Evaluation of models predicting winter wheat yield as a function of winter wheat and jointed goatgrass densities

Three models that empirically predict crop yield from crop and weed density were evaluated for their fit to 30 data sets from multistate, multiyear winter wheat-jointed goatgrass interference experiments. The purpose of the evaluation was to identify which model would generally perform best for the prediction of yield (damage function) in a bioeconomic model and which model would best fulfill criteria for hypothesis testing with limited amounts of data. Seven criteria were used to assess the fit of the models to the data. Overall, Model 2 provided the best statistical description of the data. Model 2 regressions were most often statistically significant, as indicated by approximate F tests, explained the largest proportion of total variation about the mean, gave the smallest residual sum of squares, and returned residuals with random distribution more often than Models 1 and 3. Model 2 performed less well based on the remaining criteria. Model 3 outperformed Models 1 and 2 in the number of parameters estimated that were statistically significant. Model I outperformed Models 2 and 3 in the proportion of regressions that converged on a solution and more readily exhibited an asymptotic relationship between winter wheat yield and both winter wheat and jointed goatgrass density under the constraint of limited data. In contrast, Model 2 exhibited a relatively linear relationship between yield and crop density and little effect of increasing jointed goatgrass density on yield, thus overpredicting yield at high weed densities when data were scarce. Model 2 had statistical properties that made it superior for hypothesis testing; however, Model 1's properties were determined superior for the damage function in the winter wheat-jointed goatgrass bioeconomic model because it was less likely to cause bias in yield predictions based on data sets of minimum size.