  

  rx <- residuals(ax)

  ry <- residuals(ay)

  

  return(cor(rx, ry))

}

pcor(df)

Let confirm with the package ppcor:

library("ppcor")

ppcor:::pcor(df)$estimate[2, 1]

Note that I use ppcor:::pcor() to be sure that the version of pcor in the package is used.

It works: we obtained the same result.

It should be noted that ppcor:::pcor() is more rapid than my version of pcor() even if it estimate 3 partial correlations and me only one !

> system.time(

+   for (i in 1:10000) ppcor:::pcor(df)$estimate[2, 1]

+ )

utilisateur     système      écoulé 

      2.629       0.097       2.777 

> system.time(

+   for (i in 1:10000) pcor(df)

+ )

utilisateur     système      écoulé 

     18.385       0.733      19.403