Dynamic Single‐Index Scalar‐On‐Function Model
Bibliographic record
Abstract
Environmental exposures often exhibit temporal variability, prompting extensive research to understand their dynamic impacts on human health. There has been a growing interest in studying time-dependent exposure mixtures beyond a single exposure. However, current analytic methods typically assess each exposure individually or assume an additive relationship. This paper aims to fill the gap in method development for evaluating the joint effects of multiple time-dependent exposures on a scalar outcome. We introduce a dynamic single-index scalar-on-function model to characterize the exposure mixture's time-varying effect through a non-parametric bivariate exposure-time-outcome surface function. Utilizing B-spline tensor product bases to approximate the surface function, we propose a profiling algorithm for model estimation and establish large-sample properties for the resulting single-index estimators. In addition, we introduce a non-parametric hypothesis testing procedure to determine whether the surface function varies over time at each fixed mixture level and a model averaging solution to circumvent the issue of knot selection for spline approximations. The performance of our proposed methods is examined through extensive simulations and further illustrated using real-world applications.
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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 | 0.005 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".