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'.

A coefficient is NaN where the controlling variables explain either of the two variables completely, since the partial correlation is then undefined: no variation is left to correlate. This covers a controlling variable that duplicates one of them and any set of them that spans it.

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.

The data are centered, and the controlling variables rescaled, before the regression, which leaves the result unchanged in exact arithmetic and keeps it accurate in floating point. Shifting or rescaling a controlling variable, or giving the two variables very different scales, does not change the coefficient. MATLAB’s coefficient does change in those cases: a large shift gives a different value, a small-scaled controlling variable is dropped, and very different scales overflow to NaN.

See also: partialcorri, corr, corrcoef, tiedrank

Source Code: partialcorr