A functional mixed model for scalar on function regression with application to a functional MRI study

• Published in: Biostatistics (Oxford, England) Vol. 22; no. 3; pp. 439 - 454
• Main Authors: Ma, Wanying, Xiao, Luo, Liu, Bowen, Lindquist, Martin A
• Format: Journal Article
• Language: English
• Published: England Oxford University Press 17.07.2021
• Subjects: Brain - diagnostic imaging; Computer Simulation; Humans; Magnetic Resonance Imaging; Principal Component Analysis; fMRI; Variance component testing; Functional mixed model; Functional data analysis; Functional principal component; Repeated measurements
• ISSN: 1465-4644; 1468-4357; 1468-4357
• DOI: 10.1093/biostatistics/kxz046

Motivated by a functional magnetic resonance imaging (fMRI) study, we propose a new functional mixed model for scalar on function regression. The model extends the standard scalar on function regression for repeated outcomes by incorporating subject-specific random functional effects. Using functional principal component analysis, the new model can be reformulated as a mixed effects model and thus easily fit. A test is also proposed to assess the existence of the subject-specific random functional effects. We evaluate the performance of the model and test via a simulation study, as well as on data from the motivating fMRI study of thermal pain. The data application indicates significant subject-specific effects of the human brain hemodynamics related to pain and provides insights on how the effects might differ across subjects.