Prediction Assessment of Shrinkage Estimators of Multiplicative Models for Multi‐Environment Cultivar Trials

Multiplicative statistical models such as the additive main effects and multiplicative interaction model (AMMI), the genotypes regression model (GREG), the sites regression model (SREG), the completely multiplicative model (COMM), and the shifted multiplicafive model (SHMM) are useful for studying patterns of yield response across sites and estimating realized cuitivar responses in specific environments. Traditionally the series of multiplicative terms is truncated at some point beyond which further terms are believed to have little statistical significance or predictive value. Shrinkage estimators have been advocated as a model fitting method superior to model truncation. In this study, by data splitting and cross validation, we evaluated the predictive accuracy of (i) truncated multiplicative models, (ii) shrinkage estimators of multiplicative models, (iii) Best Linear Unbiased Predictors (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 turgidum L. var. durum ) and bread ( Triticum aestivum L.)] and four maize ( Zea mays L.) cultivar trials, with and without adjustment for replicate differences within environments. Shrinkage estimates of multiplicative models were 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 eliminates the need for cross validation or tests of hypotheses as criteria for determining the number of multiplicative terms to be retained. If random cross validation is used to choose a truncated model, data should be adjusted for replicate differences within environments.