Prediction assessment of shrinkage estimators of multiplicative models formulti-environment cultivar trials

Multiplicative statistical models such as the additive main effects and mul tiplicative interaction model (AMMI), the genotypes regression model (GREG) , the sites regression model (SREG), the completely multiplicative model (C OMM), and the shifted multiplicative model (SHMM) are useful for studying p atterns of yield response across sites and estimating realized cultivar res ponses in specific environments. Traditionally the series of multiplicative terms is truncated at some point beyond which further terms are believed t o have little statistical significance or predictive value. Shrinkage estim ators have been advocated as a model fitting method superior to model trunc ation. In this study, by data splitting and cross validation, rye evaluated the predictive accuracy of (i) truncated multiplicative models, (ii) shrin kage estimators of multiplicative models, (iii) Best Linear Unbiased Predic tors (BLUP) of the cell means based on a two-way random effects model with interaction, and (iv) empirical cell means in one wheat [durum (Triticum tu rgidum L. var. durum) and bread (Triticum aestivum L.)] and four maize (Zea mays L.) cultivar trials, with and without adjustment for replicate differ ences within environments. Shrinkage estimates of multiplicative models wer e at least as good as the better choice of truncated models fitted by least squares or BLUPs. Shrinkage estimation yields potentially better estimates of cultivar performance than do truncated multiplicative models and elimin ates the need for cross validation or tests of hypotheses as criteria for d etermining the number of multiplicative terms to be retained. If random cro ss validation is used to choose a truncated model, data should be adjusted for replicate differences within environments.