Another Look at Bayesian Analysis of AMMI Models for Genotype-Environment Data
- 407 Downloads
Linear–bilinear models are frequently used to analyze two-way data such as genotype-by-environment data. A well-known example of this class of models is the additive main effects and multiplicative interaction effects model (AMMI). We propose a new Bayesian treatment of such models offering a proper way to deal with the major problem of overparameterization. The rationale is to ignore the issue at the prior level and apply an appropriate processing at the posterior level to be able to arrive at easily interpretable inferences. Compared to previous attempts, this new strategy has the great advantage of being directly implementable in standard software packages devoted to Bayesian statistics such as WinBUGS/OpenBUGS/JAGS. The method is assessed using simulated datasets and a real dataset from plant breeding. We discuss the benefits of a Bayesian perspective to the analysis of genotype-by-environment interactions, focusing on practical questions related to general and local adaptation and stability of genotypes. We also suggest a new solution to the estimation of the risk of a genotype not exceeding a given threshold.
Key WordsAdaptation AMMI models Bayesian inference Genotype-by-environment interaction Overparameterization Singular-value decomposition Stability
Unable to display preview. Download preview PDF.
- Cornelius, P., Crossa, J., and Seyedsadr, M. (1996), “Statistical Tests and Estimators of Multiplicative Models for Genotype by Environment Interaction,” in Genotype by Environment Interaction, eds. M. S. Kang and H. G. Gauch, Boca Raton, FL: CRC Press, pp. 199–234. Google Scholar
- Eskridge, K., and Mumm, R. (1992), “Choosing Plant Cultivars Based on the Probability of Outperforming a Check,” Theoretical and Applied Genetics, 84, 494—500. Google Scholar
- Gauch, H. (1990), “Using Interaction to Improve Yield Estimates,” in Genotype by Environment Interaction, ed. M. S. Kang, Boca Raton, FL: CRC Press, pp. 141–150. Google Scholar
- — (2012), “rstiefel: Random Orthonormal Matrix Generation on the Stiefel Manifold,” available at http://CRAN.R-project.org/package=rstiefel, R Package Version 0.9.
- Josse, J., and Denis, J. (2012), “Inferring Biadditive Models Within the Bayesian Paradigm,” Tech. Rep., INRA, MIA. Google Scholar
- Martyn, P. (2003), “Jags: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling,” in Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), March 20–22, Vienna, Austria. Google Scholar
- Perez-Elizalde, S., Jarquin, D., and Crossa, J. (2011), “A General Bayesian Estimation Method of Linear-Bilinear Models Applied to Plant Breeding Trials with Genotype X Environment Interaction,” Journal of Agricultural, Biological, and Environmental Statistics, 17 (1), 15–37. CrossRefMathSciNetGoogle Scholar
- R Core Team (2013), “R: A Language and Environment for Statistical Computing,” R Foundation for Statistical Computing, Vienna, Austria, available at http://www.R-project.org/.