Correlation adjusted penalization in regression analysis
Bibliographic record
Abstract
The PhD thesis introduces two new types of correlation adjusted penalization methods to address the issue of multicollinearity in regression analysis. The main purpose is to achieve simultaneous shrinkage of parameter estimators and variable selection for multiple linear regression and logistic regression when the predictor variables are highly correlated. The motivation is that when there is serious issue of multicollinearity, the variances of parameter estimators are significantly large. The new correlation adjusted penalization methods shrink the parameter estimators and their variances to alleviate the problem of multicollinearity. The latest important trend to deal with multicollinearity is to apply penalization methods for simultaneous shrinkage and variable selection. In the literature, the following penalization methods are popular: ridge, bridge, LASSO, SCAD, and OSCAR. Few papers have used correlation based penalization methods, and these correlation based methods in the literature do not work when some correlations are either 1 or -1. This means that these correlation based methods fail if at least two predictor variables are perfectly correlated. We introduce two new types of correlation adjusted penalization methods that work whether or not the predictor variables are perfectly correlated. The types of correlation adjusted penalization methods introduced in my thesis are intuitive and innovative. We investigate important theoretical properties of these new types of penalization methods, including bias, mean squared error, data argumentation and asymptotic properties, and plan to apply them to real data sets in the near future.
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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 | 0.016 | 0.052 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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".