Explained Variance in Two-Level Models: A New Approach
Why this work is in the frame
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Bibliographic record
Abstract
The proportion of explained variance is well defined in linear models, but Snijders and Bosker demonstrated that this concept is ill defined in linear multilevel models. Whenever a researcher adds a level 1 predictor to the model, the level 2 variance may increase because the level 2 variance also depends on the level 1 variance. This problem is more pronounced when there are few observations per cluster. The authors present a solution that allows researchers to decompose variance components from null models into parts explained and unexplained by level 1 predictors. The authors also offer an extension that incorporates level 2 predictors. This approach is based on multivariate multilevel modeling and provides a complete decomposition of the gross (or null model) variance components. The approach is also implemented in the user-written Stata program twolevelr2, and the online supplement contains worked code for implementation in R. The authors illustrate this method with an example analyzing sibling similarities in lifetime income.
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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 | 0.004 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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