Total least squares bias in climate fingerprinting regressions with heterogeneous noise variances and correlated explanatory variables
Bibliographic record
Abstract
Abstract Regression‐based “fingerprinting” methods in climate science employ total least squares (TLS) or orthogonal regression to remedy attenuation bias arising from measurement error due to reliance on climate model‐generated explanatory variables. Proving the consistency of multivariate TLS requires assuming noise variances are equal across all variables in the model. This assumption has been challenged empirically in the climate context but little is known about TLS biases when the assumption is violated. Monte Carlo analysis is used herein to examine coefficient biases when the noise variances are not equal. The analysis allows the explanatory variables to be negatively correlated which is typical in climate applications. Ordinary least squares (OLS) exhibits the expected attenuation bias which vanishes as the noise variances on the explanatory variables disappear. In some cases, TLS corrects attenuation bias but more typically imparts large and generally positive biases. OLS performs well when the true value of whereas TLS performs quite poorly. This implies that TLS is not well suited for tests of the null. When TLS tends to exhibit opposite biases to OLS. Diagnostic information specific to each data sample should be consulted before using TLS to avoid spurious inferences and replacing OLS attenuation bias with other, potentially larger biases.
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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 | 0.028 | 0.124 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".