# What is the interpretation of “generalized” partial correlations?

The usual partial correlation between X and Y given the set of variables Z is the Pearson correlation between residuals resulting from the liner regression of X on Z and Y on Z. It can be computed using the recursive formula (see wikipedia) from the correlation matrix.

My question is what is the interpretation of the partial correlation if the correlation matrix contains other correlation coefficients, like Kendall's tau or Spearman's rho, and not Pearson correlation coefficients.

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