Evaluating Bayesian Variable Selection Approaches for Nonlinear Random Effects Models

Longitudinal data modeling attracts special interest from researchers and practitioners because of its capacity to help understand individual and mean trends of growth and development over time. One feature of longitudinal design is the collection of extensive information on participants to help explain the underlying growth process. However, selecting which covariates or independent variables (i.e., predictors) to include in a statistical model is challenging especially with the goals of avoiding both overfitting and underfitting. The present study demonstrates and compares multiple Bayesian variable selection methods for the selection of covariates to explain longitudinal growth processes, including both shrinkage methods (e.g., horseshoe) and stochastic variable search method (e.g., spike-and-slab priors and their extension to a Normal Mixture of Inverse Gammas), via an extensive Monte Carlo simulation study using a piecewise random effects model with unknown change point as an example. Our goal is to provide recommendations for researchers and practitioners about the advantages and limitations of Bayesian variable selection methods for variable selection in longitudinal studies, including model convergence and parameter estimation precision and accuracy.