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When Do Interaction/Moderation Effects Stabilize in Linear Regression?

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Summary
This summary is machine-generated.

Accurate estimation of two-way interactions in linear regression is challenging. Monte Carlo simulations reveal that sample size and predictor reliability are key to stable interaction estimates, with large sample sizes needed for typical psychology studies.

Keywords:
interactionsmoderationopen dataopen materialspowerpreregistrationsample sizestability

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Area of Science:

  • Statistics
  • Psychometrics
  • Social Sciences

Background:

  • Two-way interaction effects in linear regression are crucial for understanding complex relationships.
  • Estimating and testing interactions for statistical significance is often difficult due to small effect sizes and low reliability.

Purpose of the Study:

  • To establish stability thresholds for two-way interactions between continuous variables using Monte Carlo simulations.
  • To investigate the influence of reliability, main effect size, collinearity, and interaction effect size on interaction estimate stability.

Main Methods:

  • Utilized Monte Carlo simulations to assess the stability of two-way interaction estimates.
  • Defined stability using modified corridor and point of stability metrics.
  • Examined various combinations of predictor reliability, main effect size, collinearity, and interaction effect size.

Main Results:

  • Interaction estimate stability is primarily determined by sample size and predictor reliability.
  • Realistic psychology field studies require a sample size of n = 3,800 for stability, with 72% statistical power.
  • Small sample sizes (n <= 100) led to a high percentage (11-45%) of incorrectly signed interaction estimates.

Conclusions:

  • Many published interaction findings in psychology may be unstable due to insufficient sample size and predictor reliability.
  • Analyses with highly reliable predictors (e.g., experimental group assignment) may stabilize at lower sample sizes.
  • Researchers should ensure adequate sample size and reliability before conducting two-way interaction tests, especially when hypotheses are pre-specified.