Another look at regression analysis using ranked set samples with application to an osteoporosis study
Bibliographic record
Abstract
Statistical learning with ranked set samples has shown promising results in estimating various population parameters. Despite the vast literature on rank-based statistical learning methodologies, very little effort has been devoted to studying regression analysis with such samples. A pressing issue is how to incorporate the rank information of ranked set samples into the analysis. We propose two methodologies based on a weighted least squares approach and multilevel modeling to better incorporate the rank information of such samples into the estimation and prediction processes of regression-type models. Our approaches reveal significant improvements in both estimation and prediction problems over already existing methods in the literature and the corresponding ones with simple random samples. We study the robustness of our methods with respect to the misspecification of the distribution of the error terms. Also, we show that rank-based regression models can effectively predict simple random test data by assigning ranks to them a posteriori using judgment poststratification. Theoretical results are augmented with simulations and an osteoporosis study based on a real data set from the Bone Mineral Density (BMD) program of Manitoba to estimate the BMD level of patients using easy to obtain covariates.
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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 | 0.015 | 0.050 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".