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

TL;DR

This paper introduces a Bayesian variable selection method for high-dimensional non-linear mixed-effects models, utilizing the SAEM algorithm for efficient covariate selection, demonstrated on simulated data and a plant breeding application.

Contribution

It develops a novel Bayesian approach combining spike-and-slab priors with SAEM for fast, effective covariate selection in complex models, outperforming traditional MCMC methods.

Findings

The method achieves high selection accuracy on simulated data.

It is significantly faster than MCMC algorithms.

Successfully applied to genetic marker identification in plant breeding.

Abstract

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 MCMC (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.