Definition
Partial correlation coefficient is a coefficient to describe the relationship between \( X \) and \( Y \) when taking away the effects of control variable \( Z \), which can be used to test conditional independence. For given random variables \( X \), \( Y \) and control random variable \( Z = \left\{ {{Z_1},{Z_1}, \cdots, {Z_n}} \right\} \), partial correlation coefficient \( {\rho_{{XY \cdot Z}}} \) is defined as the linear correlation between two residuals, respectively, resulting from linear regression of \( X \) with \( Z \) and linear regression of \( Y \) with \( Z \). Since the n-order partial correlation can be easily computed from (n − 1)-order partial correlations, \( {\rho_{{XY \cdot Z}}} \) can be computed with a dynamic programming method with a complexity of \( O\left( {{n^3}} \right) \). Specially, when \( n = 1 \),
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Wang, J. (2013). Partial Correlation Coefficient. In: Dubitzky, W., Wolkenhauer, O., Cho, KH., Yokota, H. (eds) Encyclopedia of Systems Biology. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9863-7_373
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DOI: https://doi.org/10.1007/978-1-4419-9863-7_373
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9862-0
Online ISBN: 978-1-4419-9863-7
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