Table of Contents
ISRN Agronomy
Volume 2013 (2013), Article ID 978780, 17 pages
Research Article

Deterministic Imputation in Multienvironment Trials

1Departamento de Ciências Exatas, Universidade de São Paulo/ESALQ, Cx.P.09, CEP. 13418-900, Piracicaba, SP, Brazil
2College of Engineering, Mathematics and Physical Sciences Harrison Building, University of Exeter, North Park Road, Exeter, EX4 4QF, UK

Received 26 June 2013; Accepted 16 August 2013

Academic Editors: A. Escobar-Gutierrez and W. P. Williams

Copyright © 2013 Sergio Arciniegas-Alarcón et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes five new imputation methods for unbalanced experiments with genotype by-environment interaction (). The methods use cross-validation by eigenvector, based on an iterative scheme with the singular value decomposition (SVD) of a matrix. To test the methods, we performed a simulation study using three complete matrices of real data, obtained from interaction trials of peas, cotton, and beans, and introducing lack of balance by randomly deleting in turn 10%, 20%, and 40% of the values in each matrix. The quality of the imputations was evaluated with the additive main effects and multiplicative interaction model (AMMI), using the root mean squared predictive difference (RMSPD) between the genotypes and environmental parameters of the original data set and the set completed by imputation. The proposed methodology does not make any distributional or structural assumptions and does not have any restrictions regarding the pattern or mechanism of missing values.