Bayesian group and sparse-group LASSO with spike-and-slab priors in quantile mixed models: an application to child growth data

Identifying risk factors that exhibit significant associations with child growth and development is crucial for preventing unhealthy growth and supporting children’s overall development. Given that children have a diverse range of growth patterns, it is particularly relevant to evaluate these associations across quantiles rather than simply focusing on the mean or median values. In this paper, we develop a Bayesian variable selection method within quantile regression (QR) and quantile mixed models (QMMs). In particular, these methods are designed to analyse longitudinal data, such as child growth data. This novel methodology combines several key components, including the Bayesian sparse group LASSO method, a likelihood function based on the scale mixture representation of the asymmetric Laplace (AL) distribution. It also incorporates spike-and-slab priors for regression coefficients and utilises linear mixed models based on a decomposition for the covariance matrix of random effects. By combining these elements, our approach offers a comprehensive solution for simultaneous selection and estimation of fixed and random effects in QMMs. We assess the performance of the proposed method through simulation studies, which demonstrate its strong variable selection and predictive capabilities. Furthermore, we illustrate its practical utility by applying it to the Growing Up in Scotland (GUS) dataset, providing practical insights into its real-world applicability.