Table 1
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Formulas for computing partial variances and partial correlations |
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| Definition |
True value |
Estimate |
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| Covariance matrix: |
cov(Xk, Xl) = σkl |
Σ = (σkl) |
S = (skl) |
| Concentration matrix: |
Ω = Σ-1 |
Ω = (ωkl) |
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| Variances: |
var(Xk) = σkk =  |
σkk |
skk |
| Partial variances |
var(Xk|X≠k) =  =  =  |
|
 |
| Correlations: |
corr(Xk, Xl) = ρkl = σkl (σkk σll)-1/2 |
P = (ρkl) |
R = (rkl) |
| Partial correlations: |
corr(Xk, Xl|X≠k, l) =  |
 |
 |
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Index i runs from 1 to n (sample size), and indices k and l run from 1 to p (dimension). A tilde denotes a "partial" quantity. | |||
Opgen-Rhein and Strimmer BMC Systems Biology 2007 1:37 doi:10.1186/1752-0509-1-37 |
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