Predictive ability of AMMI and factorial analytical models in the study of unbalanced multi-environment data
Efficient analysis of datasets from multi-environment trials (MET) is of paramount importance in plant breeding programs. Several methods have been proposed for this purpose, each of them having advantages and disadvantages, depending on the objectives of the study. We examined the robustness in the predictive power of models that have been widely used in the study of genotype-by-environment interaction such as AMMI (additive main-effects and multiplicative interaction) models via EM algorithm, Bayesian AMMI models with homogeneity (BAMMI), heterogeneity of variances (BAMMI-H) and the Analytical Factorial model (FA). To check the efficiency of these methods, genotype and genotype- by- environment interaction effects were simulated and further unbalances were included at levels of 10, 33 and 50% loss of genotypes in the environments. To evaluate the predictive power of the proposed models, the PRESS (prediction error sum square) statistics and the Cor (correlation between predicted and observed value) were used. The genotype-environment interaction models had low sensitivity to missing data since all models showed correlations above 0.5 in all scenarios - even with high unbalance levels (50%). In general, there were differences in predictive accuracy among the models in different scenarios, with a slight advantage for the Bayesian models in the correlation among observed and predicted data ranging from 0.79 to 0.855 compared to 0.591 to 0.853 obtained from the competing models. Similar results were observed for the PRESS (4.988 to 8.027) in Bayesian models compared to competing models (5.411 to 23,361). Overall, there was slight advantage of the Bayesian models in unbalanced scenarios.