Simplifying Bias Correction for Selective Sampling: A Unified Distribution-Free Approach to Handling Endogenously Selected Samples
Bibliographic record
Abstract
Unlike random sampling, selective sampling draws units based on the outcome values, such as over-sampling rare events in choice outcomes and extreme activities on continuous and count outcomes.Despite high cost effectiveness for marketing research, such endogenously selected samples must be carefully analyzed to avoid selection bias.We introduce a unified and efficient approach based on semiparametric odds ratio (SOR) models applicable for categorical, continuous and count response data collected using selective sampling.Unlike extant samplingadjusting methods and Heckman-type selection models, the proposed approach requires neither modeling selection mechanisms nor imposing parametric distributional assumptions on the response variables, eliminating both sources of mis-specification bias.Using this approach, one can quantify and test for the relationships among variables as if samples had been collected via random sampling, simplifying bias correction of endogenously selected samples.We evaluate and illustrate the method using extensive simulation studies and two real data examples: endogenously stratified sampling for linear/nonlinear regressions to identify drivers of the shareof-wallet outcome for cigarettes smokers, and using truncated and on-site samples for count data models of store shopping demand.The evaluation shows that selective sampling followed by applying the SOR approach reduces required sample size by more than 70% compared with random sampling, and that in a wide range of selective sampling scenarios SOR offers novel solutions outperforming extant methods for selective samples with opportunities to make better managerial decisions.
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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 | 0.058 | 0.198 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.005 | 0.006 |
| Research integrity | 0.002 | 0.003 |
| 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".