Total Least Squares Bias when Explanatory Variables are Correlated
Why this work is in the frame
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Bibliographic record
Abstract
Total Least Squares (TLS) or orthogonal regression is used to remedy attenuation bias in optimal fingerprinting regressions. Consistency properties in multivariate applications require strong assumptions about unobservable variance ratios. Monte Carlo analysis is used herein to examine coefficient biases when the explanatory variables are correlated and have heterogeneous error variances. Ordinary Least Squares (OLS) exhibits the expected attenuation bias patterns which vanish as the noise variances on the explanatory variable disappear. TLS is generally more biased than OLS except under homogeneous noise variances. When the explanatory variables are negatively correlated TLS imparts a large upward bias which gets worse as the noise variance on the explanatory variable gets smaller. In general without specific diagnostic information TLS should not be considered an improvement on OLS and can yield extremely biased coefficients.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.039 | 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 it