candisc-package {candisc} | R Documentation |

## 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.

### Details

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 `mlm`

s 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 new vignette, `vignette("diabetes", package="candisc")`

, illustrates
some of these methods. A more comprehensive collection of examples is
contained in the vignette for the heplots package,

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

.

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 <friendly@yorku.ca>

### 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,
doi:10.1198/106186007X208407.

Friendly, M. & Kwan, E. (2003). Effect Ordering for Data Displays,
*Computational Statistics and Data Analysis*, **43**, 509-539.
doi: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.
doi:10.15446/rce.v37n2spe.47934.

Friendly, M. & Sigal, M. (2017). Graphical Methods for Multivariate Linear
Models in Psychological Research: An R Tutorial, *The Quantitative
Methods for Psychology*, 13 (1), 20-45.
doi:10.20982/tqmp.13.1.p020.

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*version 0.9.0 Index]