Heterogeneity of Variances in the Bayesian AMMI Model for Multienvironment Trial Studies

Silva, Carlos Pereira da; Oliveira, Luiz Antonio Andrade de; Nuvunga, Joel Jorge; Pamplona, Andrezza Kéllen Alves; Balestre, Márcio

doi:10.2135/cropsci2018.10.0641

Cited by 15 publications

(25 citation statements)

References 38 publications

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“…The low coincidence among the hybrids evaluated in the different environments makes it difficult to estimate genetic and phenotypic parameters, especially genetic variance and, above all, the SH × environment interaction. This difficulty has been reported in the literature by diverse authors in recent years (Smith et al, 2001;Möhring and Piepho, 2009;Smith et al, 2015;Nuvunga et al, 2015;Silva et al, 2019).…”

Section: Discussionmentioning

confidence: 72%

“…To deal with unbalanced data, some proposals have been implemented more recently for analysis of experiments with plants using, for example, analysis in two steps, in which weighting is considered in the second step in accordance with the number of replications, with the experimental design, and with residual variance (Smith et al, 2001;Möhring and Piepho, 2009;Welham et al, 2010;Piepho et al, 2012). Other alternatives are multiplicative models (Smith et al, 2015;Nuvunga et al, 2015), sequential analysis, which considers all the hybrids evaluated in the previous generations (Piepho and Möhring, 2006) and models that consider the use of heterogeneous residual variance (Edwards and Jannink, 2006;So and Edwards, 2011;Orellana et al, 2014;Hu et al, 2014;Andrade et al, 2015;Silva et al, 2019).…”

Section: Discussionmentioning

confidence: 99%

“…The fact of considering homogeneous residual variance or not leads to a difference above all when the h 2 are of lower magnitude and, therefore, it is difficult to decide in the latter case from the results obtained in this study that the use of heterogeneous residual variance is more appropriate, since there is no way to prove which ranking is more trustworthy. In the literature, however, there are numerous reports that the use of heterogeneous variance is more advisable (Edwards and Jannink, 2006;So and Edwards, 2011;Orellana et al, 2014;Hu et al, 2014;Andrade et al, 2015;Silva et al, 2019).…”

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Mega-environment analysis of maize breeding data from Brazil

Pereira

Ramalho

Resende

et al. 2022

Sci. agric. (Piracicaba, Braz.)

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The development and recommendation of single cross maize hybrids (SH) to be used in extensive land areas (mega-environments), and in different crop seasons requires many experiments under numerous environmental conditions. The question we asked is if the data from these multi-environment experiments are sufficient to identify the best hybrid combinations. The aim of this study was to critically analyze the phenotype data of experiments of yield, established by a large seed producing company, under a high level of imbalance. Data from evaluation of 2770 SH were used from experiments conducted over four years, involving the first and second crop seasons, in 50 locations of different years and regions of Brazil. Different types of analysis were carried out and genetic and non-genetic components were estimated, with emphasis on the different interactions of the SH with the environments. Results showed that the coincidence of common hybrids in these experiments is normally small. The estimates of the correlations between of the hybrids coinciding in the environments two by two is of low magnitude. The hybrid × crop season interaction was always expressive; however, the interactions of hybrids and other environmental variables were also important. Under these conditions, alternatives were discussed for making with the information obtained from the experiments, can be more efficient on the process to obtain new hybrids by companies.

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Section: Discussionmentioning

confidence: 72%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Mega-environment analysis of maize breeding data from Brazil

Pereira

Ramalho

Resende

et al. 2022

Sci. agric. (Piracicaba, Braz.)

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“…Further details on the a posteriori complete conditionals for the singular vectors as well as the sampling process can be found in Silva et al (2018) and supplementary material.…”

Section: Bayesian Ammi Model With Heterogeneous Variances (Bammi-h)mentioning

confidence: 99%

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

Romão¹,

Nuvunga²,

Silva³

et al. 2019

Genet. Mol. Res.

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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.

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“…The standard analyses of linear-bilinear models is not flexible enough to deal with unbalanced, non-orthogonal and/or heteroscedastic data. Moreover, no uncertainty measures are presented to the resulting biplot in most applications in the literature [ 18 – 20 ]. Some authors proposed imputation methods and techniques employing preliminary correction of heteroscedasticity and re-scaling, while others proposed more suitable algorithms for weighting scores [ 21 , 22 ].…”

Section: Introductionmentioning

confidence: 99%

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

Oliveira

Silva

et al. 2021

PLoS ONE

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The genotype main effects plus the genotype × environment interaction effects model has been widely used to analyze multi-environmental trials data, especially using a graphical biplot considering the first two principal components of the singular value decomposition of the interaction matrix. Many authors have noted the advantages of applying Bayesian inference in these classes of models to replace the frequentist approach. This results in parsimonious models, and eliminates parameters that would be present in a traditional analysis of bilinear components (frequentist form). This work aims to extend shrinkage methods to estimators of those parameters that composes the multiplicative part of the model, using the maximum entropy principle for prior justification. A Bayesian version (non-shrinkage prior, using conjugacy and large variance) was also used for comparison. The simulated data set had 20 genotypes evaluated across seven environments, in a complete randomized block design with three replications. Cross-validation procedures were conducted to assess the predictive ability of the model and information criteria were used for model selection. A better predictive capacity was found for the model with a shrinkage effect, especially for unorthogonal scenarios in which more genotypes were removed at random. In these cases, however, the best fitted models, as measured by information criteria, were the conjugate flat prior. In addition, the flexibility of the Bayesian method was found, in general, to attribute inference to the parameters of the models which related to the biplot representation. Maximum entropy prior was the more parsimonious, and estimates singular values with a greater contribution to the sum of squares of the genotype + genotype × environmental interaction. Hence, this method enabled the best discrimination of parameters responsible for the existing patterns and the best discarding of the noise than the model assuming non-informative priors for multiplicative parameters.

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Heterogeneity of Variances in the Bayesian AMMI Model for Multienvironment Trial Studies

Cited by 15 publications

References 38 publications

Mega-environment analysis of maize breeding data from Brazil

Mega-environment analysis of maize breeding data from Brazil

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

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

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