Centering in Multiple Regression Does Not Always Reduce Multicollinearity: How to Tell When Your Estimates Will Not Benefit From Centering
Bibliographic record
Abstract
Within the context of moderated multiple regression, mean centering is recommended both to simplify the interpretation of the coefficients and to reduce the problem of multicollinearity. For almost 30 years, theoreticians and applied researchers have advocated for centering as an effective way to reduce the correlation between variables and thus produce more stable estimates of regression coefficients. By reviewing the theory on which this recommendation is based, this article presents three new findings. First, that the original assumption of expectation-independence among predictors on which this recommendation is based can be expanded to encompass many other joint distributions. Second, that for many jointly distributed random variables, even some that enjoy considerable symmetry, the correlation between the centered main effects and their respective interaction can increase when compared with the correlation of the uncentered effects. Third, that the higher order moments of the joint distribution play as much of a role as lower order moments such that the symmetry of lower dimensional marginals is a necessary but not sufficient condition for a decrease in correlation between centered main effects and their interaction. Theoretical and simulation results are presented to help conceptualize the issues.
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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 | 0.103 | 0.463 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.003 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.005 | 0.014 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.005 | 0.010 |
| Insufficient payload (model declined to judge) | 0.004 | 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".