Sample empirical likelihood methods for causal inference
Bibliographic record
Abstract
Abstract Causal inference plays a crucial role in understanding the true impact of interventions, medical treatments, policies, or actions, enabling informed decision making and providing insights into the underlying mechanisms that shape our world. In this article, we establish a framework for the estimation of and inference concerning average treatment effects using a two‐sample empirical likelihood function. Two different approaches to incorporating propensity scores are developed. The first approach introduces propensity‐score‐calibrated constraints in addition to the standard model‐calibration constraints; the second approach uses the propensity scores to form weighted versions of the model‐calibration constraints. The resulting estimators from both approaches are doubly robust. The limiting distributions of the two‐sample empirical likelihood ratio statistics are derived, facilitating the construction of confidence intervals and hypothesis tests for the average treatment effect. Bootstrap methods for constructing sample empirical likelihood ratio confidence intervals are also discussed for both approaches. The finite‐sample performance of each method is investigated via simulation studies.
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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 | 0.065 | 0.249 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.006 | 0.006 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.006 | 0.004 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.014 | 0.002 |
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".