A new hybrid estimator for the beta regression model: simulations and applications
Bibliographic record
Abstract
An increasingly common approach for analyzing correlations between chemical properties is the beta regression model (BRM). In the BRM, the maximum likelihood estimator (MLE) can yield unreliable estimates when the explanatory variables are highly correlated. To address this issue, we propose a new beta hybrid estimator (BHE) for the BRM, which integrates the advantages of several existing biased estimators. The proposed BHE is evaluated under five different biasing parameter selection methods, resulting in five variants (BHE1–BHE5). Using the mean squared error (MSE) criterion, we analytically and numerically compare these new variants with the MLE, beta ridge regression, beta Liu, beta Kibria–Lukman, and beta modified ridge-type estimators. Through extensive Monte Carlo simulations and two real data applications, the results reveal that the proposed BHE variants consistently outperform their competitors by achieving lower MSE across various levels 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 | 0.005 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".