Data Non-normality on AMMI Models: Box-Cox Transformations

Abstract

AMMI (Additive Main Effect Multiplicative Interaction) model for interactions in two-way table provide the major mean for studying stability and adaptability through genotype × environment interaction (GEI), which modeled by full interaction model.  Eligibility of AMMI models depends on that assumption of normally independent distributed error with a constant variance.  In the case of non-normal data distribution, the appropriateness of AMMI model is being doubtful. Transform the observation by power family of Box-Cox transformation is an effort to handle the non-normality. AMMI model then can be applied to the transformed data appropriately following by the use of ordinary least square for estimating parameters.  This approach is investigated by applying them to (i) a count data of pest population of Poisson distribution, which came from a study of leave pest in soybean genotype, and to (ii) a study of rice genotype stability of filled grain per panicle (Binomial data).  One must be carefully considered what the meaning of the transformation in the AMMI
models and Biplot AMMI.