A Semiparametric Two‐Sample Density Ratio Model With a Change Point
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Bibliographic record
Abstract
The logistic regression model for a binary outcome with a continuous covariate can be expressed equivalently as a two-sample density ratio model for the covariate. Utilizing this equivalence, we study a change-point logistic regression model within the corresponding density ratio modeling framework. We investigate estimation and inference methods for the density ratio model and develop maximal score-type tests to detect the presence of a change point. In contrast to existing work, the density ratio modeling framework facilitates the development of a natural Kolmogorov-Smirnov type test to assess the validity of the logistic model assumptions. A simulation study is conducted to evaluate the finite-sample performance of the proposed tests and estimation methods. We illustrate the proposed approach using a mother-to-child HIV-1 transmission data set and an oral cancer data set.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.005 |
| 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