Sparse Estimation in Semiparametric Finite Mixture of Varying Coefficient Regression Models
Bibliographic record
Abstract
Finite mixture of regressions (FMR) are commonly used to model heterogeneous effects of covariates on a response variable in settings where there are unknown underlying subpopulations. FMRs, however, cannot accommodate situations where covariates' effects also vary according to an "index" variable-known as finite mixture of varying coefficient regression (FM-VCR). Although complex, this situation occurs in real data applications: the osteocalcin (OCN) data analyzed in this manuscript presents a heterogeneous relationship where the effect of a genetic variant on OCN in each hidden subpopulation varies over time. Oftentimes, the number of covariates with varying coefficients also presents a challenge: in the OCN study, genetic variants on the same chromosome are considered jointly. The relative proportions of hidden subpopulations may also change over time. Nevertheless, existing methods cannot provide suitable solutions for accommodating all these features in real data applications. To fill this gap, we develop statistical methodologies based on regularized local-kernel likelihood for simultaneous parameter estimation and variable selection in sparse FM-VCR models. We study large-sample properties of the proposed methods. We then carry out a simulation study to evaluate the performance of various penalties adopted for our regularized approach and ascertain the ability of a BIC-type criterion for estimating the number of subpopulations. Finally, we applied the FM-VCR model to analyze the OCN data and identified several covariates, including genetic variants, that have age-dependent effects on OCN.
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How this classification was reachedexpand
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.006 | 0.035 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".