Bayesian multinomial multilevel logistic regression with fixed- and random-effects selection

Music City Center 

We propose a novel Bayesian multinomial multilevel logistic regression model for any setting where each observational unit belongs to a specific group and a non-ordered category. To allow for automatic selection of both fixed- and random-effects, we use Pólya-Gamma data-augmentation and develop an efficient Gibbs sampling algorithm via a hierarchical spike-and-slab prior. Inference is fast and does not rely on any analytical approximations or numerical integration. Guidelines for user-defined prior selection are developed, where the user can, for example, specify the apriori expected number of fixed- and random-effects. Simulations show that our approach is accurate and can discriminate well between different settings of fixed- and random-effects. To demonstrate the general applicability of our approach, we show that our model also applies well to three real datasets within education, medical and political sciences.

Bayesian inference

Multinomial logit

Hierarchical modeling

Gibbs sampling

Polya-Gamma augmentation

Spike and slab 

International Society for Bayesian Analysis (ISBA)