Assessing Variance Components in Multilevel Linear Models using Approximate Bayes Factors: A Case-Study of Ethnic Disparities in Birth Weight
Bibliographic record
Abstract
Racial/ethnic disparities in birthweight are a large source of differential morbidity and mortality worldwide and have remained largely unexplained in epidemiologic models. We assess the impact of maternal ancestry and census tract residence on infant birth weights in New York City and the modifying effects of race and nativity by incorporating random effects in a multilevel linear model. Evaluating the significance of these predictors involves the test of whether the variances of the random effects are equal to zero. This is problematic because the null hypothesis lies on the boundary of the parameter space. We generalize an approach for assessing random effects in the two-level linear model to a broader class of multilevel linear models by scaling the random effects to the residual variance and introducing parameters that control the relative contribution of the random effects. After integrating over the random effects and variance components, the resulting integrals needed to calculate the Bayes factor can be efficiently approximated with Laplace's method.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 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".