princomprcomp: Principal component analysis for real compositions

In compositions: Compositional Data Analysis

Principal component analysis for real compositions

Description

A principal component analysis is done in real geometry (i.e. cpt-transform) of the simplex. Some gimics simplify the interpretation of the obtained components.

Usage

 ## S3 method for class 'rcomp'
princomp(x,...,scores=TRUE,center=attr(covmat,"center"),
                           covmat=var(x,robust=robust,giveCenter=TRUE),
                           robust=getOption("robust"))
 ## S3 method for class 'princomp.rcomp'
print(x,...)
 ## S3 method for class 'princomp.rcomp'
plot(x,y=NULL,...,npcs=min(10,length(x$sdev)),
        type=c("screeplot","variance","biplot","loadings","relative"),
        main=NULL,scale.sdev=1)
 ## S3 method for class 'princomp.rcomp'
predict(object,newdata,...)

Arguments

x	an rcomp dataset (for princomp) or a result from princomp.rcomp
y	not used
scores	a logical indicating whether scores should be computed or not
npcs	the number of components to be drawn in the scree plot
type	type of the plot: "screeplot" is a lined screeplot, "variance" is a boxplot-like screeplot, "biplot" is a biplot, "loadings" displays the loadings as a barplot
scale.sdev	the multiple of sigma to use when plotting the loadings
main	title of the plot
object	a fitted princomp.rcomp object
newdata	another compositional dataset of class rcomp
...	further arguments to pass to internally-called functions
covmat	provides the covariance matrix to be used for the principle component analysis
center	provides the be used for the computation of scores
robust	Gives the robustness type for the calculation of the covariance matrix. See var.rmult for details.

Details

Mainly a princomp(cpt(x)) is performed. To avoid confusion, the meaningless last principal component is removed.
The plot routine provides screeplots (type = "s",type= "v"), biplots (type = "b"), plots of the effect of loadings (type = "b") in scale.sdev*sdev-spread, and loadings of pairwise differences (type = "r").
The interpretation of a screeplot does not differ from ordinary screeplots. It shows the eigenvalues of the covariance matrix, which represent the portions of variance explained by the principal components.
The interpretation of the biplot strongly differs from a classical one. The relevant variables are not the arrows drawn (one for each component), but rather the links (i.e., the differences) between two arrow heads, which represents the difference between the two components represented by the arrows, or the transfer of mass from one to the other.
The compositional loading plot is more or less a standard one. The loadings are displayed by a barplot as positve and negative changes of amounts.
The loading plot can work in two different modes: If scale.sdev is set to NA it displays the composition being represented by the unit vector of loadings in cpt-transformed space. If scale.sdev is numeric we use this composition scaled by the standard deviation of the respective component.
The relative plot displays the relativeLoadings as a barplot. The deviation from a unit bar shows the effect of each principal component on the respective differences.

Value

princomp gives an object of type c("princomp.rcomp","princomp") with the following content:

sdev	the standard deviation of the principal components.
loadings	the matrix of variable loadings (i.e., a matrix which columns contain the eigenvectors). This is of class "loadings". The last eigenvalue is removed since it should contain the irrelevant scaling.
Loadings	the loadings as an rmult-object
center	the cpt-transformed vector of means used to center the dataset
Center	the rcomp vector of means used to center the dataset
scale	the scaling applied to each variable
n.obs	number of observations
scores	if scores = TRUE, the scores of the supplied data on the principal components. Scores are coordinates in a basis given by the principal components and thus not compositions
call	the matched call
na.action	not clearly understood

predict returns a matrix of scores of the observations in the newdata dataset. The other routines are mainly called for their side effect of plotting or printing and return the object x.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

cpt,rcomp, relativeLoadings princomp.acomp, princomp.rplus,

Examples

data(SimulatedAmounts)
pc <- princomp(rcomp(sa.lognormals5))
pc
summary(pc)
plot(pc)           #plot(pc,type="screeplot")
plot(pc,type="v")
plot(pc,type="biplot")
plot(pc,choice=c(1,3),type="biplot")
plot(pc,type="loadings")
plot(pc,type="loadings",scale.sdev=-1) # Downward
plot(pc,type="relative",scale.sdev=NA) # The directions
plot(pc,type="relative",scale.sdev=1) # one sigma Upward 
plot(pc,type="relative",scale.sdev=-1) # one sigma Downward
biplot(pc)
screeplot(pc)
loadings(pc)
relativeLoadings(pc,mult=FALSE)
relativeLoadings(pc)
relativeLoadings(pc,scale.sdev=1)
relativeLoadings(pc,scale.sdev=2)

pc$sdev^2
cov(predict(pc,sa.lognormals5))

compositions documentation built on April 14, 2023, 12:26 a.m.