R: Compositional Goodness of fit test

gof {compositions} | R Documentation

## Compositional Goodness of fit test

### Description

Goodness of fit tests for compositional data.

### Usage

    acompGOF.test(x,...)
    acompNormalGOF.test(x,...,method="etest")
    ## S3 method for class 'formula'
    acompGOF.test(formula, data,...,method="etest")
    ## S3 method for class 'list'
    acompGOF.test(x,...,method="etest")
    gsi.acompUniformityGOF.test(x,samplesize=nrow(x)*20,R=999)
    acompTwoSampleGOF.test(x,y,...,method="etest",data=NULL)

### Arguments

`x` | a dataset of compositions (acomp)
`y` | a dataset of compositions (acomp)
`samplesize` | number of observations in a reference sample specifying the distribution to compare with. Typically substantially larger than the sample under investigation
`R` | The number of replicates to compute the distribution of the test statistic
`method` | Selecting a method to be used. Currently only "etest" for using an energy test is supported.
`...` | further arguments to the methods
`formula` | an anova model formula defining groups in the dataset
`data` | unused

### Details

The compositional goodness of fit testing problem is essentially a multivariate goodness of fit test. However there is a lack of standardized multivariate goodness of fit tests in R. Some can be found in the `energy`-package.

In principle there is only one test behind the Goodness of fit tests provided here, a two sample test with test statistic.

\frac{∑_{ij} k(x_i,y_i)}{√{∑_{ij} k(x_i,x_i)∑_{ij} k(y_i,y_i)}}

The idea behind that statistic is to measure the cos of an angle between the distributions in a scalar product given by

(X,Y)=E[k(X,Y)]=E[\int K(x-X)K(x-Y) dx]

where k and K are Gaussian kernels with different spread. The bandwith is actually the standarddeviation of k.
The other goodness of fit tests against a specific distribution are based on estimating the parameters of the distribution, simulating a large dataset of that distribution and apply the two sample goodness of fit test.

For the moment, this function covers: two-sample tests, uniformity tests and additive logistic normality tests. Dirichlet distribution tests will be included soon.

### Value

A classical `"htest"` object

`data.name` | The name of the dataset as specified
`method` | a name for the test used
`alternative` | an empty string
`replicates` | a dataset of p-value distributions under the Null-Hypothesis got from nonparametric bootstrap
`p.value` | The p.value computed for this test

### Missing Policy

Up to now the tests can not handle missings.

### Author(s)

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

### References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

### See Also

`fitDirichlet`,`rDirichlet`, `runif.acomp`, `rnorm.acomp`,

### Examples

    ## Not run:
    x <- runif.acomp(100,4)
    y <- runif.acomp(100,4)

    erg <- acompTwoSampleGOF.test(x,y)
    #continue
    erg
    unclass(erg)
    erg <- acompGOF.test(x,y)

    x <- runif.acomp(100,4)
    y <- runif.acomp(100,4)
    dd <- replicate(1000,acompGOF.test(runif.acomp(100,4),runif.acomp(100,4))$p.value)
    hist(dd)

    dd <- replicate(1000,acompGOF.test(runif.acomp(20,4),runif.acomp(100,4))$p.value)
    hist(dd)
    dd <- replicate(1000,acompGOF.test(runif.acomp(10,4),runif.acomp(100,4))$p.value)

    hist(dd)
    dd <- replicate(1000,acompGOF.test(runif.acomp(10,4),runif.acomp(400,4))$p.value)
    hist(dd)
    dd <- replicate(1000,acompGOF.test(runif.acomp(400,4),runif.acomp(10,4),bandwidth=4)$p.value)
    hist(dd)

    dd <- replicate(1000,acompGOF.test(runif.acomp(20,4),runif.acomp(100,4)+acomp(c(1,2,3,1)))$p.value)

    hist(dd)

    # test uniformity

    attach("gsi") # the uniformity test is only available as an internal function
    x <- runif.acomp(100,4)
    gsi.acompUniformityGOF.test.test(x)

    dd <- replicate(1000,gsi.acompUniformityGOF.test.test(runif.acomp(10,4))$p.value)
    hist(dd)
    detach("gsi")

    ## End(Not run)

[Package compositions version 2.0-0 Index]