Estimating Diabrotica virgifera virgifera damage functions with field trial data: applying an unbalanced nested error component model

We apply the double-nested unbalanced panel data model developed by Antweiler [J. Econometrics 101 (2001) 295] to estimate a damage function for western corn rootworm (Diabrotica virgifera virgifera) using commonly available field data. These data are from experiments collecting maize yields and measures of maize root injury due to rootworm larval feeding for different treatments, with multiple replicates at many locations over several years, which creates nested panel data. The nested panel becomes unbalanced when the number of replicates, locations or years of data differs during the course of the study. We use Antweiler's (2001) method to estimate damage functions with data from four irrigated locations in northern Italy from 2006 to 2008 and from four dryland locations in the state of Illinois from 2005 to 2007 to predict the expected percentage of yield lost based on the observed node injury scale of Oleson et al. [J. Econ. Entomol. 98 (2005) 1]. Estimated coefficients imply that a one unit difference in the node injury scale is on average associated with a 17.9% yield loss for the Illinois locations and a 2.9% loss for the locations in Italy. We attribute the lower yield loss for the Italian locations to the use of irrigation. Estimated variance components were relatively large, indicating the tremendous variability in losses observed for plots with similar node injury scale differences. Given the large variation in observed yield losses and the large estimated random effects, the damage function is more appropriate for larger-scale, longer-term estimates of yield loss from the western corn rootworm rather than for field-scale estimates. These estimates are the first damage function estimates for the node injury scale in maize and should be considered preliminary, an initial baseline for comparison and refinement as additional data are collected and analysed in the US and Europe.