Recently, the genotype plus genotype x environment interaction (GGE) biplot methodology has been used to investigate genotype x environment interactions in several crop species, but has not been applied to the common bean (Phaseolus vulgaris L.) crop in Brazil. The aim of this study was to identify common bean genotypes that exhibit high grain yield and stability in the State of Mato Grosso do ...

This chapter presents ViSta-PrnCmp, the module for Principal Components Analysis (PCA) in ViSta. This procedure is capable of analyzing numerical variables so they can be represented on a lower dimensionality space. The visualization for ViSta-PrnCmp includes a scatterplot-matrix of component scores; a bi-dimensional biplot; a tri-dimensional (spin-plot) version of the biplot; a box-diamond-dot...

A simple geometry allows the main properties of matrix approximations used in biplot displays to be developed. It establishes orthogonal components of an analysis of variance, from which different contributions to approximations may be assessed. Particular attention is paid to approximations that share the same singular vectors, in which case the solution space is a convex cone. Two and three-d...

Collinearity diagnostics are widely used, but the typical tabular output used in almost all software makes it hard to tell what to look for and how to understand the results. We describe a simple improvement to the standard tabular display, a graphic rendition of the salient information as a ‘‘tableplot,’’ and graphic displays designed to make the information in these diagnostic methods more re...

Plant biologists in fields of ecology, evolution, genetics and breeding frequently use multivariate methods. This paper illustrates Principal Component Analysis (PCA) and Gabriel's biplot as applied to microarray expression data from plant pathology experiments.

We compare two methods for visualising contingency tables and develop a method called the ratio map which combines the good properties of both. The first is a biplot based on the logratio approach to compositional data analysis. This approach is founded on the principle of subcompositional coherence, which assures that results are invariant to considering subsets of the composition. The second ...

Understanding three-dimensional projections created by dimensionality reduction from high-variate datasets is very challenging. In particular, classical three-dimensional scatterplots used to display such projections do not explicitly show the relations between the projected points, the viewpoint used to visualize the projection, and the original data variables. To explore and explain such rela...

A graphical display of PLS regression of a data set is presented. Biplots in regression analysis has many advantages, including demonstrating the association between samples and variables graphically. The PLS biplot provides a single graphical representation of the samples alongside the predictor and response variables, as well as their interrelationships.