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Asymptotic Confidence Regions for Biadditive Models: Interpreting Genotype‐Environment Interactions

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  • Jean‐Baptiste Denis
  • John C. Gower

Abstract

An understanding of how genotypes of an agricultural crop interact with the environment in which they are grown is important for assessing plant production. A breeding trial for 21 genotypes of rye‐grass grown at seven locations is used to illustrate the interpretation of genotype‐environment interactions. Statisticians have proposed many ways of modelling these interactions, but a subclass of bilinear models, that we term biadditive, fits especially well. We emphasize assessing and interpreting the interaction parameters of biadditive models by constructing confidence regions in biplot representations. When a biadditive model is valid, this new development underpins better informed decisions on variety recommendation and genotype selection.

Suggested Citation

  • Jean‐Baptiste Denis & John C. Gower, 1996. "Asymptotic Confidence Regions for Biadditive Models: Interpreting Genotype‐Environment Interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 479-493, December.
    • Handle: RePEc:bla:jorssc:v:45:y:1996:i:4:p:479-493
    DOI: 10.2307/2986069
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    Cited by:

    1. Hans-Peter Piepho, 1999. "Fitting A Regression Model for Genotype-By-Environment Data on Heading Dates in Grasses by Methods for Nonlinear Mixed Models," Biometrics, The International Biometric Society, vol. 55(4), pages 1120-1128, December.
    2. Fithian, William & Josse, Julie, 2017. "Multiple correspondence analysis and the multilogit bilinear model," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 87-102.
    3. Azaïs, Jean-Marc & Ribes, Aurélien, 2016. "Multivariate spline analysis for multiplicative models: Estimation, testing and application to climate change," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 38-53.
    4. John C. Gower & Sugnet Gardner-Lubbe & Niel J. Le Roux, 2018. "Interaction: Fisher’s Optimal Scores Revisited," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 92-112, March.
    5. Zhiqiu Hu & Rong-Cai Yang, 2013. "A New Distribution-Free Approach to Constructing the Confidence Region for Multiple Parameters," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-13, December.

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