CanonicalDistanceAnalysis: MANOVA and Canonical Analysis of Distances

In MultBiplotR: Multivariate Analysis Using Biplots in R

MANOVA and Canonical Analysis of Distances

Description

Performs a MANOVA and a Canonical Analysis based on of Distance Matrices (usally for continuous data)

Usage

CanonicalDistanceAnalysis(Prox, group, dimens = 2, Nsamples = 1000, 
PCoA = "Standard", ProjectInd = TRUE)

Arguments

Prox	A object containing proximities
group	A factor with the group structure of the rows
dimens	The dimension of the solution
Nsamples	Number of samples for the permutation test. Number of permutations.
PCoA	Type of Principal Coordinates for the Canonical Analysis calculated from the Principal coordinates of the Mean Matrix. "Standard" : Standard Principal Coordinates Analysis, "Weighted": Weighted Principal Coordinates Analysis, "WPCA")
ProjectInd	Should the individual points be Projected onto the representation For the moment only available for Continuous Data.

Details

Performs a MANOVA and a Canonical Analysis based on of Distance Matrices (usally for continuous data). The MANOVA statistics is calculated from a decomposition of the distance matrix based on a factor of a external classification. The significance of the test is calculated using a premutation test. The approach depens only on the distances and then is useful with any kind of data.

The Canonical Representation is calculated from a Principal Coordinates Analysis od the distance matrix among the means. Thus, it is only possible for continuous data. The PCoA representation can be "Standard" using the means directly, "Weighted" weighting each group with its sample size or using weighted Princiopal Components Analysis of the matrix of means.

A measure of the quality of representation of the groups is provided. When possible, the measure is also provided for the individual points.

Soon, a biplot representation will also be developed.

Value

An object of class "CanonicalDistanceAnalysis" with:

Distances	The Matrix of Distances from which the Analysis has been made
Groups	A factor containing the group struture of the individuals
TSS	Total sum of squares
BSS	Between groups sum of squares
WSS	Within groups sum of squares
Fexp	Experimental pseudo F-value
pvalue	p value based on the permutation test
Nsamples	p value based on the permutation test
ExplainedVariance	Variances explained by the PCoA
MeanCoordinates	Coordinates of the groups for the graphical representation
Qualities	Qualities of the representation of the groups
CummulativeQualities	Cummulative qualities of the representation of the groups
RowCoordinates	Coordinates of the individuals for the graphical representation

Note

The MANOVA and the representation of the means can be applied to any Distance althoug the projection of the individuals can be made only for continuous data.

Author(s)

Jose Luis Vicente Villardon

References

Gower, J. C., & Krzanowski, W. J. (1999). Analysis of distance for structured multivariate data and extensions to multivariate analysis of variance. Journal of the Royal Statistical Society: Series C (Applied Statistics), 48(4), 505-519.

Krzanowski, W. J. (2004). Biplots for multifactorial analysis of distance. Biometrics, 60(2), 517-524.

Examples

data(iris)
group=iris[,5]
X=as.matrix(iris[1:4])
D=ContinuousProximities(X,  coef = 1)
CDA=CanonicalDistanceAnalysis(D, group, dimens=2)
summary(CDA)
plot(CDA)

MultBiplotR documentation built on Nov. 21, 2023, 5:08 p.m.