A case for beta regression in the natural sciences
Bibliographic record
Abstract
Abstract Data in the natural sciences are often in the form of percentages or proportions that are continuous and bounded by 0 and 1. Statistical analysis assuming a normal error structure can produce biased and incorrect estimates when data are doubly bounded. Beta regression uses an error structure appropriate for such data. We conducted a literature review of percent and proportion data from 2004 to 2020 to determine the types of analyses used for (0, 1) bounded data. Our literature review showed that before 2012, angular transformations accounted for 93% of analyses of proportion or percent data. After 2012, angular transformation accounted for 52% of analyses and beta regression accounted for 14% of analyses. We compared a linear model with angular transformation with beta regression using data from two fields of the natural sciences that produce continuous, bounded data: biogeochemistry and ecological elemental composition. We found little difference in model diagnostics, likelihood ratios, andp‐values between the two models. However, we found substantially different coefficient estimates from the back‐calculated beta regression and angular transformation models. Beta regression provides reliable parameter estimates in natural science studies where effect sizes are considered as important as hypothesis testing.
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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 | 0.282 | 0.559 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.007 | 0.010 |
| Science and technology studies | 0.002 | 0.024 |
| Scholarly communication | 0.011 | 0.017 |
| Open science | 0.006 | 0.007 |
| Research integrity | 0.007 | 0.019 |
| Insufficient payload (model declined to judge) | 0.010 | 0.003 |
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".