The definition and measurement of heterogeneity
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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