# varAcomp: Variances and covariances of amounts and compositions In compositions: Compositional Data Analysis

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38``` ``` 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 `var` `use` see `var` `method` see `cov` `...` further arguments to `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 `var`, `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, `var` and `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

`cdt`, `clrvar2ilr`, `clo`, `mean.acomp`, `acomp`, `rcomp`, `aplus`, `rplus`, `variation`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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))) ```