Compositional Goodness of fit test
Goodness of fit tests for compositional data.
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)
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 |
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.
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 <- 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.