Open Access
2024 A functional nonlinear mixed effects modeling framework for longitudinal functional responses
Linglong Kong, Xinchao Luo, Jinhan Xie, Lixing Zhu, Hongtu Zhu
Author Affiliations +
Electron. J. Statist. 18(1): 1355-1393 (2024). DOI: 10.1214/24-EJS2226


In this paper, we introduce a functional nonlinear mixed effects modeling framework designed to quantify the random, nonlinear relationship between individual spatiotemporal functional trajectories and longitudinal responses. Our proposed framework accounts for within-individual variability through a spatiotemporal process. We detail an estimation method for determining fixed and random effect functions and spatiotemporal covariance operators and establish their asymptotic properties, including uniform consistency and weak convergence. We also develop global linear hypothesis tests and bootstrap-based simultaneous confidence bands for fixed effect functions. To assess the finite-sample performance of our method, we perform a numerical analysis using both simulated and real-world datasets. Our results demonstrate that the proposed model class is significantly more flexible and effective in detecting functional fixed effects compared to existing nonlinear mixed effects models. We apply our approach to an autism research database to investigate the impact of age and spatial dynamics on fractional anisotropy along the corpus callosum white matter fiber skeleton.

Funding Statement

Linglong Kong was partially supported by grants from the Canada CIFAR AI Chairs program, the Alberta Machine Intelligence Institute (AMII), and Natural Sciences and Engineering Council of Canada (NSERC), and the Canada Research Chair program from NSERC. Lixing Zhu was supported by the National Scientific Foundation of China (NSFC12131006). The research of Hongtu Zhu was partially supported by the National Institute On Aging (NIA) of the National Institutes of Health (NIH) under Award Numbers RF1AG082938.


The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.


Download Citation

Linglong Kong. Xinchao Luo. Jinhan Xie. Lixing Zhu. Hongtu Zhu. "A functional nonlinear mixed effects modeling framework for longitudinal functional responses." Electron. J. Statist. 18 (1) 1355 - 1393, 2024.


Received: 1 May 2023; Published: 2024
First available in Project Euclid: 15 March 2024

Digital Object Identifier: 10.1214/24-EJS2226

Primary: 60J05 , 62G05 , 62G08 , 62G20

Keywords: Functional random effect , Functional response , global test statistic , longitudinal response , simultaneous confidence band , weak convergence

Vol.18 • No. 1 • 2024
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