The Additive Main effects and Multiplicative Interaction (AMMI) statistical model has been demonstrated effective for understanding genotype-environment interactions in yields, estimating yields more accurately, selecting superior genotypes more reliably, and allowing more flexible and efficient experimental designs. However, AMMI had required data for every genotype and environment combination or treatment; i.e., missing data were inadmissible. The present paper addresses the problem. The Expectation-Maximization (EM) algorithm is implemented for fitting AMMI depite missing data. This missing-data version of AMMI is here termed "EM-AMMI". EM-AMMI is used to quantify the direct and indirect information in a yield trial, providing theoretical insight into the gain in accuracy observed and into the process of imputing missing data. For a given treatment, the direct yield data are the replicates of that treatment, and the indirect data are all the other yield data in the trial. EM-AMMI is used to inpute missing data for a New York soybean yield trial. Important applications arise from both unintentional and intentional missing data. Empirical measurements demonstrate good predictive success, and statistical theory attributes this success to the Stein effect.