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Some recently obtained results on cross validation, hypothesis test and estimation procedures for multiplicative models applied to multi-site crop variety trials are presented. The PRESS statistic is more sensitive to overfitting and choice of model form than data-splitting cross-validation. Because of their extreme liberality, Gollob F-tests should not be used to test multiplicative terms. FGH tests effectively control Type I error, but are conservative for tests of terms for which the previous term is small. "Simulation tests" have greater power than F GH tests, but still effectively control Type I error rates. Simulation results and cross validation in two examples suggest that BL UPstyle shrinkage estimators of multiplicative terms produce fitted models with predictive value at least as good as the best truncated models and would eliminate the need for cross validation as a criterion for model choice. Shrinkage estimators of multiplicative models were better than BLUPs computed under the assumption of random unpatterened interaction in one example and were at least as good in the second example. Both were much better than empirical cell means in both examples. It is suggested that variety performance estimates derived from shrinkage estimators of multiplicative models should replace empirical cell means routinely reported in experiment station crop variety trial bulletins.

TESTS AND ESTIMATORS OF MULTIPLICATIVE MODELS FOR VARIETY TRIALS