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candisc

Visualizing Generalized Canonical Discriminant and Canonical Correlation Analysis

Version 1.0.3

This package includes functions for computing and visualizing generalized canonical discriminant analyses and canonical correlation analysis for a multivariate linear model (MLM). The goal is to provide ways of visualizing such models in a low-dimensional space corresponding to dimensions (linear combinations of the response variables) of maximal relationship to the predictor variables.

Traditional canonical discriminant analysis is restricted to a one-way MANOVA design and is equivalent to canonical correlation analysis between a set of quantitative response variables and a set of dummy variables coded from the factor variable. The candisc package generalizes this to multi-way MANOVA designs for all terms in a multivariate linear model (i.e., an mlm object), computing canonical scores and vectors for each term (giving a "candiscList" object).

For mlms with more than a few response variables, these methods often provide a much simpler interpretation of the nature of effects in low-D canonical space than heplots for pairs of responses or an HE plot matrix of all responses in variable space.

Visualization methods

The graphic functions are designed to provide low-rank (1D, 2D, 3D) visualizations of terms in a "mlm" via the plot.candisc() method, which plots the observations in canonical space, together with variable vectors showing the relations of the response y variables to the canonical variables Can1, Can2. This is the same idea as that of a biplot (Gabriel, 1971).

The HE plot heplot.candisc() and heplot3d.candisc() methods use a similar framework, but replace the observations and groupwise data ellipses in the plot with representations of the H ellipsoid, representing between-group variation in the means and the E ellipsoid reflecting the pooled within-group variation.

Analogously, a multivariate linear (regression) model with quantitative predictors can also be represented in a reduced-rank space by means of a canonical correlation transformation of the Y and X variables to uncorrelated canonical variates, named with the prefix Ycan and Xcan. Computation for this analysis is provided by cancor() and related methods. Visualization of these results in canonical space are provided by the plot.cancor(), heplot.cancor() and heplot3d.cancor() methods.

Variable ordering

The relations among response variables in linear models can also be useful for “effect ordering” (Friendly & Kwan (2003)) for variables in other multivariate data displays, such as heatmaps or “corrgrams” (Friendly, 2002) of correlations. to make the displayed relationships more coherent. The function varOrder() implements a collection of these methods.

Discriminant analysis

Some of these visualization methods have now been extended to discriminant analysis, for example from MASS:lda() or MASS:lda(), beginning with a simplified interface to prediction, in predict_discrim().

  • A new plotting method, plot_discrim(), provides ggplot2 plots of the classification regions and decision boundaries in data space and in discriminant space.
  • cor_lda() calculates correlations between the observed variables and the discriminant dimensions.

Installation

CRAN version install.packages("candisc")
Development version remotes::install_github("friendly/candisc")

Or, install from r-universe:

install.packages('candisc', repos = c('https://friendly.r-universe.dev')

Vignettes

  • A new vignette, vignette("diabetes", package="candisc"), illustrates some of these methods.

  • A more comprehensive collection of examples, illustrating multivariate regression and MANOVA methods, is contained in the vignettes for the heplots package, browseVignettes(package = "heplots").

Citation

To cite package candisc in publications use:

Friendly M., Fox J. (2025). candisc: Visualizing Generalized Canonical Discriminant and Canonical Correlation Analysis_. R package version 1.0.0, https://CRAN.R-project.org/package=heplots.

For the theory on which these methods are based, also cite:

Friendly, M. (2007). “HE plots for Multivariate General Linear Models.” Journal of Computational and Graphical Statistics, 16(2), 421-444. https://doi.org/10.1198/106186007X208407.

References

Friendly, M. (2002). Corrgrams: Exploratory displays for correlation matrices. The American Statistician, 56(4), 316–324. https://doi.org/10.1198/000313002533

Friendly, M., & Kwan, E. (2003). Effect Ordering for Data Displays. Computational Statistics and Data Analysis, 43(4), 509–539. https://doi.org/10.1016/S0167-9473(02)00290-6

Gabriel, K. R. (1971). The Biplot Graphic Display of Matrices with Application to Principal Components Analysis. Biometrics, 58(3), 453–467.