The R2D2 prior for generalized linear mixed models.

Area of Science:

• Statistics
• Computational Statistics
• Bayesian Inference

Background:

• Traditional Bayesian analysis prioritizes individual parameter priors.
• Prioritizing model fit offers an alternative, potentially simplifying complex models.
• Generalized linear mixed models (GLMMs) are widely used but can be complex to parameterize.

Purpose of the Study:

• To propose a novel Bayesian prior construction based on model fit.
• To induce priors on individual parameters from a prior on the Bayesian coefficient of determination (R-squared).
• To provide a flexible and computationally feasible method for Bayesian GLMMs.

Main Methods:

• A beta prior distribution is placed on the Bayesian R-squared.
• Closed-form expressions are derived for the induced prior on the global variance parameter in GLMMs.
• Approximation strategies using the generalized beta prime distribution are developed for computational ease.

Main Results:

• The proposed method successfully induces priors on model parameters from a prior on model fit.
• Derived closed-form expressions and effective approximation strategies facilitate implementation.
• The approach demonstrates strong performance in high-dimensional settings and for modeling random effects.

Conclusions:

• Prioritizing model fit offers a flexible alternative to parameter-specific priors in Bayesian analysis.
• The method is readily implementable in standard Bayesian software.
• This approach is particularly advantageous for complex models, including high-dimensional GLMMs and random effects modeling.