Pendugaan parameter model AMMI dengan komputasi menggunakan pendekatan bayes

Abstract

Statistics on the application of plant breeding research has long used primarily in quantitative genetics. Modeling requirements for selection is needed to support efforts to obtain improved varieties. In modeling, there are two main paradigms used to estimate model parameters as the frequentist and Bayesian. Standard AMMI is a classical method has been used extensively for modeling and analysis genotype and environmental interactions. Homogeneity variance error is one of assumptions that must be satisfied in this method. Heterogeneity of variance error can lead to errors in conclusions regarding treatment effect. This study focuses attention on the computational efficiency of Bayesian in AMMI model parameters assumed in the data with heterogeneous variance error and evaluate the suitability of the configuration of genotype and environment interactions in Biplot AMMI. In the data with heterogeneous variance error, there are various differences between the treatment which is likely to cause a reduction in the efficiency of variance estimators in suspected treatment effect. Data transformation is usually used to overcome the problem of heterogeneity variance error. However, it is often quite difficult to obtain a suitable transformation and interpretations of treatment effect obtained from the transformation of data. Therefore we need another approach that can overcome the problem of heterogeneity variance error. The continued development of computerization, the Bayesian approach is a method that has been used to estimate parameters of linier-bilinier model. Bayesian approach is utilizing prior information about parameters to be expected and information from the sample that will be combined to get a posterior distribution. In this paper was evaluated the use of Bayesian approach to estimate model parameters and configuration AMMI biplot. There are two types of data used in this study, the simulated data and real data results of multilocation trials. Each type of data has homogeneous and heterogeneous variance. Prior distribution was a conjugate prior and values for posterior distribution were estimated by Gibbs sampling algorithm. The analysis showed that the Bayesian approach was quite efficient to estimate genotype and environment interaction effect. In fact, AMMI-BS using the BIC to determine the number of principal components of the interaction has a higher efficiency than AMMI-B. Bayesian approach to efficient enough in assuming an interaction effect can be seen from the variance that are smaller than standard AMMI. If the estimation of bilinier components of each method is used to construct the AMMI biplot to know the configuration of interaction structure, there are relatively similar in configuration among the three methods.