Beyond the General Linear Model: Linear Mixed-Effects Modeling of fMRI Data from the Human Connectome Project

Abstract

We present a validated, containerised pipeline for Linear Mixed-Effects (LME) analysis of task fMRI, built for reproducibility: the fitting backend must be declared explicitly, outputs are versioned, and every step records a manifest of software, hardware, and parameters. The implementation is cross-validated against the R reference standard lme4 (mean \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{|\Delta \text {ICC}| = 2.2\times 10^{-6}}$$\end{document} across 21 regions; significance concordance 21/21) and benchmarked at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{19\times }$$\end{document} the per-voxel cost of the GLM, completing a whole-brain analysis in under six hours with 100% convergence. In a case study on emotion task data from 142 HCP subjects (283 runs), voxelwise agreement with the conventional General Linear Model (GLM) is high (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{r = 0.94}$$\end{document}), with LME more conservative under FDR correction (74,004 vs. 108,627 significant voxels at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{q < 0.05}$$\end{document}; Dice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{= 0.77}$$\end{document}). An intermediate LME omitting the run fixed effect is almost indistinguishable from the GLM (Dice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{= 0.99}$$\end{document}), locating the sensitivity difference in the run covariate rather than in hierarchical variance decomposition. Whole-brain ICC mapping shows heterogeneous within-subject variability (mean ICC \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{= 0.199}$$\end{document}), and run effects are significant in 13/21 ROIs, surviving adjustment for head motion. This decomposition strategy offers a reusable diagnostic for sensitivity differences between statistical approaches.