ccompgof {compositions}

Compositional Goodness of fit test

Description

Goodness of fit tests for count compositional data.

Usage

PoissonGOF.test(x,lambda=mean(x),R=999,estimated=missing(lambda))
ccompPoissonGOF.test(x,simulate.p.value=TRUE,R=1999)
ccompMultinomialGOF.test(x,simulate.p.value=TRUE,R=1999)

Arguments

x

a dataset integer numbers (PoissonGOF) or count compositions (compPoissonGOF)

lambda

the expected value to check against

R

The number of replicates to compute the distribution of the test statistic

estimated

states whether the lambda parameter should be considered as estimated for the computation of the p-value.

simulate.p.value

should all p-values be infered by simulation.

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.

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 <- acompGOF.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)


x <- runif.acomp(100,4)
acompUniformityGOF.test(x)

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

hist(dd)


## End(Not run)