Visualizing Generalized Canonical Discriminant and Canonical Correlation Analysis
Source:R/candisc-package.R
candisc-package.RdThis 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 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").
The organization of functions in this package and the heplots package may change in a later version.
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.