Model selection and its consequences for different split‐plot designs with spatial covariance and trend

Abstract

With 1 figure and 10 tables AbstractSplit‐plot designs play an important role in agricultural field trials, particularly in plant breeding. Analysis of split‐plot experiments may be performed by classical randomization‐based anova‐type models. In addition, spatial covariance can be modelled to improve precision. This study investigates the properties of alternative variance–covariance structures (random blocks, spatial covariance) using Monte‐Carlo simulation for design scenarios commonly found in plant breeding and variety testing. We investigate the efficiency of model selection by information criteria (AICC, BIC). Our results indicate that efficient model selection can be expected when there are marked differences among models with respect to the empirical error rates (type I error and power) as well as the precision of effect estimates (MSE). A comparison of approximations to the denominator degrees of freedom shows that for spatial models use of the Kenward–Roger method gives reasonable control of the nominal type I error rate.