Approaches for Quantifying the ICC in Multilevel Logistic Models: A Didactic Demonstration
Bibliographic record
Abstract
Multilevel modeling techniques have gained traction among experimental psychologists for their ability to account for dependencies in nested data structures. Increasingly, these techniques are extended to the analysis of binary data (e.g., correct or incorrect responses). Despite their popularity, the information in logistic multilevel models is often underutilized when researchers focus solely on fixed effects and ignore important heterogeneity that exists between participants. In this tutorial, we review four techniques for estimating and quantifying the relative degree of between-person variability in logistic multilevel models in an accessible manner using real data. First, we introduce logistic multilevel modeling, including the interpretation of fixed and random effects. Second, we review the challenges associated with the estimation and interpretation of within- and between-participant variation in logistic multilevel models, particularly computing the intraclass correlation coefficient (ICC), which is usually a first, simple step in a linear MLM. Third, we demonstrate four existing methods of quantifying the ICC in logistic multilevel models and discuss their relative advantages and disadvantages. Fourth, we present bootstrapping methods to make statistical inference about these ICC estimates. To facilitate reuse, we developed R code to implement the discussed techniques, which is provided throughout the text and as supplemental materials.
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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 | 0.021 | 0.094 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.025 | 0.008 |
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".