Likelihood identifiability and parameter estimation with nonignorable missing data
Bibliographic record
Abstract
Abstract We identify sufficient conditions to resolve the identification problem under nonignorable missingness, especially the identifiability of the observed likelihood when some of the covariate values are missing not at random, or, simultaneously, the response is also missing not at random. It is more difficult to tackle these cases than the nonignorable nonresponse case, and, to the best of our knowledge, the simultaneously missing case has never been discussed before. Under these conditions, we propose some parameter estimation methods. As an illustration, when some of the covariate values are missing not at random, we adopt a semiparametric logistic model with a tilting parameter to model the missingness mechanism and use an imputed estimating equation based on the generalized method of moments to estimate the parameters of interest and the tilting parameter simultaneously. This approach avoids the requirement for other independent surveys or a validation sample to estimate the unknown tilting parameter. The asymptotic properties of our proposed estimators are derived, and the proofs can be modified to show that our methods of estimation, which are based on inverse probability weighting, augmented inverse probability weighting, and estimating equation projection, have the same asymptotic efficiency when the tilting parameter is either known or unknown but estimated by some other method. In simulation studies, we compare our methods with various alternative approaches and find that our methods are more robust and effective.
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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 | 0.035 | 0.234 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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".