Simple fixed-effects inference for complex functional models

TL;DR

This paper introduces straightforward inferential methods for fixed effects in complex functional mixed effects models, using bootstrap techniques to provide reliable confidence intervals and hypothesis tests, demonstrated through simulations and application to aging data.

Contribution

It presents a simple bootstrap-based approach for fixed effects inference in complex functional models, applicable to correlated functional data.

Findings

High coverage probability of confidence intervals

Accurate size of hypothesis tests in simulations

Effective application to longitudinal aging data

Abstract

We propose simple inferential approaches for the fixed effects in complex functional mixed effects models. We estimate the fixed effects under the independence of functional residuals assumption and then bootstrap independent units (e.g. subjects) to estimate the variability of and conduct inference in the form of hypothesis testing on the fixed effects parameters. Simulations show excellent coverage probability of the confidence intervals and size of tests. Methods are motivated by and applied to the Baltimore Longitudinal Study of Aging (BLSA), though they are applicable to other studies that collect correlated functional data.