The GGE Biplot on Rcim Model for Assessing The Genotypeenvironment Interaction with Simulating Outliers: Robustness in R-Squared Procrustes

Abstract

The genotype by environment interaction (GEI) analysis was usually done by Additive Main Effects and Multiplicative Interaction (AMMI) model with Biplot features, and recently there was a Row Column Interaction Model (RCIM) alternatively. In the Biplot of genotype (G) and genotype by environment (GE) interactions, known as the GGE Biplot, the main effect of environment (E) was deleted, while the main effect of G and the interaction effect of GE is kept and combined. Subsequently, continuing our recent research of the robustness of the GGE Biplot in RCIM models, this paper aims to develop the GGE Biplot by RCIM model to analyze the GEI with outlying observations. We used the RCIM model with Asymptotic Laplace Distribution (ALD) that was applied on the simulated data with scattered and single environment outliers to evaluate the robustness of the GGE Biplot. In addition, the robustness was evaluated using the R-squared statistic of the Procrustes analysis. It is shown that the GGE Biplot of RCIM with the ALD family function provides better robustness than the Gaussian. A noticeable superiority of the GGE Biplot with RCIM ALD appeared as the percentage of single environment outliers reach the number of rows of the data matrix.