R-squared Measures for Multilevel Mixture Models with Random Effects
Bibliographic record
Abstract
Multilevel regression mixtures involving both discrete latent classes and continuous random effects are an increasingly popular approach for accommodating nested data structures. However, their application has outpaced the development of effect size measures to aid model interpretation. In response, we provide a general framework of R-squared measures for multilevel regression mixtures with random effects as well as either classes only at level-1 (L1MIX), or classes only at level-2 (L2MIX), or classes at both levels (L1L2MIX). This work extends and unites a previous suite of R-squared measures for multilevel mixtures with latent classes but no random effects (Rights & Sterba, 2018) and a suite of R-squared measures for multilevel models with random effects but no latent classes (Rights & Sterba, 2019).The general framework provided here includes total and class-specific measures that each allow the researcher to distinguish among distinct sources of explained variance in the fitted model. We provide software for implementing these measures and provide two illustrative empirical examples.
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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 | 0.039 | 0.213 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.031 | 0.011 |
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".