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-linearterms. The latter are typically modelled via smoothing splines. Additive mixed models extendadditive 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, certaindisease mechanisms and energy expenditure in humans, when repeated measurements areavailable. We propose a novel additive mixed model for quantile regression. Our methods aremotivated by an application to physical activity based on a data set with more than half a millionaccelerometer measurements in children of the UK Millennium Cohort Study. In a simulationstudy, we assess the proposed methods against existing alternatives