Imputing missing values in multi-Environment trialsusing the singular value decomposition: An empirical comparison

Missing values for some genotype-environment combinations are commonly encountered in multienvironment trials. The recommended methodology for analyzing such unbalanced data combines the Expectation-Maximization (EM) algorithm with the additive main effects and multiplicative interaction (AMMI) model. Recently, however, four imputation al gorithms based on the Singular Value Decomposition of a matrix (SVD) have been reported in the literature (Biplot imputation, EM+SVD, GabrielEigen imputation, and distribution free multiple imputation - DFMI). These algorithms all fill in the missing values, thereby removing the lack of ba lance in the original data and permitting simpler standard analyses to be performed. The aim of this paper is to compare these four algorithms with the gold standard EM-AMMI. To do this, we report the results of a simulation study based on three complete sets of real data (eucalyptus, sugar cane and beans) for various imputation percentages. The methodologies were compared using the normalised root mean squared error, the Procrustes similarity statistic and the Spearman correlation coefficient. The conclusion is that imputation using the EM algorithm plus SVD provides competitive results to those obtained with the gold standard. It is also a n excellent alternative to imputation with an additive model, which in practice ignores the genotype-byenvironment interaction and therefore may not be ap propriate in some cases.