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

Piepho, Hans PeterWilliams, Emlyn2025-05-302025-05-300323-3847http://www.scopus.com/inward/record.url?scp=85198017990&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733755488Finlay–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.This study was supported by the German Research Foundation (grant PI 377/20\u20102). Funding: Hans\u2010Peter Piepho acknowledges funding by the German Research Foundation (grant PI 377/20\u20102).enPublisher Copyright: © 2024 The Author(s). Biometrical Journal published by Wiley-VCH GmbH.crop improvementenvironmental covariatesfactorial regressionFinlay–Wilkinson regressiongenotype–environment interactionlatent environmental effectmulti-environment trialspredictionrandom effectstarget population of environmentsFactor-Analytic Variance–Covariance Structures for Prediction Into a Target Population of Environments202410.1002/bimj.20240000885198017990