Resolving design of experiments for factorial layouts with applications to fraser valley dairy farm productivity
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
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].
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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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