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Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models.

Johannes Forkman1, Hans-Peter Piepho2

  • 1Department of Crop Production Ecology, Swedish University of Agricultural Sciences, PO Box 7043, 750 07 Uppsala, Sweden.

Biometrics
|March 5, 2014
PubMed
Summary

Parametric bootstrap methods effectively test multiplicative terms in genotype-by-environment interaction (GGE) and additive main effects and multiplicative interaction (AMMI) models. The simple parametric bootstrap is recommended for selecting model terms in multi-environment trials.

Keywords:
AMMIGGEGenotype–environment interactionMulti‐environment trialsPrincipal component analysisSingular value decomposition

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Area of Science:

  • Agronomy
  • Biometrics
  • Statistical Genetics

Background:

  • Genotype-by-environment (GGE) and additive main effects and multiplicative interaction (AMMI) models are crucial for analyzing multi-environment trial data.
  • These models partition genotype-by-environment interaction into multiplicative terms using singular value decomposition.
  • Determining the optimal number of multiplicative terms to retain is essential for accurate analysis.

Purpose of the Study:

  • To propose and evaluate parametric bootstrap methods for testing the significance of multiplicative terms in GGE and AMMI models.
  • To compare the performance of bootstrap methods against approximate F-tests and cross-validation.

Main Methods:

  • Developed two parametric bootstrap methods: a full and a simple version.
  • Assessed model performance using Type I error rate and statistical power in a simulation study.
  • Compared bootstrap methods with traditional F-tests and cross-validation techniques.

Main Results:

  • Both bootstrap methods demonstrated good performance in controlling Type I error rates and achieving high statistical power.
  • The simple parametric bootstrap method showed particular ease of use due to its reliance on standard normal distributions.
  • Bootstrap methods proved effective in selecting the appropriate number of multiplicative terms for GGE and AMMI models.

Conclusions:

  • Parametric bootstrap methods provide a robust approach for significance testing of multiplicative terms in GGE and AMMI models.
  • The simple parametric bootstrap method is recommended for practical application in multi-environment trial analysis.
  • The proposed techniques are also applicable to principal component analysis for component testing.