Using Generalized Additive Models to Detect and Estimate Threshold Associations
Why this work is in the frame
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Bibliographic record
Abstract
In a variety of research settings, investigators may wish to detect and estimate a threshold in the association between continuous variables. A threshold model implies a non-linear relationship, with the slope changing at an unknown location. Generalized additive models (GAMs) (Hastie and Tibshirani, 1990) estimate the shape of the non-linear relationship directly from the data and, thus, may be useful in this endeavour.We propose a method based on GAMs to detect and estimate thresholds in the association between a continuous covariate and a continuous dependent variable. Using simulations, we compare it with the maximum likelihood estimation procedure proposed by Hudson (1966).We search for potential thresholds in a neighbourhood of points whose mean numerical second derivative (a measure of local curvature) of the estimated GAM curve was more than one standard deviation away from 0 across the entire range of the predictor values. A threshold association is declared if an F-test indicates that the threshold model fit significantly better than the linear model.For each method, type I error for testing the existence of a threshold against the null hypothesis of a linear association was estimated. We also investigated the impact of the position of the true threshold on power, and precision and bias of the estimated threshold.Finally, we illustrate the methods by considering whether a threshold exists in the association between systolic blood pressure (SBP) and body mass index (BMI) in two data sets.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it