Handling Outlier in Two-Ways Table Data: The Robustness of Row-Column Interaction Model

As part of our recent statistical research on modelling of the two-ways table data, here we will to investigate of the robustness of Row Column Interaction Model (RCIM). Row Column Interaction Model is a Reduced-Rank Vector Generalized Linear Models (RR-VGLM) class of modelling with the first linear predictor is modelled by the sum of the column effect, row effect, and interaction effect. The interaction effect was shown as a reduced-rank regression. We focused on outlying observations in the two ways data table. Outliers known as sample points that have unique characteristics, they differ from the majority of the whole sample. But there are some outliers that are difficult to identify due to the location and size of the data. Our previous proposed of handling outlier in Additive Main Effect and Multiplicative (AMMI) modelling by applying Robust Alternating Regression in Factor Analytics model. The two models will be compared in analysing two-ways table data that containing some outliers. In this research, two-ways table data are generated randomly follows normal distribution on Additive Main Effect and Multiplicative Interaction model by first two principal components (or AMMI2 for short), with two different types of outlier's placement. The RCIM model seem provide a better result in fitting the data than Robust factor model, the RCIM model have smaller error, even for Normal distribution or Asymmetric Laplace Distribution (ALD).