On the testing of equivalent variables: Perfect correlations and correlational topology
Bibliographic record
Abstract
When two variables effectively represent the same variable, redundancy may spur statistical complications. For example, in a psychological network model, the partial associations between that variable and other variables in the network may become distorted. The networktools R package contains the goldbricker function to screen for redundant variables, whereby difference-based null hypothesis testing is used to determine whether two variables have the same zero-order correlations with other variables (same topology). But this approach has logical drawbacks, does not directly consider whether two variables are highly correlated, and has never been formally evaluated. We adapted two equivalence testing (ET) approaches – one that tests topology and one that tests the correlation between two variables directly – and evaluated their performance relative to goldbricker in three simulation studies. In a third study, we introduce a latent variable modeling approach that considers variables to be less than perfectly reliable. While goldbricker had good ability to flag variables with redundant topology, it had high false positive rates at small sample sizes and exhibited a tendency to not flag pairs with trivial differences in topology at large sample sizes. The ET-based approaches maintained better false positive rates and a more desirable pattern of results at larger sample sizes. An empirical example with data from the Patient Reported Outcomes Measurement Information System is provided. We argue that there are better alternatives to goldbricker, and tradeoffs between ET and the latent variable modeling approach are critically 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 | 0.182 | 0.647 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.005 |
| Bibliometrics | 0.007 | 0.008 |
| Science and technology studies | 0.004 | 0.023 |
| Scholarly communication | 0.007 | 0.017 |
| Open science | 0.005 | 0.012 |
| Research integrity | 0.005 | 0.008 |
| Insufficient payload (model declined to judge) | 0.008 | 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".