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Nonparametric varying coefficient (NVC) models are useful for modelingtime-varying effects on responses that are measured repeatedly for the samesubjects. When the number of covariates is moderate or large, it is desirableto perform variable selection from the varying coefficient functions. However,existing methods for variable selection in NVC models either fail to accountfor within-subject correlations or require the practitioner to specify aparametric form for the correlation structure. In this paper, we introduce thenonparametric varying coefficient spike-and-slab lasso (NVC-SSL) for Bayesianhigh-dimensional NVC models. Through the introduction of functional randomeffects, our method allows for flexible modeling of within-subject correlationswithout needing to specify a parametric covariance function. We further proposeseveral scalable optimization and Markov chain Monte Carlo (MCMC) algorithms.For variable selection, we propose an Expectation Conditional Maximization(ECM) algorithm to rapidly obtain maximum a posteriori (MAP) estimates. Our ECMalgorithm scales linearly in the total number of observations $N$ and thenumber of covariates $p$. For uncertainty quantification, we introduce anapproximate MCMC algorithm that also scales linearly in both $N$ and $p$. Wedemonstrate the scalability, variable selection performance, and inferentialcapabilities of our method through simulations and a real data application.These algorithms are implemented in the publicly available R package NVCSSL onthe Comprehensive R Archive Network.

Scalable high-dimensional Bayesian varying coefficient models with unknown within-subject covariance