“…Most commonly, the functions occur along a grid of time points, which could be called longitudinally correlated functional data , but can also occur over other continuous variables such as IOP for our glaucoma data. There are a number of papers that focus on functional predictor regression (Goldsmith et al, 2012; Gertheiss, Goldsmith, Crainiceanu and Greven, 2013; Kundu et al, 2016; Islam et al, 2016) or estimate multi-level principal components (Greven et al, 2010; Zipunnikov et al, 2011; Chen and Müller, 2012; Li and Guan, 2014; Zipunnikov et al, 2014; Park and Staicu, 2015; Shou et al, 2015; Hasenstab et al, 2017) for serially correlated functions, but these papers do not deal directly with functional response regression, i.e. do not regress the functions on covariates while accounting for this serial correlation in the error structure.…”