Estimation and variable selection in nonlinear mixed-effects models

Abstract: We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters. The objective is to identify relevant covariates and estimate model parameters. We combine a penalized LASSO-type estimator with an eBIC model choice criterion to select the covariates of interest. Then we estimate the parameters by maximum likelihood in the reduced model. We calculate the LASSO-type penalized estimator by a weighted proximal gradient descent algorithm with an adaptive learning rate. This choice allows us in particular to consider models that do not necessarily belong to the curved exponential family. We compare first the performance of the proposed methodology with those of the glmmLasso procedure in a linear mixed effects model in a simulation study. We then illustrate its performance in a nonlinear mixed-effects logistic growth model through simulation.