Variance–covariance structure and its influence on variety assessment in regional crop trials

Abstract

The primary method used to analyze regional crop variety trials is based on the analysis of variance (ANOVA), which requires a homogenous variance–covariance of data. While other models are available, the problem of how the models should be assessed and which model is more suitable for a given trial's data has not been solved. This restricts the applicability of the models. Therefore, a mixed linear model with flexible variance–covariance structures is proposed. Relationships are introduced for various variance–covariance structures of mixed models, and other models for analyzing crop regional trials. Using data from regional corn trials in northeastern and northern China, an assessment was made of the information criterion and likelihood-ratio-test, along with the goodness of fit of variance–covariance structures. This regional trial data facilitated comparison between an ANOVA model and a mixed linear model with an optimal variance–covariance structure. The results showed that the variance–covariance of varietal effects over environmental influences was not homogeneous, as is required in the ANOVA model. Instead, it was found to be heterogeneous in all trials considered. On average, the ratio of significant varietal differences for the same variety was only 86% when comparing the ANOVA model and the optimal mixed linear model. Also, there were obvious differences in the yield ranking of varieties between the two models. The mean standard error of a difference of varietal effects in the optimally-fitted mixed linear model was smaller than that in the ANOVA model.