A resampling test for principal component analysis of genotype-by-environment interaction

In crop science, genotype-by-environment interaction is often explored using the “genotype main effects and genotype-by-environment interaction effects” (GGE) model. Using this model, a singular value decomposition is performed on the matrix of residuals from a fit of a linear model with main effects of environments. Provided that errors are independent, normally distributed and homoscedastic, the significance of the multiplicative terms of the GGE model can be tested using resampling methods. The GGE method is closely related to principal component analysis (PCA). The present paper describes i) the GGE model, ii) the simple parametric bootstrap method for testing multiplicative genotype-by-environment interaction terms, and iii) how this resampling method can also be used for testing principal components in PCA.