A bias-reduced estimator for generalized Poisson regression with application to carbon dioxide emission in Canada
Bibliographic record
Abstract
The generalized Poisson regression model (GPRM) provides a flexible framework for modeling count data, especially those exhibiting over- or underdispersion. Although the generalized Poisson maximum likelihood estimator is considered the standard method for estimating the parameters of this model, its reliability and accuracy are severely affected by the presence of multicollinearity among explanatory variables. Multicollinearity inflates the variance of parameter estimates, undermining the validity of statistical inference and ultimately leading to unstable and unreliable estimators. To mitigate these problems, this study presents the ridge estimator as a robust alternative within the GPRM framework. Several new strategies are proposed for selecting the optimal value of the ridge parameter. The statistical properties of the proposed ridge estimator were theoretically studied. Theoretical comparisons and extensive Monte Carlo simulations demonstrated a clear and significant superiority of the ridge estimator under multicollinearity conditions, confirming its robustness and efficiency. To demonstrate the scientific and practical relevance of the proposed estimator, it was applied to a real-world case study modeling carbon dioxide emissions in Canada. The results of this experimental application conclusively confirmed the simulation and theoretical comparison results, with the ridge estimator providing more stable and interpretable results than the conventional method, making it a valuable tool for researchers and decision makers in analyzing multicollinear environmental and economic data.
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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 | 0.011 | 0.036 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| 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".