Bayesian Estimation and Economic Analysis of Under-Replicated Field Trials With a Linear Response Plateau Function
Bibliographic record
Abstract
The linear response with plateau (LRP) is widely used in agronomic and agricultural economic studies of crop yield response. This empirical example uses data from an under-replicated experiment to compare maize (Zea maize L.) yield response to nitrogen under different plant and corridor row spacing. Not all replications received a 0-nitrogen rate, making estimation of the LRP difficult because data for the intercept terms is absent. We leverage information from other treatments using Bayesian methods to estimate the yield response of each treatment using a LRP function, given limited replication and absence of check plots for some treatments. We use a linearized LRP, which bypasses using the “min” operator typically required to estimate LRP functions. Economically optimal nitrogen rates were determined and net returns from treatments compared from the perspective of risk-averse producers. The wide plant/narrow row treatment was most profitable when the decision rule was to apply nitrogen. The statistical procedure used here may be useful for exploratory analyses of pilot agronomic trials that may include unbalanced and under-replicated treatments.
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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 | 0.057 | 0.130 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".