gof {compositions}

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{\sum_{ij} k(x_i,y_i)}{\sqrt{\sum_{ij} k(x_i,x_i)\sum_{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)