Longitudinal and Spatial Analyses Applied to Corn Yield Data from a Long-Term Rotation

The statistical analysis of yield data from a long term rotation trial presents a number of challenges, as illustrated by a 10 year study on the effects of reduced chemical inputs and different cropping sequences, most of which involved corn (Zea mays L.) (King and Buchanan, 1993). Important features of the yield data from this trial include considerable unbalance, possible correlations across time and space, possible heterogeneity in the error variances across years, and the availability of pretreatment measurements of soil properties. We investigated a number of analyses of the rotation trial corn yields, restricting attention to models that could be implemented using standard software, specifically Proc Mixed in SAS (SAS Institute, 1999). These analyses included several types of split plot, repeated measures and spatial analyses, each with and without soil covariates. Diagnostic graphs and AIC values indicated that the model should allow for heterogeneity across years in the error variance. The precision of contrasts in years with high (respectively, low) error variance was underestimated (respectively, overestimated) in analyses that assumed constant variance. Allowing spatial correlations resulted in a small reduction in estimates of precision, and including soil covariates was important in two of nine years. The best models were a repeated measures with banded covariance, as well as autoregressive repeated measures and isotropic spatial models, both modified to allow heterogeneity of the error variance across years. Estimates and t-values for specific treatment effects were similar for these models.