Research Article Predictive ability of AMMI and factorial analytical models in the study of unbalanced multi-environment data

Abstract

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-byenvironment 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-byenvironment 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 ©FUNPEC-RP www.funpecrp.com.br Genetics and Molecular Research 18 (3): gmr18176 R.F. Romão et al. 2value) 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.

Shrinkage in the Bayesian analysis of the GGE model: A case study with simulation

“…Crossa et al [ 30 ] and Perez-Elizalde et al [ 31 ], in turn, showed how to incorporate inference to the AMMI-2 biplot by drawing credibility regions to describe the effect of GEI. The literature also presents further development of this method [ 20 , 32 – 35 ].…”

Missing‐value imputation using the robust singular‐value decomposition: Proposals and numerical evaluation

“…A reference that can serve as a starting point for this study is the comparison made by Romão et al. (2019) of the factorial analytic model with the EM‐AMMI algorithm.…”

Bayesian GGE model for heteroscedastic multienvironmental trials

“…Conventional implementations of AMMI and GGE have many limitations associated with the standard method of estimating fixed effects. They do not consider heteroscedasticity, although theoretically, there are procedures based on SVD for the same purpose (Rodrigues et al., 2014; Yan, 2014); however, such procedures are adjusted in two stages and may lead to loss of information (Gogel et al., 2018; Romão et al., 2019).…”

“…(2012) empirically demonstrated the flexibility of the Bayesian model to incorporate uncertainty into the AMMI model fitted with two first principal components biplot through bivariate credibility regions built for genotypic and environmental scores, as well as using information from previous experiments incorporated through prior distributions. Other contributions to this method have been recently published (da Silva et al., 2015, 2019; de Oliveira et al., 2015, 2016; Jarquin et al., 2016; Romão et al., 2019).…”