  The bilevel functional data under consideration has two sources of repeated
measurements. One is to densely and repeatedly measure a variable from each
subject at a series of regular time/spatial points, which is named as
functional data. The other is to repeatedly collect one functional data at each
of the multiple visits. Compared to the well-established single-level
functional data analysis approaches, those that are related to high-dimensional
bilevel functional data are limited. In this article, we propose a
high-dimensional functional mixed-effect model (HDFMM) to analyze the
association between the bilevel functional response and a large scale of scalar
predictors. We utilize B-splines to smooth and estimate the
infinite-dimensional functional coefficient, a sandwich smoother to estimate
the covariance function and integrate the estimation of covariance-related
parameters together with all regression parameters into one framework through a
fast updating MCMC procedure. We demonstrate that the performance of the HDFMM
method is promising under various simulation studies and a real data analysis.
As an extension of the well-established linear mixed model, the HDFMM model
extends the response from repeatedly measured scalars to repeatedly measured
functional data/curves, while maintaining the ability to account for the
relatedness among samples and control for confounding factors.
