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On the uncanny relationship between nonnormality and moderated multiple regression.

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Area of Science:

  • Social Sciences
  • Statistics
  • Econometrics

Background:

  • Moderated multiple regression is widely used in social sciences to model nonlinear associations.
  • A key issue is that nonnormality can create spurious interaction effects.

Purpose of the Study:

  • To theoretically investigate the link between nonnormality and interaction terms in regression models.
  • To clarify when observed effects represent true interactions versus artifacts of data distribution.

Main Methods:

  • Generalized Isserlis' theorem for elliptical densities.
  • Theoretical analysis of product-interaction terms within elliptical density families.
  • Examination of unidimensional symmetric but jointly nonsymmetric variables.

Main Results:

  • Elliptical density families, including multivariate normal, cannot inherently generate product-interaction terms.
  • Asymmetry in data distributions can induce a product-interaction term, mimicking a true effect.
  • Nonnormality can lead to a nonzero coefficient in moderated multiple regression.

Conclusions:

  • Researchers must carefully consider whether an interaction term is theoretically justified or a result of data nonnormality.
  • Distinguishing true interactions from nonnormality-induced effects is crucial for accurate social science modeling.