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Bayesian Estimation of the Additive Main Effects and Multiplicative Interaction Model
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Abstract
ABSTRACT
Much research has been conducted using least squares estimates of the linear–bilinear model additive main effects and multiplicative interaction (AMMI). The main difficulty with the standard linear–bilinear models is that statistical inference on the bilinear effects of genotype × environment interaction cannot be incorporated easily into the biplot of the first two components. This research proposes a Bayesian approach for the inference on the parameters of the AMMI model using a Gibbs sampler that saves computing time and makes the algorithm stable. Data from one maize (Zea mays L.) multi‐environment trial (MET) was used for illustration. Vague but proper prior distributions were introduced. Results show that the various Markov chain Monte Carlo convergence criteria were met for all parameters. Bivariate highest posterior density (HPD) regions for the Bayesian–AMMI interactions are shown in the biplot of the first two bilinear components; these regions offer a statistical inference on the bilinear parameters and allow visualizing homogeneous groups of environments and genotypes.
Citing Literature
Number of times cited according to CrossRef: 6
- Carlos Pereira Silva, Luciano Antonio Oliveira, Joel Jorge Nuvunga, Andrezza Kellen Alves Pamplona, Marcio Balestre, Heterogeneity of Variances in the Bayesian AMMI Model for Multienvironment Trial Studies, Crop Science, 10.2135/cropsci2018.10.0641, 59, 6, (2455-2472), (2019).
- Luiz Antonio Yanes Bernardo Júnior, Carlos Pereira Silva, Luciano Antonio Oliveira, Joel Jorge Nuvunga, Luiz Paulo Miranda Pires, Renzo Garcia Von Pinho, Marcio Balestre, AMMI Bayesian Models to Study Stability and Adaptability in Maize, Agronomy Journal, 10.2134/agronj2017.11.0668, 110, 5, (1765-1776), (2018).
- Luciano Antonio Oliveira, Carlos Pereira Silva, Paulo Eduardo Teodoro, Francisco Eduardo Torres, Agenor Martinho Corrêa, Leonardo Lopes Bhering, Performance of Cowpea Genotypes in the Brazilian Midwest Using the Bayesian Additive Main Effects and Multiplicative Interaction Model, Agronomy Journal, 10.2134/agronj2017.03.0183, 110, 1, (147-154), (2018).
- Diego Jarquín, Sergio Pérez‐Elizalde, Juan Burgueño, José Crossa, A Hierarchical Bayesian Estimation Model for Multienvironment Plant Breeding Trials in Successive Years, Crop Science, 10.2135/cropsci2015.08.0475, 56, 5, (2260-2276), (2016).
- Fred A. Eeuwijk, Daniela V. Bustos‐Korts, Marcos Malosetti, What Should Students in Plant Breeding Know About the Statistical Aspects of Genotype × Environment Interactions?, Crop Science, 10.2135/cropsci2015.06.0375, 56, 5, (2119-2140), (2016).
- Luciano Antonio de Oliveira, Carlos Pereira da Silva, Joel Jorge Nuvunga, Alessandra Querino Da Silva, Marcio Balestre, Credible Intervals for Scores in the AMMI with Random Effects for Genotype, Crop Science, 10.2135/cropsci2014.05.0369, 55, 2, (465-476), (2015).
