Perfect collinearity not created equal: measuring and visualizing the severity of multi-collinearity of modern omics data
Bibliographic record
Abstract
Abstract Multi-collinearity frequently occurs in modern statistical applications and when ignored, can negatively impact model selection and statistical inference. Though perfect collinearity is always present in “ n < p ” data, we demonstrate that perfect collinearity arises differently, from diverse data redundancy patterns and/or data dimensions. Classic tools and measures that were developed for “ n > p ” data cannot be used to distinguish or visualize these patterns in the high-dimensional regime. Here we propose 1) new individualized measures that can be used to visualize patterns of perfect collinearity, and subsequently 2) global measures to assess the overall burden of multi-collinearity irrespective of data dimensions. We applied these measures to the human X chromosome data to understand similarity and differences in linkage disequilibrium structure due to sex and genetic features. The measures can highlight gene regions of excessive multi-collinearity and contrast the severity of perfect collinearity between different sexes. Utility of these measures to high-dimensional statistical application were also discussed.
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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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 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".