Designing a Pseudo R-Squared Goodness-of-Fit Measure in Generalized Linear Models
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Bibliographic record
Abstract
The coefficient of determination is a function of residuals in the General Linear Models. The deviance, logit, standardized and the studentized residuals were examined in generalized linear models in order to determine the behaviour of residuals in this class of models and thereby design a new pseudo R-squared goodness-of-fit measure. The Newton-Raphson estimation procedure was adopted. It was observed that these residuals exhibit patterns that are unique to the subpopulations defined by levels of categorical predictors. Residuals block on the basis of signs, where positive signs indicate success responses and negative signs failure responses. It was also observed that the deviance is a close approximation of the studentized residual. The logit residual is two times the size of the standardized residuals. Borrowing from the Nagelkerke's improvement of Cox and Snell's goodness-of-fit measure in generalized linear models and the coefficient of determination counterpart of the general linear model, a new pseudo R squared goodness-of-fit test which uses predicted probabilities and a monotonic link function is here proposed to serve both the linear and Generalized Linear Models.
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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 | 0.015 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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