Shrinkage estimation and selection for a logistic regression model
Bibliographic record
Abstract
This paper considers the problem of variable selection and the esti- mation for a logistic regression model via shrinkage and three penalty methods. We develop a large sample theory for the shrinkage estimators including as- ymptotic distributional bias and risk. We show that if the shrinkage dimension exceeds two, the asymptotic risk of the shrinkage estimator is strictly less than the classical estimators for a wide class of models. This reduction holds glob- ally in the parameter space. Furthermore, we consider three different penalty estimators: the LASSO, adaptive LASSO, and SCAD and compare their rel- ative performance with the shrinkage estimators numerically. A Monte Carlo simulation study is conducted for different combinations of inactive predictors and the performance of each method is evaluated in terms of a simulated mean squared error. This study indicates that shrinkage method is comparable to the LASSO, adaptive LASSO, and SCAD when the number of inactive pre- dictors in the model is relatively large. A real data example is presented to illustrate the proposed methodologies.
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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 | 0.027 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".