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REGULAR ARTICLE
Imputing missing values in multi-environment trials using the singular value decomposition: An empirical comparison
Sergio Arciniegas-Alarcón, Marisol García-Peña, Wojtek Krzanowski, Carlos Tadeu dos Santos Dias
Commun. Biometry Crop Sci. (2014) 9 (2), 54-70.
ABSTRACT
Missing values for some genotype-environment combinations are commonly encountered
in multi-environment 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 algorithms
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 balance 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 an excellent alternative to imputation with an additive model,
which in practice ignores the genotype-by-environment interaction and therefore may not be appropriate in some cases.
Key Words: AMMI; genotype x environment interaction; imputation; missing values; singular value decomposition.
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