Unified Estimation Method for Partially Linear Models With Nonmonotone Missing at Random Data
Bibliographic record
Abstract
Partially linear models are commonly used in observational studies of the causal effect of treatment and/or exposure when there are observed confounding variables. The models are robust and asymptotically distribution-free for testing the causal null hypothesis. In this research, we investigate methods for estimating the partially linear models with data missing at random in all the variables, including the response, the treatment, and the confounding variables. We develop a general estimation method for inference in partially linear models with nonmonotone missing at random data. It proposes using partially linear working models to improve the estimation efficiency of the standard complete case method. It can be shown that the new estimator is consistent, which does not depend on the correctness of the working models. In addition, we recommend bootstrap estimates for the asymptotic variances and semiparametric models for the missing data probabilities. It is computationally simple and can be directly implemented in standard software. Simulation studies are provided to examine its performance. A real data example with sparsely observed missingness patterns is used to illustrate the 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 | 0.013 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 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".