candisc-package: Visualizing Generalized Canonical Discriminant and Canonical...

In candisc: Visualizing Generalized Canonical Discriminant and Canonical Correlation Analysis

Description

This package includes functions for computing and visualizing generalized canonical discriminant analyses and canonical correlation analysis for a multivariate linear model. 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).

The graphic functions are designed to provide low-rank (1D, 2D, 3D) visualizations of terms in a mlm via the plot.candisc method, and the HE plot heplot.candisc and heplot3d.candisc methods. For mlms with more than a few response variables, these methods often provide a much simpler interpretation of the nature of effects in canonical space than heplots for pairs of responses or an HE plot matrix of all responses in variable space.

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, 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.

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

A few of these methods are illustrated in the vignette for the heplots package,

vignette("HE-examples", package="heplots").

Details

Package:	candisc
Type:	Package
Version:	0.7-3
Date:	2016-11-20
License:	GPL (>= 2)

The organization of functions in this package and the heplots package may change in a later version.

Author(s)

Michael Friendly and John Fox

Maintainer: Michael Friendly <[e-mail]>

References

Friendly, M. (2007). HE plots for Multivariate General Linear Models. Journal of Computational and Graphical Statistics, 16(2) 421–444. http://datavis.ca/papers/jcgs-heplots.pdf

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

Friendly, M. & Sigal, M. (2014). Recent Advances in Visualizing Multivariate Linear Models. Revista Colombiana de Estadistica , 37(2), 261-283. http://dx.doi.org/10.15446/rce.v37n2spe.47934.

Friendly, M. & Sigal, M. (2016). Graphical Methods for Multivariate Linear Models in Psychological Research: An R Tutorial, The Quantitative Methods for Psychology, in press.

Gittins, R. (1985). Canonical Analysis: A Review with Applications in Ecology, Berlin: Springer.

See Also

heplot for details about HE plots.

candisc, cancor for details about canonical discriminant analysis and canonical correlation analysis.

candisc documentation built on May 2, 2019, 6:37 p.m.