New two parameter hybrid estimator for zero inflated negative binomial regression models
Why this work is in the frame
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Bibliographic record
Abstract
The zero-inflated negative binomial regression (ZINBR) model is used for modeling count data that exhibit both overdispersion and zero-inflated counts. However, a persistent challenge in the efficient estimation of parameters within ZINBR models is the issue of multicollinearity, where high correlations between predictor variables can compromise the stability and reliability of the maximum likelihood estimator (MLE). We propose a new two-parameter hybrid estimator, designed for the ZINBR model, to address this problem. This estimator aims to mitigate the effects of multicollinearity by incorporating a combination of existing biased estimators. To test the effectiveness of the proposed estimator, we conduct a comprehensive theoretical comparison with conventional biased estimators, including the Ridge and Liu, the Kibria-Lukman, and the modified Ridge estimators. An extended Monte Carlo simulation study complements the theoretical results, evaluating the estimator's performance under various multicollinearity conditions. The simulation results, evaluated by metrics such as mean squared error (MSE) and mean absolute error (MAE), show that the proposed hybrid estimator consistently outperforms conventional methods, especially in high multicollinearity. Furthermore, we apply it to two real-world datasets. The experimental application demonstrates the superior performance of the estimator in producing stable and accurate parameter estimates. The simulation study and experimental application results strongly suggest that the new two-parameter hybrid estimator offers significant progress in parameter estimation in ZINBR models, especially in complex scenarios due to multicollinearity.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it