Biplots of Linear‐Bilinear Models for Studying Crossover Genotype × Environment Interaction
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Bibliographic record
Abstract
Linear‐bilinear models, such as the Shifted Multiplicative Model (SHMM) and Sites Regression Model (SREG), have been used to develop clustering procedures for finding subsets of sites (or cultivars) without cultivar crossover interaction (non‐COI). Biplots of these models are useful for visual evaluation of cultivar responses across environments. The main purposes of this study were to investigate (i) SREG 2 and SHMM 2 biplots with the first multiplicative components constrained to be non‐COI SREG 1 and SHMM 1 solutions, (ii) how the biplots can be used for identifying subsets of sites and cultivars with different levels of COI and with non‐COI, and (iii) how these biplots compare with results obtained when clustering only sites or cultivars without cultivar rank change. Transformed and untransformed data from two multienvironment cultivar trials were used for illustration. Biplots from SHMM 2 and SREG 2 models graphically display the interaction variation due to low level COI or non‐COI (first multiplicative term) versus the interaction variation due to COI (second multiplicative term). The biplots obtained by means of the non‐COI first term constrained solution of the SREG 2 and SHMM 2 models have the same interpretability properties as the standard biplots obtained by means of the unconstrained solution. With the unconstrained and constrained solutions, it is possible to identify subsets of sites and cultivars with low level COI and non‐COI. Biplots based on unscaled or scaled data produced similar results. Groups of sites and cultivars with low level COI and non‐COI were similar to those found when only sites (or cultivars) were clustered into non‐COI groups using the SHMM and SREG clustering approach.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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