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 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").
| Package: | candisc |
| Type: | Package |
| Version: | 0.8-3 |
| Date: | 2020-04-20 |
| License: | GPL (>= 2) |
The organization of functions in this package and the heplots package may change in a later version.
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.
heplot for details about HE plots.
candisc, cancor for details about canonical discriminant analysis
and canonical correlation analysis.