BiGaRx - Unified Classical and Canonical Biplots

Classical and canonical biplots computed from a single singular value decomposition (SVD) engine. Includes the two biplots of Gabriel (1971) <doi:10.1093/biomet/58.3.453>: the GH-biplot, named after its row markers G and column markers H, which preserves the column metric (covariances and correlations between variables), and the JK-biplot, named after its row markers J and column markers K, which preserves the row metric (distances between individuals). Also includes the HJ-biplot of Galindo (1986) <https://upcommons.upc.edu/entities/publication/e17797dd-e20b-4fe5-b34a-f4cde41695ed>, which combines the row markers J and the column markers H so that rows and columns are both represented with maximum quality. Options include configurable preprocessing, supplementary rows and columns, quality of representation, contributions, goodness of fit, bootstrap confidence intervals following Nieto, Galindo, Leiva and Vicente-Galindo (2014) <doi:10.15446/rce.v37n2spe.47944>, and imputation of missing values by iterative low-rank approximation following Gabriel and Zamir (1979) <doi:10.1080/00401706.1979.10489819>. The canonical biplot, also known as the multivariate analysis of variance (MANOVA) biplot, follows Amaro, Vicente-Villardon and Galindo (2004) <https://www.redalyc.org/pdf/339/33908807.pdf>. It is available for one-way designs and for two-way designs with total, row, column and interaction biplots. It comes with multivariate tests, pairwise comparisons with Hotelling's T-squared statistic, log-ratio transformations for compositional data and confidence regions for the group means. The regions are circles or the ellipses of Krzanowski (1989) <doi:10.1093/biomet/76.1.107>, computed consistently in the scale of the within-groups covariance matrix. Plots use base graphics or 'ggplot2'.