The Use of Geoadditive Models to Estimate the Spatial Distribution of Grain Weight in an Agronomic Field: a Comparison with Kriging with External Drift

The goal of this study is to analyse the spatial distribution of a wheat production indicator in a field trial located in southeastern Italy, in order to ascertain how the plant characteristics and spatial dependence influence its quantity. In standard agronomical applications this kind of data, recorded in georeferenced locations jointly with crop and soil variables, is quite commonly mapped by using kriging with external drift. Such a predictor assumes covariates to have a linear effect on the crop response variables, but it is well known how this assumption is seldom verified and often violated in a typical agronomic trial. In this work we propose the use of geoadditive models for analysing grain weight of a wheat crop in the presence of other covariates, because these models allow the user to investigate both linear and nonlinear relationships between response and exploratory variables simultaneously with modelling. Moreover, in addition to the original geoadditive model formulation by Kammann andWand (2003), the use of the exponential and the Gaussian spatial correlation structures was explicitly considered. Different models were compared using a set of cross validation criteria. The results showed that the geoadditive model with an exponential correlation structure was preferred to kriging with external drift in terms of unbiasedness of the predictor, accuracy of the mean squared prediction and goodness of fit for this agricultural trial.