A functional nonlinear mixed effects modeling framework for longitudinal functional responses
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.013 | 0.020 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".