Incorporating spatial structure into inclusion probabilities for Bayesian variable selection in generalized linear models with the spike-and-slab elastic net.

Spike-and-slab priors model predictors as arising from a mixture of distributions: those that should (slab) or should not (spike) remain in the model. The spike-and-slab lasso (SSL) is a mixture of double exponentials, extending the single lasso penalty by imposing different penalties on parameters based on their inclusion probabilities. The SSL was extended to Generalized Linear Models (GLM) for application in genetics/genomics, and can handle many highly correlated predictors of a scalar outcome, but does not incorporate these relationships into variable selection. When images/spatial data are used to model a scalar outcome, relevant parameters tend to cluster spatially, and model performance may benefit from incorporating spatial structure into variable selection. We propose to incorporate spatial information by assigning intrinsic autoregressive priors to the logit prior probabilities of inclusion, which results in more similar shrinkage penalties among spatially adjacent parameters. Using MCMC to fit Bayesian models can be computationally prohibitive for large-scale data, but we fit the model by adapting a computationally efficient coordinate-descent-based EM algorithm. A simulation study and an application to Alzheimer's Disease imaging data show that incorporating spatial information can improve model fitness.