On Generalization of Additive Main Effect and Multiplicative Interaction (AMMI) Models: An Approach of Row Column Interaction Models for Counting Data

Abstract

Additive Main Effect and Multiplicative Interaction (AMMI) model was commonly used to analyze Genotype Environment × Interaction with normal response variables, now it had been generalized for categorical or other non-normal response variables, called GAMMI model. This devel opment was conducted by introducing multiplicative terms to the Gen eralized Linear Model (GLM). This research round up our previous work on developing an approach of Row Column Interaction Models (RCIMs) comprise to GAMMI model and focus to get more generalized for count ing data with overdispersed and zeros problems. A few interesting things here are (i) an issue of distribution on GLM sense and (ii) an issue of model’s complexity that is the number of multiplicative terms to fit the interaction effect more properly. On the distribution issue of counting data, we will focus on Poisson, Negative Binomial (NB), and zero inflated problems with Zero Inflated Poisson (ZIP) and Zero Inflated NB (ZINB) Hadi, A. F., Sa’diyah, H. and Iswanto, R. distribution. A simulation conducted by adding outlier(s) on a Poisson counting data for overdispersed condition, and adding zeros observation on the data for illustrating the zero problems. We propose the NB model for overdispersed data and model of ZIP or ZINB for data with both, overdispersed and zero problem. In the case of both illnesses conditions happened simultaneously, the mean square error of NB and ZINB will in crease slightly. But the ZINB was resulting the simplest model of RCIM with less number of interaction terms.