A General Bayesian Estimation Method of Linear-Bilinear Models Applied to Plant Breeding Trials With Genotype x Environment Interaction
A General Bayesian Estimation Method of Linear-Bilinear Models Applied to Plant Breeding Trials With Genotype x Environment Interaction
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DOI：
10.1007/s13253-011-0063-9
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发表时间：
2012-04-01
影响因子：
1.4
通讯作者：
Crossa, Jose
中科院分区：
文献类型：
--
作者：
Perez-Elizalde, Sergio;Jarquin, Diego;Crossa, Jose
双向交互表的统计分析出现在许多不同的研究领域。本研究提出了冯米塞斯-费舍尔分布作为一个先验的一组正交矩阵的线性双线性模型的研究和解释相互作用的双向表。模拟和经验的植物育种数据用于说明，经验数据包括一个多环境试验，在连续两年建立。对于模拟的数据，模糊的，但适当的先验分布，并为真实的植物育种数据，从第一年的观察被用来引出第二年的试验数据的模型参数的先验。后验分数的双变量最高后验密度（HPD）区域显示在双标图中，并使用贝叶斯因子检验双线性项的显著性。植物育种试验的结果表明，这种一般的贝叶斯方法育种试验和检测组的基因型和环境，导致显着的基因型x环境的相互作用的有用性。目前的贝叶斯推断方法是通用的，并可以扩展到其他线性双线性模型，通过固定某些参数等于零，放松一些模型的约束。
Statistical analyses of two-way tables with interaction arise in many different fields of research. This study proposes the von Mises-Fisher distribution as a prior on the set of orthogonal matrices in a linear-bilinear model for studying and interpreting interaction in a two-way table. Simulated and empirical plant breeding data were used for illustration; the empirical data consist of a multi-environment trial established in two consecutive years. For the simulated data, vague but proper prior distributions were used, and for the real plant breeding data, observations from the first year were used to elicit a prior for parameters of the model for data of the second year trial. Bivariate Highest Posterior Density (HPD) regions for the posterior scores are shown in the biplots, and the significance of the bilinear terms was tested using the Bayes factor. Results of the plant breeding trials show the usefulness of this general Bayesian approach for breeding trials and for detecting groups of genotypes and environments that cause significant genotype x environment interaction. The present Bayes inference methodology is general and may be extended to other linear-bilinear models by fixing certain parameters equal to zero and relaxing some model constraints.