Deterministic Imputation in Multienvironment Trials

Abstract

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.

Missing value imputation in multi-environment trials: Reconsidering the Krzanowski method

“…For a fixed r value (0< r <1), if the (pi + j)-th random number was lower than r, then the element in the (i+1, j) position of the matrix was deleted (i =0,1,...,n-1; j =1,...,p). The expected proportion of missing values in the matrix will be r (Krzanowski 1988, Arciniegas-Alarcón et al 2013). This technique was used with r = 0.1, 0.2 and 0.35.…”

“…These changes are influenced by different environmental conditions; and in crop science literature they are commonly referred to as genotype-by-environment interactions, or G×E. Some useful references can be found in Arciniegas-Alarcón et al (2013).…”

Missing‐value imputation using the robust singular‐value decomposition: Proposals and numerical evaluation

“…For the preprocessing step in G × E data, data can be imputed using various schemes and a list of the main references since 1975 can be found in Arciniegas‐Alarcón et al. (2013). However, the EM‐AMMI method (Gauch & Zobel, 1990) can be considered to be the gold standard.…”

Alternativas de análise para experimentos G × E multiatributo

“…Essa característica nãoé, necessariamente, verdadeira para os métodos de imputação estocástica (Bello, 1993;Arciniegas-Alarcón et al, 2013).…”