Linear, bilinear, and linear-bilinear fixed and mixed models for analyzing genotype × environment interaction in plant breeding and agronomy
Bibliographic record
Abstract
The purpose of this manuscript is to review various statistical models for analyzing genotype × environment interaction (GE). The objective is to present parsimonious approaches other than the standard analysis of variance of the two-way effect model. Some fixed effects linear-bilinear models such as the sites regression model (SREG) are discussed, and a mixed effects counterpart such as the factorial analytic (FA) model is explained. The role of these linear-bilinear models for assessing crossover interaction (COI) is explained. One class of linear models, namely factorial regression (FR) models, and one class of bilinear models, namely partial least squares (PLS) regression, allows incorporating external environmental and genotypic covariables directly into the model. Examples illustrating the use of various statistical models for analyzing GE in the context of plant breeding and agronomy are given. Key words: Least squares, singular value decomposition, environmental and genotypic covariables
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How this classification was reachedexpand
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 | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".