Credible Intervals for Scores in the AMMI with Random Effects for Genotype

Oliveira, Luiz Antonio Andrade de; Silva, Carlos Pereira da; Nuvunga, Joel Jorge; Silva, Alessandra Querino da; Balestre, Márcio

doi:10.2135/cropsci2014.05.0369

Cited by 23 publications

(42 citation statements)

References 42 publications

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“…The yield of husked ears was the variable evaluated, which was expressed as t/ha. These data were the same as those used by Antonio de Oliveira et al (2015).…”

Section: Methodsmentioning

confidence: 99%

“…In addition, traditional biplot analysis is merely a descriptive procedure, i.e., it includes no measure of the uncertainty regarding the genotypic and environmental scores plotted (Yan and Tinker, 2006;Yang et al, 2009). Furthermore, frequentist inference procedures in biplot analysis have been subject to criticism, whether for the assumptions regarding the distribution of the individual interaction scores required in parametric methods or for using problematic resampling procedures of nonparametric methods Yan et al, 2010;Hu and Yang, 2013a;Antonio de Oliveira et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, theoretical and practical questions regarding this approach were analyzed by Liu (2001), who derived a set of conditional posterior distributions, thus reducing the computational cost of the model and further stabilizing the algorithms. These studies were recently resumed and further developed by Crossa et al (2011), Antonio de Oliveira et al (2015, and Josse et al (2014), who incorporated credible regions into the biplots, and also by Perez-Elizalde et al (2011), who demonstrated how historical experimental data may be used in the inference process.…”

Section: Introductionmentioning

confidence: 99%

“…For such purposes, some parameters must be fixed to zero and some constraints in the models must be relaxed, as noted by Liu (2001), Crossa et al (2011), andPerez-Elizalde et al (2011). However, applications of the Bayesian method in the literature have been limited to the AMMI model (Viele and Srinivasan, 2000;Crossa et al, 2011;Perez-Elizalde et al, 2011;Josse et al, 2014;Antonio de Oliveira et al, 2015) and the Factor-Analytic model (de los Campos and Gianola, 2007). Thus, it would be interesting to explore the advantages of Bayesian analysis for GGE biplot models and to assess its implications for the interpretation of biplots.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bayesian GGE biplot models applied to maize multi-environments trials

Oliveira¹,

Silva²,

Nuvunga³

et al. 2016

Genet. Mol. Res.

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ABSTRACT. The additive main effects and multiplicative interaction (AMMI) and the genotype main effects and genotype x environment interaction (GGE) models stand out among the linear-bilinear models used in genotype x environment interaction studies. Despite the advantages of their use to describe genotype x environment (AMMI) or genotype and genotype x environment (GGE) interactions, these methods have known limitations that are inherent to fixed effects models, including difficulty in treating variance heterogeneity and missing data. Traditional biplots include no measure of uncertainty regarding the principal components. The present study aimed to apply the Bayesian approach to GGE biplot models and assess the implications for selecting stable and adapted genotypes. Our results demonstrated that the Bayesian approach applied to GGE models with non-informative priors was consistent with the traditional GGE biplot analysis, although the credible region incorporated into the biplot enabled distinguishing, based on probability, the performance of genotypes, and their relationships with the environments in the biplot. Those regions also enabled the identification of groups of genotypes and environments with similar effects in terms of adaptability and stability. The relative position of genotypes and environments in biplots is highly affected by the experimental accuracy. Thus, incorporation of uncertainty in biplots is a key tool for breeders to make decisions regarding stability selection and adaptability and the definition of mega-environments.

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“…The yield of husked ears was the variable evaluated, which was expressed as t/ha. These data were the same as those used by Antonio de Oliveira et al (2015).…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian GGE biplot models applied to maize multi-environments trials

Oliveira¹,

Silva²,

Nuvunga³

et al. 2016

Genet. Mol. Res.

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show abstract

“…Therefore, Bayesian approach can be very useful in maintenance varieties, seed production, because Bayesian credible information can help to understand the probability distribution over the parameters through rich statistical inferences of means . Bayesian approach in analysis crop variety trials have been discussed by many authors (Gelman et al, 2002): ; ; De los Campos et al (2009);Forkman and Piepho (2013);de Oliveira et al, (2014); Omer et al (2015) and Singh et al (2015). Bayesian credible intervals based on Bayesian theories are conceptually different ways to quantify parametric and predictive uncertainties, because are always numerically identical when consistent prior information is used (Lu et al, 2012).…”

Section: Research Articlementioning

confidence: 99%

Bayesian Credible Intervals for Maize Grain Yields of the Maintenance Varieties Evaluated in Sudan

Omer

Abdalla

Alzain³

et al. 2017

Int J Appl Sci Biotechnol

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Improved of maintenance crop varieties developed at agricultural research corporation, Wad median, Sudan is intended for seed foundation which is recently established. This study was undertaken to establish statistical investigation using Bayesian estimation for credible interval or posterior interval as a Bayesian strategy for a maintenance variety. Data on grain yield (kg/ha) on a maize crop variety were used. Bayesian posterior information can be annoying to investigate but are important in maintenance varieties that foundational claims are used to make general recommendations for practice. Half normal informative priors set were used. The heritability of yield (varieties)) was (h = 0.75). Predicted posterior means of varieties were shown with a Bayesian interval for scientific inference in the maintenance maize grain yield. Bayesian approach is useful for reducing uncertainty on decisions based on economic evaluation of new maize varieties in Sudan, the use of credible intervals for grain yield allow for early decisions.

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Bayesian GGE model for heteroscedastic multienvironmental trials

Oliveira

Silva

et al. 2022

Crop Science

Self Cite

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The dissection of genotype × environment interaction (GEI) is a crucial aspect of the final stages of plant breeding pipelines and recommendation of cultivars. Linearbilinear models used to analyze this interaction, such as the additive main effects and multiplicative interaction (AMMI) and genotype plus GEI (GGE), often assume homogeneity of the residual variances across environments which affects the estimates and therefore, interpretations and conclusions. Our main objective was to propose a GGE model that considers heteroscedasticity across environments using Bayesian inference and to evaluate its implications in the interpretation of real and simulated data. The GGE model assuming common variance was also fitted for comparison purposes. The great flexibility of the Bayesian inference is transferred to the biplots, allowing the construction of credible regions for genotypic and environmental scores. The inference on the stability and adaptability of genotypes might change when heteroscedasticity is ignored. When real data are used, different patterns of correlations between environments also affect the representativeness and discrimination of the target environment. The modeling of heteroscedasticity allowed the clustering of environments into subgroups, with similar effects for GEI. The proposed GGE model was more adequate and realistic to deal with scenarios of heterogeneous variance in multienvironment trials, which can be useful for exploiting the GEI.Abbreviations: AE, average environment; AEA, axis of the average environment; AEC, average environment coordination; AMMI, additive main effects and multiplicative interaction model; BGGE, Bayesian GGE model under homogeneity of residual variances across sites; BGGEH, Bayesian GGE model under heterogeneity of residual variances across sites; FA, Factor-Analytic Model; G, Genotype; GEI, Genotype × environment interaction; GGE, Genotype main effect + genotype × environment interaction; HPD, Highest posterior density; IG, ideal genotype; MCMC, Markov chain Monte Carlo; MET, Multienvironmental trial; MLM, mixed linear model; SS GGE , total sum of squares for G + GEI; SVD, Singular value decomposition.

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Credible Intervals for Scores in the AMMI with Random Effects for Genotype

Cited by 23 publications

References 42 publications

Bayesian GGE biplot models applied to maize multi-environments trials

Bayesian GGE biplot models applied to maize multi-environments trials

Bayesian Credible Intervals for Maize Grain Yields of the Maintenance Varieties Evaluated in Sudan

Bayesian GGE model for heteroscedastic multienvironmental trials

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