candisc {candisc} | R Documentation |

`candisc`

performs a generalized canonical discriminant analysis for
one term in a multivariate linear model (i.e., an `mlm`

object),
computing canonical scores and vectors. It represents a transformation
of the original variables into a canonical space of maximal differences
for the term, controlling for other model terms.

In typical usage,
the `term`

should be a factor or interaction corresponding to a
multivariate test with 2 or more degrees of freedom for the
null hypothesis.

candisc(mod, ...) ## S3 method for class 'mlm' candisc(mod, term, type = "2", manova, ndim = rank, ...) ## S3 method for class 'candisc' coef(object, type = c("std", "raw", "structure"), ...) ## S3 method for class 'candisc' plot(x, which = 1:2, conf = 0.95, col, pch, scale, asp = 1, var.col = "blue", var.lwd = par("lwd"), var.labels, var.cex = 1, var.pos, rev.axes=c(FALSE, FALSE), ellipse=FALSE, ellipse.prob = 0.68, fill.alpha=0.1, prefix = "Can", suffix=TRUE, titles.1d = c("Canonical scores", "Structure"), points.1d = FALSE, ...) ## S3 method for class 'candisc' print(x, digits=max(getOption("digits") - 2, 3), LRtests=TRUE, ...) ## S3 method for class 'candisc' summary(object, means = TRUE, scores = FALSE, coef = c("std"), ndim, digits = max(getOption("digits") - 2, 4), ...)

`mod` |
An mlm object, such as computed by |

`term` |
the name of one term from |

`type` |
type of test for the model |

`manova` |
the |

`ndim` |
Number of dimensions to store in (or retrieve from, for the |

`object, x` |
A candisc object |

`which` |
A vector of one or two integers, selecting the canonical dimension(s) to plot. If the canonical
structure for a |

`conf` |
Confidence coefficient for the confidence circles around canonical means plotted in the |

`col` |
A vector of the unique colors to be used for the levels of the term in the |

`pch` |
A vector of the unique point symbols to be used for the levels of the term in the |

.

`scale` |
Scale factor for the variable vectors in canonical space. If not specified, a scale factor is calculated to make the variable vectors approximately fill the plot space. |

`asp` |
Aspect ratio for the |

`var.col` |
Color used to plot variable vectors |

`var.lwd` |
Line width used to plot variable vectors |

`var.labels` |
Optional vector of variable labels to replace variable names in the plots |

`var.cex` |
Character expansion size for variable labels in the plots |

`var.pos` |
Position(s) of variable vector labels wrt. the end point. If not specified, the labels are out-justified left and right with respect to the end points. |

`rev.axes` |
Logical, a vector of |

`ellipse` |
Draw data ellipses for canonical scores? |

`ellipse.prob` |
Coverage probability for the data ellipses |

`fill.alpha` |
Transparency value for the color used to fill the ellipses. Use |

`prefix` |
Prefix used to label the canonical dimensions plotted |

`suffix` |
Suffix for labels of canonical dimensions. If |

`titles.1d` |
A character vector of length 2, containing titles for the panels used to plot the canonical scores and structure vectors, for the case in which there is only one canonical dimension. |

`points.1d` |
Logical value for |

`means` |
Logical value used to determine if canonical means are printed |

`scores` |
Logical value used to determine if canonical scores are printed |

`coef` |
Type of coefficients printed by the summary method. Any one or more of "std", "raw", or "structure" |

`digits` |
significant digits to print. |

`LRtests` |
logical; should likelihood ratio tests for the canonical dimensions be printed? |

`...` |
arguments to be passed down. In particular, |

Canonical discriminant analysis is typically carried out in conjunction with
a one-way MANOVA design. It represents a linear transformation of the response variables
into a canonical space in which (a) each successive canonical variate produces
maximal separation among the groups (e.g., maximum univariate F statistics), and
(b) all canonical variates are mutually uncorrelated.
For a one-way MANOVA with g groups and p responses, there are
`dfh`

= min( g-1, p) such canonical dimensions, and tests, initally stated
by Bartlett (1938) allow one to determine the number of significant
canonical dimensions.

Computational details for the one-way case are described
in Cooley & Lohnes (1971), and in the *SAS/STAT User's Guide*, "The CANDISC procedure:
Computational Details," http://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_candisc_sect012.htm.

A generalized canonical discriminant analysis extends this idea to a general
multivariate linear model. Analysis of each term in the `mlm`

produces
a rank *dfh* H matrix sum of squares and crossproducts matrix that is
tested against the rank *dfe* E matrix by the standard multivariate
tests (Wilks' Lambda, Hotelling-Lawley trace, Pillai trace, Roy's maximum root
test). For any given term in the `mlm`

, the generalized canonical discriminant
analysis amounts to a standard discriminant analysis based on the H matrix for that
term in relation to the full-model E matrix.

The plot method for candisc objects is typically a 2D plot, similar to a biplot.
It shows the canonical scores for the groups defined by the `term`

as
points and the canonical structure coefficients as vectors from the origin.

If the canonical structure for a `term`

has `ndim==1`

, or `length(which)==1`

,
the 1D representation consists of a boxplot of canonical scores and a vector diagram
showing the magnitudes of the structure coefficients.

An object of class `candisc`

with the following components:

`dfh ` |
hypothesis degrees of freedom for |

`dfe ` |
error degrees of freedom for the |

`rank ` |
number of non-zero eigenvalues of |

`eigenvalues ` |
eigenvalues of |

`canrsq ` |
squared canonical correlations |

`pct ` |
A vector containing the percentages of the |

`ndim ` |
Number of canonical dimensions stored in the |

`means ` |
A data.frame containing the class means for the levels of the factor(s) in the term |

`factors ` |
A data frame containing the levels of the factor(s) in the |

`term ` |
name of the |

`terms ` |
A character vector containing the names of the terms in the |

`coeffs.raw ` |
A matrix containing the raw canonical coefficients |

`coeffs.std ` |
A matrix containing the standardized canonical coefficients |

`structure ` |
A matrix containing the canonical structure coefficients on |

`scores ` |
A data frame containing the predictors in the |

Michael Friendly and John Fox

Bartlett, M. S. (1938). Further aspects of the theory of multiple regression. Proc. Camb. Phil. Soc. 34, 33-34.

Cooley, W.W. & Lohnes, P.R. (1971). Multivariate Data Analysis, New York: Wiley.

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

grass.mod <- lm(cbind(N1,N9,N27,N81,N243) ~ Block + Species, data=Grass) Anova(grass.mod, test="Wilks") grass.can1 <-candisc(grass.mod, term="Species") plot(grass.can1) # library(heplots) heplot(grass.can1, scale=6, fill=TRUE) # iris data iris.mod <- lm(cbind(Petal.Length, Sepal.Length, Petal.Width, Sepal.Width) ~ Species, data=iris) iris.can <- candisc(iris.mod, data=iris) #-- assign colors and symbols corresponding to species col <- c("red", "brown", "green3") pch <- 1:3 plot(iris.can, col=col, pch=pch) heplot(iris.can) # 1-dim plot iris.can1 <- candisc(iris.mod, data=iris, ndim=1) plot(iris.can1)

[Package *candisc* version 0.8-5 Index]