Applications of spatial models to ordinal data

Models have been developed to account for heterogeneous spatial variation in field trials. These spatial models have been shown to successfully increase the quality of phenotypic data resulting in improved effectiveness of selection by plant breeders. The models were developed for continuous data types such as grain yield and plant height, but data for most traits, such as in iron deficiency chlorosis (IDC), are recorded on ordinal scales. Is it reasonable to make spatial adjustments to ordinal data by simply applying methods developed for continuous data? The objective of the research described herein is to evaluate methods for spatial adjustment on ordinal data, using soybean IDC as an example. Spatial adjustment models are classified into three different groups: group I, moving average grid adjustment; group II, geospatial autoregressive regression (SAR) models; and group III, tensor product penalized P-splines. Comparisons of eight models sampled from these three classes demonstrate that spatial adjustments depend on severity of field heterogeneity, the irregularity of the spatial patterns, and the model used. SAR models generally produce better performance metrics than other classes of models. However, none of the eight evaluated models fully removed spatial patterns indicating that there is a need to either adjust existing models or develop novel models for spatial adjustments of ordinal data collected in fields exhibiting discontinuous transitions between heterogeneous patches.