The danger of conflating level‐specific effects of control variables when primary interest lies in level‐2 effects
Why this work is in the frame
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Bibliographic record
Abstract
In the multilevel modelling literature, methodologists widely acknowledge that a level-1 variable can have distinct within-cluster and between-cluster effects, and that failing to disaggregate these can yield a slope estimate that is an uninterpretable, conflated blend of the two. Methodologists have stated, however, that including conflated slopes of level-1 variables in a model is not problematic if substantive interest lies only in effects of level-2 predictors. Researchers commonly follow this advice and use methods that do not disaggregate effects of level-1 control variables (e.g., grand mean centering) when examining effects of level-2 predictors. The primary purpose of this paper is to show that this is a dangerous practice. When level-specific effects of level-1 variables differ, failing to disaggregate them can severely bias estimation of level-2 predictor slopes. We show mathematically why this is the case and highlight factors that can exacerbate such bias. We corroborate these findings with simulations and present an empirical example, showing how such distortions can severely alter substantive conclusions. We ultimately recommend that simply including the cluster mean of the level-1 variable as a control will alleviate the problem.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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 it