Dataset Information

A Bayesian Shrinkage Approach for AMMI Models.

ABSTRACT: Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (? = 0.05) in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct posterior distribution retaining more GEI pattern in the first components and discarding noise without Gaussian assumption as requested in F-based tests or deal with parametric problems as observed in traditional AMMI shrinkage method.

SUBMITTER: da Silva CP

PROVIDER: S-EPMC4497624 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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A Bayesian Shrinkage Approach for AMMI Models.

da Silva Carlos Pereira CP de Oliveira Luciano Antonio LA Nuvunga Joel Jorge JJ Pamplona Andrezza Kéllen Alves AK Balestre Marcio M

PloS one 20150709 7

Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the ...[more]

PMID: 26158452

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Project description:BackgroundPrediction and classification algorithms are commonly used in clinical research for identifying patients susceptible to clinical conditions such as diabetes, colon cancer, and Alzheimer's disease. Developing accurate prediction and classification methods benefits personalized medicine. Building an excellent predictive model involves selecting the features that are most significantly associated with the outcome. These features can include several biological and demographic characteristics, such as genomic biomarkers and health history. Such variable selection becomes challenging when the number of potential predictors is large. Bayesian shrinkage models have emerged as popular and flexible methods of variable selection in regression settings. This work discusses variable selection with three shrinkage priors and illustrates its application to clinical data such as Pima Indians Diabetes, Colon cancer, ADNI, and OASIS Alzheimer's real-world data.MethodsA unified Bayesian hierarchical framework that implements and compares shrinkage priors in binary and multinomial logistic regression models is presented. The key feature is the representation of the likelihood by a Polya-Gamma data augmentation, which admits a natural integration with a family of shrinkage priors, specifically focusing on Horseshoe, Dirichlet Laplace, and Double Pareto priors. Extensive simulation studies are conducted to assess the performances under different data dimensions and parameter settings. Measures of accuracy, AUC, brier score, L1 error, cross-entropy, and ROC surface plots are used as evaluation criteria comparing the priors with frequentist methods as Lasso, Elastic-Net, and Ridge regression.ResultsAll three priors can be used for robust prediction on significant metrics, irrespective of their categorical response model choices. Simulation studies could achieve the mean prediction accuracy of 91.6% (95% CI: 88.5, 94.7) and 76.5% (95% CI: 69.3, 83.8) for logistic regression and multinomial logistic models, respectively. The model can identify significant variables for disease risk prediction and is computationally efficient.ConclusionsThe models are robust enough to conduct both variable selection and prediction because of their high shrinkage properties and applicability to a broad range of classification problems.

Dataset Information

A Bayesian Shrinkage Approach for AMMI Models.

Publications

A Bayesian Shrinkage Approach for AMMI Models.

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