corpcor: rebuild.cov – R documentation

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rebuild.cov

Rebuild and Decompose the (Inverse) Covariance Matrix

Description

rebuild.cov takes a correlation matrix and a vector with variances and reconstructs the corresponding covariance matrix.

Conversely, decompose.cov decomposes a covariance matrix into correlations and variances.

decompose.invcov decomposes a concentration matrix (=inverse covariance matrix) into partial correlations and partial variances.

rebuild.invcov takes a partial correlation matrix and a vector with partial variances and reconstructs the corresponding concentration matrix.

Usage

rebuild.cov(r, v)
rebuild.invcov(pr, pv)
decompose.cov(m)
decompose.invcov(m)

Arguments

`r`	correlation matrix
`v`	variance vector
`pr`	partial correlation matrix
`pv`	partial variance vector
`m`	a covariance or a concentration matrix

Details

The diagonal elements of the concentration matrix (=inverse covariance matrix) are the precisions, and the off-diagonal elements are the concentrations. Thus, the partial variances correspond to the inverse precisions, and the partial correlations to the negative standardized concentrations.

Value

rebuild.cov and rebuild.invcov return a matrix.

decompose.cov and decompose.invcov return a list containing a matrix and a vector.

Author(s)

Korbinian Strimmer (https://strimmerlab.github.io).

Examples

# load corpcor library
library("corpcor")

# a correlation matrix and some variances
r = matrix(c(1, 1/2, 1/2, 1),  nrow = 2, ncol=2)
r
v = c(2, 3)

# construct the associated covariance matrix
c = rebuild.cov(r, v)
c

# decompose into correlations and variances
decompose.cov(c)


# the corresponding concentration matrix
conc = pseudoinverse(c) 
conc

# decompose into partial correlation matrix and partial variances
tmp = decompose.invcov(conc)
tmp
# note: because this is an example with two variables,
# the partial and standard correlations are identical!


# reconstruct the concentration matrix from partial correlations and
# partial variances 
rebuild.invcov(tmp$pr, tmp$pv)

corpcor

Efficient Estimation of Covariance and (Partial) Correlation

v1.6.10

GPL (>= 3)

Authors

Juliane Schafer, Rainer Opgen-Rhein, Verena Zuber, Miika Ahdesmaki, A. Pedro Duarte Silva, and Korbinian Strimmer.

Initial release

2021-09-16