# Correlation Matrix to (Semi) Partial Correlations

Source:`R/cor_to_pcor.R`

, `R/cor_to_spcor.R`

`cor_to_pcor.Rd`

Convert a correlation matrix to a (semi)partial correlation matrix. Partial correlations are a measure of the correlation between two variables that remains after controlling for (i.e., "partialling" out) all the other relationships. They can be used for graphical Gaussian models, as they represent the direct interactions between two variables, conditioned on all remaining variables. This means that the squared partial correlation between a predictor X1 and a response variable Y can be interpreted as the proportion of (unique) variance accounted for by X1 relative to the residual or unexplained variance of Y that cannot be accounted by the other variables.

## Usage

```
cor_to_pcor(cor, tol = .Machine$double.eps^(2/3))
pcor_to_cor(pcor, tol = .Machine$double.eps^(2/3))
cor_to_spcor(cor = NULL, cov = NULL, tol = .Machine$double.eps^(2/3))
```

## Arguments

- cor
A correlation matrix, or a partial or a semipartial correlation matrix.

- tol
Relative tolerance to detect zero singular values.

- pcor
A correlation matrix, or a partial or a semipartial correlation matrix.

- cov
A covariance matrix (or a vector of the SD of the variables). Required for semi-partial correlations.

## Details

The semi-partial correlation is similar to the partial correlation statistic. However, it represents (when squared) the proportion of (unique) variance accounted for by the predictor X1, relative to the total variance of Y. Thus, it might be seen as a better indicator of the "practical relevance" of a predictor, because it is scaled to (i.e., relative to) the total variability in the response variable.

## Examples

```
cor <- cor(iris[1:4])
# Partialize
cor_to_pcor(cor)
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 1.0000000 0.6285707 0.7190656 -0.3396174
#> Sepal.Width 0.6285707 1.0000000 -0.6152919 0.3526260
#> Petal.Length 0.7190656 -0.6152919 1.0000000 0.8707698
#> Petal.Width -0.3396174 0.3526260 0.8707698 1.0000000
cor_to_spcor(cor, cov = sapply(iris[1:4], sd))
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 1.00000000 0.30389212 0.3890689 -0.1357714
#> Sepal.Width 0.55758743 1.00000000 -0.5385056 0.2599849
#> Petal.Length 0.18506103 -0.13959991 1.0000000 0.3167424
#> Petal.Width -0.09001634 0.09394365 0.4415000 1.0000000
# Inverse
round(pcor_to_cor(cor_to_pcor(cor)) - cor, 2) # Should be 0
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 0 0 0 0
#> Sepal.Width 0 0 0 0
#> Petal.Length 0 0 0 0
#> Petal.Width 0 0 0 0
```