Partial Covariance Matrix

Compute a matrix of partial (co)variances for a group of variables with respect to another.

Take \(\Sigma\) as the covariance matrix of dimension p. Now consider dividing \(\Sigma\) into two groups of variables. The partial covariance matrices are calculate by: $$ \Sigma_{11.2} = \Sigma_{11} - \Sigma_{12} \Sigma_{22}^{-1} \Sigma_{21} $$ $$ \Sigma_{22.1} = \Sigma_{22} - \Sigma_{21} \Sigma_{11}^{-1} \Sigma_{12} $$

cov2pcov(m, vars1, vars2 = seq(1, ncol(m))[-vars1])

Arguments

m	a square numeric matrix.
vars1	a numeric vector indicating the position (rows or columns in m) of the set of variables at which to compute the partial covariance matrix.
vars2	a numeric vector indicating the position (rows or columns in m) of the set of variables at which to adjust the partial covariance matrix.

Value

A square numeric matrix.

Author

Anderson Rodrigo da Silva <anderson.agro at hotmail.com>

See also

cov

Examples

(Cl <- cov(longley))
#>              GNP.deflator       GNP Unemployed Armed.Forces Population
#> GNP.deflator    116.45763 1063.6041   625.8666     349.0254   73.50300
#> GNP            1063.60412 9879.3537  5612.4370    3088.0428  685.24094
#> Unemployed      625.86663 5612.4370  8732.2343   -1153.7876  446.27415
#> Armed.Forces    349.02537 3088.0428 -1153.7876    4843.0410  176.40981
#> Population       73.50300  685.2409   446.2742     176.4098   48.38735
#> Year             50.92333  470.9779   297.3033     138.2433   32.91740
#> Employed         36.79666  343.3302   164.9103     111.7681   23.46197
#>                   Year  Employed
#> GNP.deflator  50.92333  36.79666
#> GNP          470.97790 343.33021
#> Unemployed   297.30333 164.91027
#> Armed.Forces 138.24333 111.76811
#> Population    32.91740  23.46197
#> Year          22.66667  16.24093
#> Employed      16.24093  12.33392
cov2pcov(Cl, 1:2)
#>              GNP.deflator      GNP
#> GNP.deflator     1.421147 2.143536
#> GNP              2.143536 8.134020

# End (Not run)