Abstract
There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ( p ≫ n ) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating smooth functions, damaging predictive performance. Moreover, most of these GAMs consider an "all-in-all-out" approach for functional selection, rendering them difficult to answer if nonlinear effects are necessary. While some Bayesian models can address these shortcomings, using Markov chain Monte Carlo algorithms for model fitting creates a new challenge, scalability. Hence, we propose Bayesian hierarchical generalized additive models as a solution: we consider the smoothing penalty for proper shrinkage of curve interpolation via reparameterization. A novel two-part spike-and-slab LASSO prior for smooth functions is developed to address the sparsity of signals while providing extra flexibility to select the linear or nonlinear components of smooth functions. A scalable and deterministic algorithm, EM-Coordinate Descent, is implemented in an open-source R package BHAM. Simulation studies and metabolomics data analyses demonstrate improved predictive and computational performance against state-of-the-art models. Functional selection performance suggests trade-offs exist regarding the effect hierarchy assumption.