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

Area of Science:

• Agricultural Science
• Statistical Genetics
• Bioinformatics

Background:

• Multi-environmental trials (MET) data analysis commonly uses genotype main effects plus genotype × environment interaction (GGE) models.
• Graphical biplots, derived from singular value decomposition of the interaction matrix, are popular for MET data visualization.
• Bayesian inference offers advantages over frequentist approaches, leading to more parsimonious models.

Purpose of the Study:

• To extend shrinkage methods to the multiplicative parameters within GGE models using the maximum entropy principle.
• To compare a Bayesian shrinkage approach with a non-shrinkage Bayesian prior for parameter estimation.
• To evaluate model performance in terms of predictive ability and model selection.

Main Methods:

• Simulated data from 20 genotypes across seven environments in a randomized block design with three replications.
• Application of shrinkage estimators for multiplicative parameters, justified by the maximum entropy principle.
• Cross-validation for predictive ability assessment and information criteria for model selection.

Main Results:

• Shrinkage methods demonstrated superior predictive capacity, particularly in unorthogonal scenarios with random genotype removal.
• While conjugate flat priors yielded best-fitted models by information criteria in some cases, maximum entropy priors proved more parsimonious.
• The Bayesian approach effectively attributed inference to biplot-related parameters, with maximum entropy priors enhancing discrimination of interaction patterns and noise reduction.

Conclusions:

• Bayesian shrinkage methods, especially with maximum entropy priors, offer a powerful and parsimonious approach for analyzing genotype-environment interactions in MET data.
• These methods improve predictive ability and facilitate better discrimination between true interaction patterns and noise compared to non-informative priors.
• The flexibility of Bayesian inference aids in parameter interpretation within biplot representations for agricultural research.