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Interpretation problems of the partial correlation with nonnormally distributed variables

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  • András Vargha

  • Lars Bergman
  • Harold Delaney

Abstract

The partial correlation is a commonly used measure for assessing the bivariate correlation of two quantitative variables after eliminating the influence of one or more other variables. The partial correlation is generally interpreted as the correlation that would result if the variables to be eliminated were fixed (not allowed to vary and influence the other variables), which is referred to in the statistical literature as conditional correlation. The present paper demonstrates, by means of theoretical derivations and practical examples, that when the assumption of multivariate normality is violated (e.g., as a result of nonlinear relationships among the variables investigated) the usual interpretation of the partial correlation coefficient will be basically incorrect. In extreme cases the value of the partial correlation coefficient may be strongly positive, close to 1, whereas the conditional correlation may have a large negative value. To solve this problem the paper suggests to partial out a certain function (in most cases the square) of the variables whose effects are to be eliminated if nonlinear relationships are likely to occur. Copyright Springer Science+Business Media B.V. 2013

Suggested Citation

  • András Vargha & Lars Bergman & Harold Delaney, 2013. "Interpretation problems of the partial correlation with nonnormally distributed variables," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(6), pages 3391-3402, October.
    • Handle: RePEc:spr:qualqt:v:47:y:2013:i:6:p:3391-3402
    DOI: 10.1007/s11135-012-9727-y
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    1. Ed Diener & Robert Biswas-Diener, 2002. "Will Money Increase Subjective Well-Being?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 57(2), pages 119-169, February.
    2. Ed Diener & Ed Sandvik & Larry Seidlitz & Marissa Diener, 1993. "The relationship between income and subjective well-being: Relative or absolute?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 28(3), pages 195-223, March.
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    1. Massimiliano Giacalone & Demetrio Panarello & Raffaele Mattera, 2018. "Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimators," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1831-1859, July.

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