Two-Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships with Quadratic Regressions

Advances in Methods and Practice in Psychological Science (AMPPS) Forthcoming

32 Pages Posted: 22 Aug 2017 Last revised: 25 Oct 2018

See all articles by Uri Simonsohn

Uri Simonsohn

ESADE Business School; Ramon Llull University - ESADE Business School; ESADE Business School

Date Written: July 11, 2018

Abstract

Many psychological theories predict U-shaped relationships: the effect of x is positive for low values of x, but negative for high values, or vice-versa. Despite implying merely a change of sign, hypotheses about U-shapes are tested almost exclusively via quadratic regressions, imposing an arbitrary functional form assumption that can lead to a 100% false-positive rate, e.g., concluding with certainty that y=log(x) is U-shaped. Estimating two regression lines, one for low and one high values of x, allows testing for a sign change without a functional form assumption. To set the breakpoint between the lines, I introduce the Robin Hood algorithm. It delivers higher power to detect U-shapes than all other breakpoint setting alternatives considered. The paper includes simulations and re-analyses of published results.

Keywords: regression, interactoin, quadratic, u-shape, specification error

Suggested Citation

Simonsohn, Uri, Two-Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships with Quadratic Regressions (July 11, 2018). Advances in Methods and Practice in Psychological Science (AMPPS) Forthcoming , Available at SSRN: https://ssrn.com/abstract=3021690 or http://dx.doi.org/10.2139/ssrn.3021690

Uri Simonsohn (Contact Author)

ESADE Business School ( email )

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Ramon Llull University - ESADE Business School ( email )

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HOME PAGE: http://urisohn.com

ESADE Business School ( email )

Av. de Pedralbes, 60-62
Barcelona, 08034
Spain

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