cor2pcor: Compute Partial Correlation from Correlation Matrix -- and Vice Versa

Description

cor2pcor computes the pairwise partial correlation coefficients from either a correlation or a covariance matrix.

pcor2cor takes either a partial correlation matrix or a partial covariance matrix as input, and computes from it the corresponding correlation matrix.

Usage

cor2pcor(m, tol)
pcor2cor(m, tol)

Arguments

covariance matrix or (partial) correlation matrix

tol

tolerance - singular values larger than tol are considered non-zero (default value: tol = max(dim(m))*max(D)*.Machine$double.eps). This parameter is needed for the singular value decomposition on which pseudoinverse is based.

Value

A matrix with the pairwise partial correlation coefficients (cor2pcor) or with pairwise correlations (pcor2cor).

Details

The partial correlations are the negative standardized concentrations (which in turn are the off-diagonal elements of the inverse correlation or covariance matrix). In graphical Gaussian models the partial correlations represent the direct interactions between two variables, conditioned on all remaining variables.

In the above functions the pseudoinverse is employed for inversion - hence even singular covariances (with some zero eigenvalues) may be used. However, a better option may be to estimate a positive definite covariance matrix using cov.shrink.

Note that for efficient computation of partial correlation coefficients from data x it is advised to use pcor.shrink(x) and not cor2pcor(cor.shrink(x)).

References

Whittaker J. 1990. Graphical Models in Applied Multivariate Statistics. John Wiley, Chichester.

Examples

Run this code

# NOT RUN {
# load corpcor library
library("corpcor")

# covariance matrix
m.cov = rbind(
 c(3,1,1,0),
 c(1,3,0,1),
 c(1,0,2,0),
 c(0,1,0,2)
)
m.cov


# corresponding correlation matrix
m.cor.1 = cov2cor(m.cov)
m.cor.1

# compute partial correlations (from covariance matrix)
m.pcor.1 = cor2pcor(m.cov)
m.pcor.1

# compute partial correlations (from correlation matrix)
m.pcor.2 = cor2pcor(m.cor.1)
m.pcor.2



zapsmall( m.pcor.1 ) == zapsmall( m.pcor.2 )

# backtransformation
m.cor.2 = pcor2cor(m.pcor.1)
m.cor.2
zapsmall( m.cor.1 ) == zapsmall( m.cor.2 )

# }

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