A COMPARISON OF GEOSTATISTICAL AND SPATIAL AUTOREGRESSIVE APPROACHES FOR DEALING WITH SPATIALLY CORRELATED RESIDUALS IN REGRESSION ANALYSIS FOR PRECISION AGRICULTURE APPLICATIONS

Abstract

Regressions such as Grain yield=f(soil,landscape) are frequently reported in precision agriculture research, and are typically computed using conventional OLS methods, implicitly ignoring spatial correlation of the residuals. This oversight can have a marked effect on the final conclusions derived from these regressions. A further issue is, which approach should be used to account for this problem? We investigated this question using a 2 year data set that includes site- specific soil and topographic information and soybean yields and compare regression results from direct covariance representation and spatial autoregressive approaches. Our results show that the coefficients from both spatial approaches are in many cases significantly different to those from OLS, but the estimates from both spatial approaches appear to show little differences. To provide further insight into the comparison among these approaches we use a simulation of spatial random fields, with a model containing 2 independent explanatory variables and a spatially structured residual term. We then estimated the coefficients for 1000 simulations of this field and assessed their distributional properties. All methods yielded overall unbiased estimates and OLS showed the largest standard errors, while the ‘spatial’ approaches proved to be relatively consistent, although a certain neighborhood specification within the spatial autoregressive model had an evidently lower performance than the rest.