rho = partialcorr (x) returns the sample linear partial correlation coefficients between pairs of variables in the $n$-by-$p$ matrix x, controlling for the remaining columns of x. Each element rho(i,j) is the partial correlation between x(:,i) and x(:,j), adjusted for the other $p-2$ columns. rho is a symmetric $p$-by-$p$ matrix with ones on the diagonal.

rho = partialcorr (x, z) controls instead for the variables in the $n$-by-$q$ matrix z, returning the $p$-by-$p$ partial correlations among the columns of x.

rho = partialcorr (x, y, z) returns the $p1$-by-$p2$ matrix of partial correlations between the columns of the $n$-by-$p1$ matrix x and the $n$-by-$p2$ matrix y, controlling for z. Element rho(i,j) is the partial correlation between x(:,i) and y(:,j).

[rho, pval] = partialcorr (…) also returns pval, a matrix of p-values for testing the hypothesis of no partial correlation against the alternative selected by 'Tail'.

The following Name/Value pairs are accepted:

'Type'

'Pearson' (default) for linear partial correlation, or 'Spearman' for rank partial correlation (computed on the ranks of the data). 'Kendall' is not supported and raises an error, as in MATLAB.

'Rows'

'all' (default) uses all rows regardless of missing values (any NaN yields a NaN result); 'complete' uses only the rows with no missing values across all supplied variables; 'pairwise' uses, for each computed coefficient, the rows with no missing values among just the variables involved in that coefficient.

'Tail'

The alternative hypothesis for pval: 'both' (default, nonzero correlation), 'right' (greater than zero), or 'left' (less than zero).

The partial correlation is computed by regressing each of the two variables on the controlling variables (with an intercept) and correlating the residuals. The p-value uses a Student’s $t$ statistic with $n\; -\; 2\; -\; k$ degrees of freedom, where $k$ is the number of controlling variables and $n$ the number of observations used.

See also: partialcorri, corr, corrcoef, tiedrank

Source Code: partialcorr