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Empirically assessing noisy necessary conditions with activation functions

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Abstract

Ceiling lines were recently proposed to identify necessary conditions as constraints on the outcome in a scatterplot. However, these lines do not work very well on large data sets with random observation error. This paper suggests an alternate way of empirically assessing probabilistic necessary conditions in large and noisy data sets using sigmoidal activation functions, which describe the propensity of outcome at different levels of the independent variable.

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Notes

  1. In the context of philosophy, Mackie (1965) describes INUS conditions (insufficient but necessary part of a condition which is itself unnecessary but sufficient for the result).

  2. It is important to calculate the scope based on theoretically or empirically observed minimum and maximum values rather than on the scale anchors. Otherwise, an increasing d would coincide with a decreasing regression slope, which is the wrong way round.

  3. While the size of a Likert scale is known to influence measurement precision and variance (Wittink and Bayer 2003), this does not impact assessment of necessary conditions.

  4. Modifications of this formula are conceivable. For example, replacing the conditional mean with the conditional median would reduce the sensitivity to outliers even further.

  5. Note that the strength of the necessary condition s calculated on the basis of the activation function is not identical with the effect size of the necessary condition d calculated based on ceiling lines. Ceiling lines and activation curves are two different concepts, which should not be matched with each other.

  6. Given the methodological nature of the paper and illustrative purpose of this example, this paper does not develop or test formal hypotheses.

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Acknowledgements

I thank the anonymous peer reviewer for insightful feedback that helped to fine-tune the manuscript. My research has further benefited from anonymous reviewers and participants of the Academy of International Business 2018 Annual Conference in Minneapolis, MN. I gratefully acknowledge financial support provided by the Darla Moore School of Business and the Center for International Business Education and Research (CIBER) at the University of South Carolina.

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  1. Darla Moore School of Business, University of South Carolina, 1014 Greene Street, Columbia, SC, 29208, USA

    Wolfgang Messner

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Messner, W. Empirically assessing noisy necessary conditions with activation functions. Comput Manag Sci 18, 1–23 (2021). https://doi.org/10.1007/s10287-020-00377-2

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