In defense of Pratt's variable importance axioms: A response to Gromping
Bibliographic record
Abstract
In a recent paper Gromping provided a wide‐ranging review of metrics for assessing variable importance in regression analysis. There are, however, several flaws in Gromping's criticism of the well‐known metric attributed to Pratt. Among the metrics she reviewed, Pratt's metric stands out because it is the only one that provides both a theoretically based definition of variable importance, and a simple method of estimation and inference. Our response is an effort to re‐evaluate this unique metric. We give a simplified and abbreviated account of Pratt's original derivation, based on which we address the flaws in Gromping's presentation. We also discuss heuristic interpretations of Pratt's metric, and suggest a new approach for selecting one from among the many available metrics for assessing importance. This approach is intended to supplement that suggested by Gromping. Accordingly, the goal of this response is to help practitioners better understand and choose between available metrics for assessing variable importance. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis
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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 | 0.048 | 0.141 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.005 | 0.008 |
| Science and technology studies | 0.003 | 0.032 |
| Scholarly communication | 0.008 | 0.027 |
| Open science | 0.006 | 0.007 |
| Research integrity | 0.017 | 0.040 |
| 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".