Partial correlation
Definition taught in Covariance and the multivariate normal, part of Statistical learning
Partial correlation
| Type | Definition |
| Taught in | Covariance and the multivariate normal |
| Part | Statistical learning |
| Questions using it | 4 |
The partial correlation of coordinates j and k given the remaining coordinates is
\rho_{jk\mid q+1,\ldots,p} =\frac{\sigma_{jk\mid q+1,\ldots,p}}{\sqrt{\sigma_{jj\mid q+1,\ldots,p}\,\sigma_{kk\mid q+1,\ldots,p}}}.
If D_{A\mid B}=\operatorname{diag}(\Sigma_{A\mid B}), the matrix of partial correlations is
P_{A\mid B}=D_{A\mid B}^{-1/2}\,\Sigma_{A\mid B}\,D_{A\mid B}^{-1/2},
where the power -1/2 takes the reciprocal square root of each diagonal entry.
Used in
- Taught in Covariance and the multivariate normal, where the derivation and examples are.
- Also used in Graphical models
- Questions that use it (4) — Precision to graph · A tempting wrong turn (answer) · Read a Gaussian graphical model · Conditional association and sparsity
- All 8 questions on Covariance and the multivariate normal
See also
Correlation · Sample correlation coefficient · Precision matrix · Joint distribution and density · Mean vector and covariance matrix · Multivariate normal distribution · Squared Mahalanobis distance · Linear images of a normal vector