Maximum likelihood abundance estimation from capture‐recapture data when covariates are missing at random
Bibliographic record
Abstract
In capture-recapture experiments, individual covariates may be subject to missingness, especially when the number of captures is small. When the covariate information is missing at random, the inverse probability weighting method and the multiple imputation method are widely used to obtain point estimators of the abundance. These estimators are then used to construct Wald-type confidence intervals. However, such intervals may have seriously inaccurate coverage probabilities. In this paper, we propose a maximum empirical likelihood (EL) estimation approach for the abundance in the presence of missing covariates. We show that the maximum EL estimator is asymptotically normal, and that the EL ratio statistic for the abundance has a chi-square limiting distribution with one degree of freedom. Simulations indicate that the proposed estimator has a smaller mean square error than existing estimators, and the proposed EL ratio confidence interval usually has more accurate coverage probabilities than the existing Wald-type confidence intervals. We illustrate the proposed method by analyzing data collected in Hong Kong for the yellow-bellied prinia, a bird species.
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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 | 0.007 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".