Resolving design of experiments for factorial layouts with applications to fraser valley dairy farm productivity
Bibliographic record
Abstract
During the eighteenth century, agricultural experimenters began arranging treatment combinations in systematic grids, laying the groundwork for what would later become factorial design. This research revisited the resolution hierarchy of factorial layouts and developed tighter bounds on the D-efficiency of fractional plans when the number of factor levels exceeds four. A convex analysis framework expressed the information matrix as a convex combination of moment matrices associated with individual runs, and the D-optimality criterion was then cast as a log-determinant maximisation problem amenable to interior-point methods [1]. Latin square constraints were imposed as linear equalities within this optimisation, ensuring that every level of each factor appeared exactly once in each row and column of the design matrix [2]. The theoretical results were applied to a dairy farm productivity dataset from the Fraser Valley in British Columbia, Canada, where four feed-composition factors at five levels each were tested across 16 farms over two milking seasons (2020-2022). Trimmed means were used to handle the heavy-tailed distribution of milk-fat percentage, and a hazard function analysis tracked the time until individual cows dropped below a minimum production threshold [3]. The optimal fractional factorial plan identified by the convex relaxation achieved a D-efficiency of 0.89 with only 50 runs, compared with 625 runs for the full 5⁴ factorial. Variance decomposition showed that treatment effects accounted for 49.8% of total variability, block effects for 14.2%, and treatment-by-block interactions for 18.7%. A secondary cryptographic hashing step verified the integrity of the randomisation sequence, ensuring that farm-level assignments could not have been tampered with after the trial began [4].
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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 | 0.064 | 0.179 |
| Meta-epidemiology (narrow) | 0.003 | 0.003 |
| Meta-epidemiology (broad) | 0.004 | 0.005 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.008 | 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".