Analysis of Variety Yield Trials Using Two-Dimensional Separable ARIMA Processes

The two-dimensional spatial analysis procedure based on separable ARIMA processes, proposed by Cullis and Gleeson (1991 Biometrics 47, 1449-1460), is used to analyze 35 cereal yield trials with incomplete block designs. Models with different large-scale variation components and diverse small-scale variation processes, modeled as one-dimensional and two-dimensional (separable) ARIMA processes, were compared. Nineteen spatial models were considered and two criteria were used to assess spatial model adequacy: (a) the average standard error of the pairwise variety differences (SED) and (b) the mean squared error of prediction (MSE) based on a cross-validation approach. Spatial analysis is more efficient in reducing residual variation than incomplete block analysis. Although there was no one model that best fit all the trials, the two-dimensional firstorder autoregressive model was the most efficient in terms of the SED and MSE criteria (in 21 and 14 trials, respectively).