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

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.