Best-subset instrumental variable selection method using mixed integer optimization with applications to health-related quality of life and education–wage analyses
Bibliographic record
Abstract
Abstract The classical best-subset selection method has been demonstrated to be nondeterministic polynomial-time-hard and thus presents computational challenges. This problem can now be solved via advanced mixed integer optimization (MIO) algorithms for linear regression. We extend this methodology to linear instrumental variable (IV) regression and propose the best-subset instrumental variable (BSIV) method incorporating the MIO procedure. Classical IV estimation methods assume that IVs must not directly impact the outcome variable and should remain uncorrelated with nonmeasured variables. However, in practice, IVs are likely to be invalid, and existing methods can lead to a large bias relative to standard errors in certain situations. The proposed BSIV estimator is robust in estimating causal effects in the presence of unknown IV validity. We demonstrate that the BSIV using MIO algorithms outperforms two-stage least squares, Lasso-type IVs, and two-sample analysis (median and mode estimators) through Monte Carlo simulations in terms of bias and relative efficiency. We analyze two datasets involving the health-related quality of life index and proximity and the education–wage relationship to demonstrate the utility of the proposed method.
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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 | 0.011 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".