Compositional Goodness of fit test
Goodness of fit tests for count compositional data.
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)
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. |
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.
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 |
Up to now the tests can not handle missings.
K.Gerald v.d. Boogaart http://www.stat.boogaart.de
Aitchison, J. (1986) The Statistical Analysis of Compositional
Data Monographs on Statistics and Applied Probability. Chapman &
Hall Ltd., London (UK). 416p.
## 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)
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