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.

翻译：高维变量选择（即协变量数量远多于观测值）在标准回归模型中已有广泛研究，但在非线性混合效应模型（即对多个个体重复收集数据的模型）中，相关工具仍然较少。本文从贝叶斯角度探讨变量选择问题，提出一种结合spike-and-slab先验与期望最大化随机逼近算法（SAEM）的选择方法。与Lasso回归类似，通过遍历惩罚参数网格值来筛选相关协变量集合。研究表明，SAEM方法比经典MCMC（马尔可夫链蒙特卡洛）算法快得多，且该方法在模拟数据上展现出优异的变量选择性能。通过将其应用于多种非线性混合效应模型，验证了其灵活性。最后，通过植物育种中基因组辅助选择相关的遗传标记识别问题，展示了所提方法的实际应用价值。