Model ammi terampat untuk data berdistribusi bukan normal

Abstract

ALFIAN FUTUHUL HADI. Generalized AMMI for Non-Normal Data. Under supervision of AHMAD ANSORI MATTJIK and I MADE SUMERTAJAYA. 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 study of genotypes’ resistance, disease and pest (insect) incidence on a plant for example, 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. There is another way to handle this non-normality, i.e. by introducing multiplicative terms for interaction in wider class of modeling, Generalized Linear Models. An algorithm of iterative alternating generalized regression of row and column estimates its parameters. This model is known as GAMMI (Generalized Additive Main Effect Multiplicative Interaction) or GBMs (Generalized Bilinear Models). The multiplicative terms of GAMMI models can be visualized through Biplot, as in AMMI. A comparison of the two approaches above is investigated by applying them to a count data of pest population of Poisson distribution, which came from a study of leave pest in soybean genotype, and to study of rice genotype stability of filled grain per panicle (Binomial data). For data averages of filled grain per panicle, AMMI model for transformed data gives interaction matrix estimator slightly difference from of the one given by GAMMI logit-link model. R-square of Procrustes Rotation is less than 20 percent. On the other hand, for transformed data average of pest population, the two approaches do not give significant differences. Data exploration for the last case (the transformed data average of pest population) shows that its distribution character is very similar to Normal distribution. Therefore, it can be concluded that: (1) when the data distribution is close to Normal distribution, results of transformed AMMI and GAMMI are not significantly different; (2) when the data distribution is non Normal, results of the two approaches are quite different. Additional information on log-bilinear, which cannot be obtained from the transformed AMMI model, is odd ratio. This makes the GAMMI model superior compared to effort of transforming normality on Poisson distributed data.