Bayesian high-dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm

High-dimensional variable selection, with many more covariates than observations, is widely documented in standard regression models, but there are still few tools to address it in non-linear mixed-effects models where data are collected repeatedly on several individuals. In this work, variable selection is approached from a Bayesian perspective and a selection procedure is proposed, combining the use of a spike-and-slab prior and the Stochastic Approximation version of the Expectation Maximisation (SAEM) algorithm. Similarly to Lasso regression, the set of relevant covariates is selected by exploring a grid of values for the penalisation parameter. The SAEM approach is much faster than a classical Markov chain Monte Carlo algorithm and our method shows very good selection performances on simulated data. Its flexibility is demonstrated by implementing it for a variety of nonlinear mixed effects models. The usefulness of the proposed method is illustrated on a problem of genetic markers identification, relevant for genomic-assisted selection in plant breeding.