Modeling Spatially Correlated and Heteroscedastic Errors in Ethiopian Maize Trials

Abstract

The precision of estimates of genotype means and genotype comparisons in agricultural field trials can be increased by using an appropriate experimental design and spatial modeling techniques. Both randomization‐based and spatial analysis usually make the assumption of homogeneous variance, but in reality, this assumption may not generally hold true. If this is ignored, erroneous estimates of the precision of fixed effect estimates can result; therefore, some remedy should be sought in case heterogeneity of variance is detected. The objective of this study is to investigate methods of analysis accounting for possible variance heterogeneity along with the spatial trend, if any. The methods are explored using three maize trials from Ethiopia. We consider the Box–Cox transformation to stabilize variance and variance models, allowing for heterogeneity. For variance modeling we use the power‐of‐the‐mean (POM) and exponential models. The Box–Cox transformation was found to be successful in stabilizing the variance, but estimating genotype means and their SE on the original scale is challenging. The POM and exponential variance models, which avoid this problem, were found to effectively deal simultaneously with both spatial correlation and heterogeneity of variance.