Conditional Two Level Mixture with Known Mixing Proportions: Applications to School and Student Level Overweight and Obesity Data from Birmingham, England
Bibliographic record
Abstract
Two Level (TL) models allow the total variation in the outcome to be decomposed as level one and level two or ‘individual and group’ variance components. Two Level Mixture (TLM) models can be used to explore unobserved heterogeneity that represents different qualitative relationships in the outcome. In this paper, we extend the standard TL model by introducing constraints to guide the TLM algorithm towards a more appropriate data partitioning. Our constraints-based methods combine the mixing proportions estimated by parametric Expectation Maximization (EM) of the outcome and the random component from the TL model. This forms new two level mixing conditional (TLMc) approach by means of prior information. The new framework advantages are: 1. avoiding trial and error tactic used by TLM for choosing the best BIC (Bayesian Information Criterion), 2. permitting meaningful parameter estimates for distinct classes in the coefficient space and finally 3. allowing smaller residual variances. We show the benefit of our method using overweight and obesity from Body Mass Index (BMI) for students in year 6. We apply these methods on hierarchical BMI data to estimate student multiple deprivation and school Club effects.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.015 | 0.064 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".