Additive quantile regression for clustered data with an application to children's physical activity

Additive models are flexible regression tools that handle linear as well as non‐linear terms. The latter are typically modelled via smoothing splines. Additive mixed models extend additive models to include random terms when the data are sampled according to cluster designs (e.g. longitudinal). These models find applications in the study of phenomena like growth, certain disease mechanisms and energy expenditure in humans, when repeated measurements are available. We propose a novel additive mixed model for quantile regression. Our methods are motivated by an application to physical activity based on a data set with more than half a million accelerometer measurements in children of the UK Millennium Cohort Study. In a simulation study, we assess the proposed methods against existing alternatives.