A quasi F-test for functional linear models with functional covariates and its application to longitudinal data

Functional linear models are useful in analyzing data from designed experiments and observational studies with functional responses, as well as longitudinal data with a large number of repeated measures on each subject. We propose a quasi F-test for functional linear models with functional covariates and outcomes. We develop a numerical procedure and an efficient approximation for computing p-values, and present a simple way to test individual predictors. For illustration, we apply the proposed procedure to a longitudinal depression data set with repeatedly measured methamphetamine use as a predictor. We conduct a simulation study to assess the size and the power of the test.