Prediction Accuracy and Consistency in Cultivar Ranking for Factor‐Analytic Linear Mixed Models for Winter Wheat Multienvironmental Trials

Abstract

In the majority of research on models for multienvironment trials, evaluation of the prediction accuracy of models with different variance–covariance structures is focused on predicting the means for cultivar × location (C × L) combinations. In cultivar recommendation, however, it is often more important to evaluate prediction accuracy in modeling cultivar × region (C × R) combinations. The aim of this paper was to evaluate the prediction accuracy of two single‐stage linear mixed models (LMMs) with different variance–covariance structures, emphasizing factor‐analytic (FA) structures. One of the models was used to predict means for C × L combinations and the other one for C × R combinations. Additionally, we assessed implications of model choice for consistency in cultivar ranking. The data used for the analysis performed in this study were obtained from 42 locations and 47 winter wheat (Triticum aestivum L.) cultivars during three growing seasons within the Polish Post‐Registration Variety Testing System. The data were assigned to six agroecological regions. For evaluating the prediction accuracy of LMMs, we used cross validation based on a modified equation for the mean squared error of prediction. Yield rankings modeled by different variance–covariance structures were compared by Spearman's rank correlation. For each model with a different variance–covariance structure, we calculated the correlation coefficients between estimated and observed data. The model with the highest predictability for means of the C × L classification was the FA(2) variance–covariance structure. In the case of C × R means, the compound symmetry structure fared favorably, and using more complex variance–covariance structures (including heterogeneous covariances) did not increase prediction accuracy.