A random field approach to the analysis of field-plot experiments and other spatial experiments

TL;DR: An alternative approach in which the spatial heterogeneity is modeled directly is examined, similar to the model underlying a geostatistical kriging analysis and the observations are regarded collectively as a partial realization of a random field.

Abstract: Several "nearest-neighbor" methods for the analysis of data from spatial experiments (e.g., agricultural field experiments) have recently been proposed. These methods attempt to account for the effect of spatial heterogeneity on the estimation of treatment contrasts; typically, this is accomplished indirectly by differencing or by using residuals from neighboring plots to construct covariates. We examine an alternative approach in which the spatial heterogeneity is modeled directly. The model underlying our approach is similar to the model underlying a geostatistical kriging analysis and, as in the latter model, the observations are regarded collectively as a partial realization of a random field. A randomization study of uniformity trial data suggests that the random field approach often provides more accurate estimates of treatment contrasts than nearest-neighbor approaches. In addition, the random field approach is devoid of ambiguities as to the handling of border plots and is generally more flexible than nearest-neighbor approaches.