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This article in CS

  1. Vol. 51 No. 4, p. 1458-1469
    Received: June 12, 2010

    * Corresponding author(s): j.crossa@cgiar.org


Bayesian Estimation of the Additive Main Effects and Multiplicative Interaction Model

  1. José Crossa *a,
  2. Sergio Perez-Elizaldeb,
  3. Diego Jarquinb,
  4. José Miguel Cotesc,
  5. Kert Vieled,
  6. Genzhou Liue and
  7. Paul L. Corneliusf
  1. a Biometrics and Statistics Unit, Crop Research Informatics Laboratory (CRIL), International Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, 06600, Mexico D.F., Mexico
    b Biometrics and Statistics Unit, CRIL, CIMMYT, and Colegio de Postgraduados, Km. 36.5 Carretera México-Texcoco, Montecillos, Estado de México, 56230, México
    c Departamento de Ciencias Agronómicas, Facultad de Ciencias Agropecuarias, Universidad Nacional de Colombia
    d Department of Statistics, University of Kentucky, Lexington, KY, 40546-03121
    e Auxilium Pharmaceuticals, Inc., PA
    f Department of Plant and Soil Sciences and Department of Statistics, University of Kentucky, Lexington, KY, 40546-03121


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.

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