Enhancing the accuracy of modeling highly multicollinear CO2 emission data using a novel generalized Poisson Liu regression method
Bibliographic record
Abstract
Count data often exhibit dispersion patterns that the standard Poisson regression model struggles to handle, particularly in cases of overdispersion or underdispersion. The generalized Poisson regression model (GPRM) provides a more flexible alternative, extending the Poisson model to better accommodate such variations. However, parameter estimation in the GPRM typically relies on the generalized Poisson maximum likelihood estimator, which can be problematic when multicollinearity exists among explanatory variables. Biased estimation methods can be used to address this issue. This study explores the Liu estimator as a potential solution for reducing multicollinearity in the GPRM. We also propose different strategies for selecting the Liu parameter to improve estimation accuracy. The theoretical properties of the generalized Poisson Liu estimator are examined, and its performance is compared to that of the generalized Poisson maximum likelihood estimator using matrix mean squared error and scalar mean squared error as evaluation criteria. To assess its effectiveness, we conduct Monte Carlo simulations and apply the method to a carbon dioxide emission dataset in Canada. The results show that the generalized Poisson Liu estimator, particularly with an optimally chosen Liu parameter, outperforms the standard generalized Poisson maximum likelihood estimator in reducing estimation error in the presence of multicollinearity.
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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 | 0.010 | 0.040 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| 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".