In this note we show how the entries of a data matrix can be approximated by a sum of row effects, column effects and interaction terms in a robust way using a weighted L1 estimator. We discuss an algorithm to compute this fit, and show by a simulation experiment and an example that the proposed method can be a useful tool in exploring data matrices. Moreover, a robust biplot is produced as a b...

In the final phases of new soybean cultivar development, lines are cultivated in several locations across multiple seasons with the intention of identifying and selecting superior genotypes for quantitative traits. In this context, this study aimed to study the genotype-by-environment interaction for the trait grain yield (kg/ha), and to evaluate the adaptability and stability of early-cycle so...

In this paper a robust approach for fitting multiplicative models is presented. Focus is on the factor analysis model, where we will estimate factor loadings and scores by a robust alternating regression algorithm. The approach is highly robust, and also works well when there are more variables than observations. The technique yields a robust biplot, depicting the interaction structure between ...

Superior crop cultivars must be identified through multi-environment trials (MET) and on the basis of multiple traits. The objectives of this paper were to describe two types of biplots, the GGE biplot and the GT biplot, which graphically display genotype by environment data and genotype by trait data, respectively, and hence facilitate cultivar evaluation on the basis of MET data and multiple ...

This short article is to comment on the methodology and conclusions of Yang et al. (2009) concerning the use of biplots to reveal crossover genotype-by-environment interaction (GE) patterns, which was published in Crop Science. Yan et al. (2007) applied GGE (genotypic main effect plus genotype-by-environment interaction) biplot analysis to an Ontario winter wheat dataset and concluded that ther...

This study aimed to analyze the robustness of mixed models for the study of genotype-environment interactions (G x E). Simulated unbalancing of real data was used to determine if the method could predict missing genotypes and select stable genotypes. Data from multi-environment trials containing 55 maize hybrids, collected during the 2005-2006 harvest season, were used in this study. Analyses w...

Canonical variate analysis (CVA) is concerned with the analysis of J classes of samples, all described by the same variables. Generalised canonical correlation analysis (GCCA) is concerned with the analysis of K sets of variables, all describing the same samples. A generalised procrustes analysis context is used for data partitioned into J classes of samples and K sets of variables to explore t...

Test environments and classification of regional ecological zones into mega environments are the two key components in regional testing of sugarcane cultivars. This study aims to provide the theoretical basis for test environment evaluation and ecological zone division for sugarcane cultivars. In the present study, sugarcane yield data from a three-year nationwide field trial involving 21 culti...

PCA biplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Correlation biplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Distance biplots . . . . . . . . . . . . . . ...

When applied to discriminant analysis (DA) biplot methodology leads to useful graphical displays for describing and quantifying multidimensional separation and overlap among classes. The principles of ordinary scatterplots are extended in these plots by adding information of all variables on the plot. However, we show that there are fundamental di¤erences between two-class DA problems and the c...