The definition and measurement of heterogeneity
Bibliographic record
Abstract
Heterogeneity is an important concept in psychiatric research and science more broadly. It negatively impacts effect size estimates under case-control paradigms, and it exposes important flaws in our existing categorical nosology. Yet, our field has no precise definition of heterogeneity proper. We tend to quantify heterogeneity by measuring associated correlates such as entropy or variance: practices which are akin to accepting the radius of a sphere as a measure of its volume. Under a definition of heterogeneity as the degree to which a system deviates from perfect conformity, this paper argues that its proper measure roughly corresponds to the size of a system's event/sample space, and has units known as numbers equivalent. We arrive at this conclusion through focused review of more than 100 years of (re)discoveries of indices by ecologists, economists, statistical physicists, and others. In parallel, we review psychiatric approaches for quantifying heterogeneity, including but not limited to studies of symptom heterogeneity, microbiome biodiversity, cluster-counting, and time-series analyses. We argue that using numbers equivalent heterogeneity measures could improve the interpretability and synthesis of psychiatric research on heterogeneity. However, significant limitations must be overcome for these measures-largely developed for economic and ecological research-to be useful in modern translational psychiatric science.
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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 | 0.043 | 0.077 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.008 | 0.007 |
| Science and technology studies | 0.001 | 0.015 |
| Scholarly communication | 0.007 | 0.009 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".