High-Dimensional Functional Mixed-effect Model for Bilevel Repeated Measurements

Abstract: 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.