Research
New Faculty Collaborative Research Publication: The R2D2 Prior for Generalized Linear Mixed Models – Dr. Eric Yanchenko
Dr. Eric Yanchenko, Assistant Professor in AIU’s Global Connectivity Program, along with Dr. Howard D. Bondell, Professor at Melbourne University in Australia, and Dr. Brian J. Reich, Professor at North Carolina State University in the U.S.A., has published an article in The American Statistician.
Abstract and Article Link
Title: The R2D2 Prior for Generalized Linear Mixed Models
In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model instead. In this work, we propose a prior on the model fit, as measured by a Bayesian coefficient of determination (?2), which then induces a prior on the individual parameters. We achieve this by placing a beta prior on ?2 and then deriving the induced prior on the global variance parameter for generalized linear mixed models. We derive closed-form expressions in many scenarios and present several approximation strategies when an analytic form is not possible and/or to allow for easier computation. In these situations, we suggest approximating the prior by using a generalized beta prime distribution and provide a simple default prior construction scheme. This approach is quite flexible and can be easily implemented in standard Bayesian software. Lastly, we demonstrate the performance of the method on simulated and real-world data, where the method particularly shines in high-dimensional settings, as well as modeling random effects.