Comparison of various spatial models for the analysis of cultivar trials

Abstract

Because spatial variability often exists in field trials, spatial analysis is suggested for their evaluation. This paper investigated the consequences of mixed linear models with various spatial covari‐ance structures on line statistical tests and selections of plant cultivar trials by using the Satterthwaite and Kenward‐Roger methods for approximating degrees of freedom. The investigated covariance structures were experiential, spherical, Gaussian, linear, linear‐log, anisotropic power and anisotropic exponential, as well as first order autoregressive. The data used in this study were grain yields from three separate cultivar trials. The results showed that the spatial models provided a smaller standard error than the classical analysis of variance models, but only the optimally fitting spatial model could control spatial variability more effectively with less loss of error degrees of freedom and hence generally result in a higher power for line tests than the classical analysis of variance of block designs. Furthermore, the spatial models resulted in a different ranking of line selections both in comparison with the analysis of variance and under the different spatial models. The first order autoregressive model often used in the literature was generally not an optimal option for spatial analysis. The Kenward‐Roger method effectively provided a correction of the standard error for line contrasts and hence a reasonable power of spatial model analysis. These confirm the necessity of selecting the covariance structures and using the Kenward‐Roger method for approximating degrees of freedom in the spatial analysis of cultivar field trials using mixed linear models.