Comparison of Test Statistics for Testing the Regression Coefficients in the Ridge, Liu and Kibria-Lukman Logistic Regression Models: Simulation and Application
Bibliographic record
Abstract
Ridge, Liu and Kibria- Lukman regression are methods that have been proposed to solve the multicollinearity problem for both linear and non-linear regression models. This paper studies different Ridge, Liu and Kibria-Lukman regression z-type tests of the individual coefficients for logistic regression model. A simulation study was conducted to evaluate and compare the performance of the test statistics with respect to their empirical sizes and powers under different simulation conditions. Our simulations allowed us to identify among the proposed tests, which ones maintain type I error rates close to the 5% nominal level, while at the at same time showing considerable gain in statistical power over the standard Wald z-test commonly used in logistic regression model. Our paper is the first of its kind in comparing the z-type tests for these different shrinkage approaches to estimation in logistic regression. The results will be of value for applied statisticians and researchers in the area of regression models.
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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 | 0.062 | 0.271 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".