The usefulness of EM-AMMI to study the influence of missing data pattern and application to Polish post-registration winter wheat data

The study of genotype-by-environment interaction (GEI) is of key importance in plant sciences because an understanding of this allows a great improvement in complex phenotypic traits. Genotypes and environments constitute a two-way factorial design. The phenotypic data for these studies, usually arranged in two-way data tables with genotypes and environments (location-year combinations). In plant breeding programs some genotypes are often discarded and others included from year to year, which results in the presence of missing values in these data sets. Several options are available for dealing with missing values in two-way data tables. One of the most widely used alternatives is the imputation of the missing cells using an expectation-maximization (EM) algorithm together with the additive main effects and multiplicative interaction (AMMI) model. In this paper we present a simulation study to investigate the influence of the pattern of missing values on the efficiency of the expectation-maximization AMMI (EM-AMMI) algorithm. Four scenarios are considered: one with cells missing completely at random; and three patterns with cells not missing at random (block-diagonal pattern, diagonal pattern and block-diagonal pattern with checks). The results are compared in terms of precision to estimate the missing cells and genotype selection.