Performance of quantile regression methods with discrete outcomes: A simulation study with applications to environmental epidemiology
Bibliographic record
Abstract
Background: Quantile regression helps identify how associations vary across the outcome variable's distribution. Using simulations and data from the Maternal-Infant Research on Environmental Chemicals study, we showed that frequentist quantile regression can produce implausible results where the point estimates are integers or rational numbers and the outcome variable is discrete, which is common in health research. Applying "dithering" (also known as jittering) or using Bayesian quantile regression can prevent such implausible results, but the optimal strategy is unclear. Methods: We conducted simulations with discrete outcomes to compare the bias and variability of point estimates of undithered frequentist, dithered frequentist, and Bayesian quantile regression. We also compared the coverage and interval-width variance of these methods' confidence or credible intervals. Results: The dithered frequentist method generated point estimates that were less variable than the undithered frequentist method. The Bayesian method had the least variable point estimates, but when the sample size was low (n = 100), it exhibited bias when modeling a binary or discrete covariate. The dithered frequentist method with xy-bootstrapped confidence intervals had nominal coverage and produced intervals with relatively consistent widths. The Bayesian method with adjusted intervals also had nominal coverage, but more variable interval widths. The Bayesian method with unadjusted intervals had poor coverage. Conclusion: In our simulations with discrete outcomes, dithered frequentist quantile regression (particularly with xy-bootstrapped confidence intervals) had the best overall performance. The Bayesian method with adjusted intervals is an acceptable strategy, although it was biased under certain scenarios and generated credible intervals with more variable widths.
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How this classification was reachedexpand
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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".