Enriched-Data Problems and Essential Non-Identifiability
Bibliographic record
Abstract
There are two principal ways in which statistical models extend beyond the data available. First, the data may be coarsened, that is, what is actually observed is less detailed than what is planned, owing to, for example, attrition, censoring, grouping, or a combination of these. Second, the data may be augmented, that is, the observed data are hypothetically but conveniently supplemented with structures such as random effects, latent variables, latent classes, or component membership in mixture distributions. These two settings together will be referred to as enriched data. Reasons for modelling enriched data include the incorporation of substantive information, such as the need for predictions, advantages in interpretation, and mathematical and computational convenience. The fitting of models for enriched data combine evidence arising from empirical data with non-verifiable model components, i.e., that are purely assumption driven. This has important implications for the interpretation of statistical analyses in such settings. While widely known, the exploration and discussion of these issues is somewhat scattered. The user should be fully aware of the potential dangers and pitfalls that follows from this. Therefore, we provide a unified framework for enriched data and show in general that to any given model an entire class of models can be assigned, with all of its members producing the same fit to the observed data but arbitrary regarding the unobservable parts of the enriched data. The implications of this are explored for several specific settings, namely that of latent classes, finite mixtures, factor analysis, random-effects models, and incomplete data. The results are applied to a range of relevant 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 | 0.076 | 0.309 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.005 | 0.004 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.004 | 0.019 |
| Scholarly communication | 0.007 | 0.017 |
| Open science | 0.007 | 0.010 |
| Research integrity | 0.008 | 0.015 |
| Insufficient payload (model declined to judge) | 0.007 | 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".