New Recommendations on the Use of R-Squared Differences in Multilevel Model Comparisons
Why this work is in the frame
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Bibliographic record
Abstract
When comparing multilevel models (MLMs) differing in fixed and/or random effects, researchers have had continuing interest in using R-squared differences to communicate effect size and importance of included terms. However, there has been longstanding confusion regarding which R-squared difference measures should be used for which kind of MLM comparisons. Furthermore, several limitations of recent studies on R-squared differences in MLM have led to misleading or incomplete recommendations for practice. These limitations include computing measures that are by definition incapable of detecting a particular type of added term, considering only a subset of the broader class of available R-squared difference measures, and incorrectly defining what a given R-squared difference measure quantifies. The purpose of this paper is to elucidate and resolve these issues. To do so, we define a more general set of total, within-cluster, and between-cluster R-squared difference measures than previously considered in MLM comparisons and give researchers concrete step-by-step procedures for identifying which measure is relevant to which model comparison. We supply simulated and analytic demonstrations of limitations of previous MLM studies on R-squared differences and show how application of our step-by-step procedures and general set of measures overcomes each. Additionally, we provide and illustrate graphical tools and software allowing researchers to automatically compute and visualize our set of measures in an integrated manner. We conclude with recommendations, as well as extensions involving (a) how our framework relates to and can be used to obtain pseudo-R-squareds, and (b) how our framework can accommodate both simultaneous and hierarchical model-building approaches.
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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 | 0.001 |
| 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 | 0.001 | 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