Abstract
Honey, Who Shrunk the Standard Errors in my Moderated Multiple Regression?
Academy of Management Annual Meeting Proceedings, Vol.2026(1)
07/2026
DOI: 10.5465/AMPROC.2026.21146abstract
Abstract
The testing of moderated relationships using interaction terms within Ordinary Least Squares/Moderated Multiple Regression (OLS/MMR) is hampered by the low statistical power of typical sample sizes to detect interaction effects relative to the linear effects of primary terms. Despite the low power, empirical surveys report frequent support for moderation hypotheses, raising questions about potential biases. This paper derives novel methodological theory to explain this seeming contradiction. Focusing on omitted quadratic terms, we demonstrate analytically that their exclusion can create error terms that are uncorrelated with, but not independent of, included variables such as interaction terms. We show how this non-independence will artificially shrink standard errors of interaction coefficients and generate excess type 1 errors. In contrast to the existing literature on quadratic/interaction confounds, this phenomenon persists even when an interaction’s primary terms are uncorrelated. We then use Monte Carlo simulations to quantify the bias induced by small, uncontrolled-for quadratic effects. We establish that a consistently excessive quantity of false interaction positives will result: between 10% and 17% of OLS/MMR analyses are likely to incorrectly identify interaction coefficients as p < 0.05, depending upon distributional assumptions, when there is no true effect. Finally, we demonstrate the efficacy of a particular form of robust standard errors to eliminate excess false interaction positives induced by this non-independence in large and small samples alike. Our findings offer theoretical insights and practical solutions to enhance OLS/MMR accuracy in testing moderation hypotheses.
Details
- Title: Subtitle
- Honey, Who Shrunk the Standard Errors in my Moderated Multiple Regression?
- Creators
- Arturs T. Kalnins - University of Iowa
- Resource Type
- Abstract
- Publication Details
- Academy of Management Annual Meeting Proceedings, Vol.2026(1)
- DOI
- 10.5465/AMPROC.2026.21146abstract
- eISSN
- 2151-6561
- Language
- English
- Date published
- 07/2026
- Academic Unit
- Management and Entrepreneurship ; Economics
- Record Identifier
- 9985183643302771
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