Copula‐based regression models for a bivariate mixed discrete and continuous outcome
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Bibliographic record
Abstract
This paper is concerned with regression models for correlated mixed discrete and continuous outcomes constructed using copulas. Our approach entails specifying marginal regression models for the outcomes, and combining them via a copula to form a joint model. Specifically, we propose marginal regression models (e.g. generalized linear models) to link the outcomes' marginal means to covariates. To account for associations between outcomes, we adopt the Gaussian copula to indirectly specify their joint distributions. Our approach has two advantages over current methods: one, regression parameters in models for both outcomes are marginally meaningful, and two, the association is 'margin-free', in the sense that it is characterized by the copula alone. By assuming a latent variable framework to describe discrete outcomes, the copula used still uniquely determines the joint distribution. In addition, association measures between outcomes can be interpreted in the usual way. We report results of simulations concerning the bias and efficiency of two likelihood-based estimation methods for the model. Finally, we illustrate the model using data on burn injuries.
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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 | 0.011 |
| 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 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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