Using commonality analysis in multiple regressions: a tool to decompose regression effects in the face of multicollinearity
Bibliographic record
Abstract
Summary 1. In the face of natural complexities and multicollinearity, model selection and predictions using multiple regression may be ambiguous and risky. Confounding effects of predictors often cloud researchers’ assessment and interpretation of the single best ‘magic model’. The shortcomings of stepwise regression have been extensively described in statistical literature, yet it is still widely used in ecological literature. Similarly, hierarchical regression which is thought to be an improvement of the stepwise procedure, fails to address multicollinearity. 2. We propose that regression commonality analysis ( CA ), a technique more commonly used in psychology and education research will be helpful in interpreting the typical multiple regression analyses conducted on ecological data. 3. CA decomposes the variance of R 2 into unique and common (or shared) variance (or effects) of predictors, and hence, it can significantly improve exploratory capabilities in studies where multiple regressions are widely used, particularly when predictors are correlated. CA can explicitly identify the magnitude and location of multicollinearity and suppression in a regression model. In this paper, using a simulated (from a correlation matrix) and an empirical dataset (human habitat selection, migration of Canadians across cities), we demonstrate how CA can be used with correlated predictors in multiple regression to improve our understanding and interpretation of data. We strongly encourage the use of CA in ecological research as a follow‐on analysis from multiple regressions.
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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 | 0.044 | 0.172 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.006 |
| Bibliometrics | 0.009 | 0.007 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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".