varAcomp: Variances and covariances of amounts and compositions

In compositions: Compositional Data Analysis

Variances and covariances of amounts and compositions

Description

Compute the (co)variance matrix in the several approaches of compositional and amount data analysis.

Usage

  var(x,...)
    ## Default S3 method:
var(x, y=NULL, na.rm=FALSE, use, ...)
    ## S3 method for class 'acomp'
var(x,y=NULL,...,robust=getOption("robust"), 
       use="all.obs",giveCenter=FALSE)
    ## S3 method for class 'rcomp'
var(x,y=NULL,...,robust=getOption("robust"), 
       use="all.obs",giveCenter=FALSE)
    ## S3 method for class 'aplus'
var(x,y=NULL,...,robust=getOption("robust"), 
       use="all.obs",giveCenter=FALSE)
    ## S3 method for class 'rplus'
var(x,y=NULL,...,robust=getOption("robust"), 
       use="all.obs",giveCenter=FALSE)
    ## S3 method for class 'rmult'
var(x,y=NULL,...,robust=getOption("robust"), 
       use="all.obs",giveCenter=FALSE)
  cov(x,y=x,...)
    ## Default S3 method:
cov(x, y=NULL, use="everything", 
       method=c("pearson", "kendall", "spearman"), ...)
    ## S3 method for class 'acomp'
cov(x,y=NULL,...,robust=getOption("robust"), 
       use="all.obs",giveCenter=FALSE)
    ## S3 method for class 'rcomp'
cov(x,y=NULL,...,robust=getOption("robust"), 
       use="all.obs",giveCenter=FALSE)
    ## S3 method for class 'aplus'
cov(x,y=NULL,...,robust=getOption("robust"), 
       use="all.obs",giveCenter=FALSE)
    ## S3 method for class 'rplus'
cov(x,y=NULL,...,robust=getOption("robust"), 
       use="all.obs",giveCenter=FALSE)
    ## S3 method for class 'rmult'
cov(x,y=NULL,...,robust=getOption("robust"), 
    use="all.obs",giveCenter=FALSE)
          

Arguments

x	a dataset, eventually of amounts or compositions
y	a second dataset, eventually of amounts or compositions
na.rm	see stats::var

use	see stats::var

method

see stats::cov

...	further arguments to stats::var e.g. use
robust	A description of a robust estimator. FALSE for the classical estimators. See robustnessInCompositions for further details.
giveCenter	If TRUE the center used in the variance calculation is reported as a "center" attribute. This is especially necessary for robust estimations, where a reasonable center can not be computed independently for the me variance calculation.

Details

The basic functions of stats::var and stats::cov are turned to S3-generics. The original versions are copied to the default method. This allows us to introduce generic methods to handle variances and covariances of other data types, such as amounts or compositions.
If classed amounts or compositions are involved, they are transformed with their corresponding transforms, using the centered default transform (cdt). That implies that the variances have to be interpreded in a log scale level for acomp and aplus.
We should be aware that variance matrices of compositions (acomp and rcomp) are singular. They can be transformed to the correponding nonsingular variances of ilr or ipt-space by clrvar2ilr.

In R versions older than v2.0.0, stats::var and stats::cov were defined in package “base” instead of in “stats”. This might produce some misfunction.

Value

The variance matrix of x or the covariance matrix of x and y.

Author(s)

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

See Also

cdt, clrvar2ilr, clo, mean.acomp, acomp, rcomp, aplus, rplus, variation

Examples

data(SimulatedAmounts)
meanCol(sa.lognormals)
var(acomp(sa.lognormals))
var(rcomp(sa.lognormals))
var(aplus(sa.lognormals))
var(rplus(sa.lognormals))
cov(acomp(sa.lognormals5[,1:3]),acomp(sa.lognormals5[,4:5]))
cov(rcomp(sa.lognormals5[,1:3]),rcomp(sa.lognormals5[,4:5]))
cov(aplus(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5]))
cov(rplus(sa.lognormals5[,1:3]),rplus(sa.lognormals5[,4:5]))
cov(acomp(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5]))

svd(var(acomp(sa.lognormals)))

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