Factor-Analytic Variance–Covariance Structures for Prediction Into a Target Population of Environments

Finlay–Wilkinson regression is a popular method for modeling genotype–environment interaction in plant breeding and crop variety testing. When environment is a random factor, this model may be cast as a factor-analytic variance–covariance structure, implying a regression on random latent environmental variables. This paper reviews such models with a focus on their use in the analysis of multi-environment trials for the purpose of making predictions in a target population of environments. We investigate the implication of random versus fixed effects assumptions, starting from basic analysis-of-variance models, then moving on to factor-analytic models and considering the transition to models involving observable environmental covariates, which promise to provide more accurate and targeted predictions than models with latent environmental variables.