On the development of the GE and the GGE interaction Biplot in the RCIM model and the evaluation of its’ robustness to the outlying observations

Abstract

Our recent statistical research on modeling of the two-ways table data was focused especially on the robustness of Row Column Interaction Model (RCIM). It has been showed that the RCIM model provide better result in fitting the data with outliers better than others even for Normal distribution. In this paper we focus on the influenced of the outlying observations to the visualization of the interaction effects in the RCIM modeling. We proposed the Genotype by Environment (GE) and the Genotype and Genotype by Environment (GGE) graphics display by a Biplot on the RCIM model. We also evaluate the influence of the outlying observations to the two kinds of Biplot of GEI by adding the outlying observations to the data. According to the Mean Square Error (MSE) and the Procrustes analysis, the GGE Biplot of RCIM has better result than the GE. The GE Biplot fails to accommodate inflation variance by the presence of a single environmental outliers with large percentage. In addition, the GE Biplot has difficulties to hold total percentage of the variance explained