Spatial Regression Models for Field Trials: A Comparative Study and New Ideas

Naturally occurring variability within a study region harbors valuable information on relationships between biological variables. Yet, spatial patterns within these study areas, e.g., in field trials, violate the assumption of independence of observations, setting particular challenges in terms of hypothesis testing, parameter estimation, feature selection, and model evaluation. We evaluate a number of spatial regression methods in a simulation study, including more realistic spatial effects than employed so far. Based on our results, we recommend generalized least squares (GLS) estimation for experimental as well as for observational setups and demonstrate how it can be incorporated into popular regression models for high-dimensional data such as regularized least squares. This new method is available in the BioConductor R-package pengls. Inclusion of a spatial error structure improves parameter estimation and predictive model performance in low-dimensional settings and also improves feature selection in high-dimensional settings by reducing "red-shift": the preferential selection of features with spatial structure. In addition, we argue that the absence of spatial autocorrelation (SAC) in the model residuals should not be taken as a sign of a good fit, since it may result from overfitting the spatial trend. Finally, we confirm our findings in a case study on the prediction of winter wheat yield based on multispectral measurements.