A Dynamic Interaction Semiparametric Function-on-Scalar Model
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Bibliographic record
Abstract
Motivated by recent work studying massive functional data, such as the COVID-19 data, we propose a new dynamic interaction semiparametric function-on-scalar (DISeF) model. The proposed model is useful to explore the dynamic interaction among a set of covariates and their effects on the functional response. The proposed model includes many important models investigated recently as special cases. By tensor product B-spline approximating the unknown bivariate coefficient functions, a three-step efficient estimation procedure is developed to iteratively estimate bivariate varying-coefficient functions, the vector of index parameters, and the covariance functions of random effects. We also establish the asymptotic properties of the estimators including the convergence rate and their asymptotic distributions. In addition, we develop a test statistic to check whether the dynamic interaction varies with time/spatial locations, and we prove the asymptotic normality of the test statistic. The finite sample performance of our proposed method and of the test statistic are investigated with several simulation studies. Our proposed DISeF model is also used to analyze the COVID-19 data and the ADNI data. In both applications, hypothesis testing shows that the bivariate varying-coefficient functions significantly vary with the index and the time/spatial locations. For instance, we find that the interaction effect of the population aging and the socio-economic covariates, such as the number of hospital beds, physicians, nurses per 1000 people and GDP per capita, on the COVID-19 mortality rate varies in different periods of the COVID-19 pandemic. The healthcare infrastructure index related to the COVID-19 mortality rate is also obtained for 141 countries estimated based on the proposed DISeF model.
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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 | 0.025 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 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