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A default Bayes factor for testing null hypotheses about the fixed effects of linear two-level models.

Nikola Sekulovski1, Herbert Hoijtink2

  • 1Department of Psychology, University of Amsterdam.

Psychological Methods
|April 27, 2023
PubMed
Summary

This study introduces a default Bayes factor for testing hypotheses about fixed parameters in linear two-level models. It offers clear operating characteristics, simplifying evidence quantification for researchers.

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Area of Science:

  • Statistics
  • Statistical Modeling

Background:

  • Null Hypothesis Significance Tests (NHST) are standard for evaluating statistical model parameters, yielding reject/not reject decisions.
  • Bayes factors quantify evidence for hypotheses but are sensitive to prior specifications for equality-constrained hypotheses.
  • Applied researchers often find specifying priors challenging.

Purpose of the Study:

  • To propose a default Bayes factor for testing hypotheses about fixed parameters in linear two-level models.
  • To provide clear operating characteristics for this default Bayes factor.
  • To offer a practical tool for applied researchers to quantify evidence in their data.

Main Methods:

  • Generalizing an existing approach for linear regression to two-level models.
  • Proposing a new estimator for effective sample size in models with random slopes.
  • Utilizing marginal R² for fixed effects to represent effect size.

Main Results:

  • The proposed default Bayes factor demonstrates clear operating characteristics across different sample sizes and estimation methods.
  • A simulation study confirmed the robustness of the Bayes factor's performance.
  • The study provides practical examples and an R package (bain) for implementation.

Conclusions:

  • The default Bayes factor offers a reliable method for testing hypotheses on fixed coefficients in linear two-level models.
  • This approach simplifies the quantification of evidence, overcoming prior specification challenges.
  • The availability of a user-friendly function facilitates its application in research.