Disaggregating level-specific effects in cross-classified multilevel models
Bibliographic record
Abstract
In psychology and other fields, data often have a cross-classified structure, whereby observations are nested within multiple types of non-hierarchical clusters (e.g., repeated measures cross-classified by persons and stimuli). This paper discusses ways that, in cross-classified multilevel models, slopes of lower-level predictors can implicitly reflect an ambiguous blend of multiple effects (for instance, a purely observation-level effect as well as a unique between-cluster effect for each type of cluster). The possibility of conflating multiple effects of lower-level predictors is well recognized for non-cross-classified multilevel models, but has not been fully discussed or clarified for cross-classified contexts. Consequently, in published cross-classified modeling applications, this possibility is almost always ignored, and researchers routinely specify models that conflate multiple effects. In this paper, we show why this common practice can be problematic, and show how to disaggregate level-specific effects in cross-classified models. We provide a novel suite of options that include fully cluster-mean-centered, partially cluster-mean-centered, and contextual effect models, each of which provides a unique interpretation of model parameters. We further clarify how to avoid both fixed and random conflation, the latter of which is widely misunderstood even in non-cross-classified models. We provide simulation results showing the possible deleterious impact of such conflation in cross-classified models, and walk through pedagogical examples to illustrate the disaggregation of level-specific effects. We conclude by considering additional model complexities that can arise with cross-classification, providing guidance for researchers in choosing among model specifications, and describing newly available software to aid researchers who wish to disaggregate effects in practice.
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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 | 0.020 | 0.048 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".