The Practical Use of Semiparametric Models in Field Trials

This article examines the practical use of semiparametric models in the analysis of field trials--that is, models with parameterized treatment effects and additive terms derived by a data-driven approach using a locally weighted running line smoother (loess). We discuss graphical methods to identify spatial structure in the data and model selection procedures to choose the degree of smoothing. Once the spatial part of the model has been chosen, hypotheses about the treatment effects may be tested. Semiparametric models are used to analyze two barley field trials exhibiting spatial trends. The first has a single experimental treatment and a row-column design. The second has a split-plot design, and we use a semiparametric model which accounts for the randomization at the different strata of this design. We compare the semiparametric analyses with classical analyses of variance and with alternative spatial models. We find that semiparametric models give a good insight into spatial variation in the field and can improve the precision of parameter estimates.