CSarc.dens.test: A test of segregation/association based on arc density of...

In pcds: Proximity Catch Digraphs and Their Applications

A test of segregation/association based on arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data

Description

An object of class "htest" (i.e., hypothesis test) function which performs a hypothesis test of complete spatial randomness (CSR) or uniformity of Xp points in the convex hull of Yp points against the alternatives of segregation (where Xp points cluster away from Yp points) and association (where Xp points cluster around Yp points) based on the normal approximation of the arc density of the CS-PCD for uniform 2D data in the convex hull of Yp points.

The function yields the test statistic, p-value for the corresponding alternative, the confidence interval, estimate and null value for the parameter of interest (which is the arc density), and method and name of the data set used.

Under the null hypothesis of uniformity of Xp points in the convex hull of Yp points, arc density of CS-PCD whose vertices are Xp points equals to its expected value under the uniform distribution and alternative could be two-sided, or left-sided (i.e., data is accumulated around the Yp points, or association) or right-sided (i.e., data is accumulated around the centers of the triangles, or segregation).

CS proximity region is constructed with the expansion parameter t>0 and CM-edge regions (i.e., the test is not available for a general center M at this version of the function).

**Caveat:** This test is currently a conditional test, where Xp points are assumed to be random, while Yp points are assumed to be fixed (i.e., the test is conditional on Yp points). Furthermore, the test is a large sample test when Xp points are substantially larger than Yp points, say at least 5 times more. This test is more appropriate when supports of Xp and Yp has a substantial overlap. Currently, the Xp points outside the convex hull of Yp points are handled with a convex hull correction factor, ch.cor, which is derived under the assumption of uniformity of Xp and Yp points in the study window, (see the description below and the function code.) However, in the special case of no Xp points in the convex hull of Yp points, arc density is taken to be 1, as this is clearly a case of segregation. Removing the conditioning and extending it to the case of non-concurring supports is an ongoing line of research of the author of the package.

ch.cor is for convex hull correction (default is "no convex hull correction", i.e., ch.cor=FALSE) which is recommended when both Xp and Yp have the same rectangular support.

See also (\insertCiteceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textualpcds).

Usage

CSarc.dens.test(
  Xp,
  Yp,
  t,
  ch.cor = FALSE,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95
)

Arguments

Xp	A set of 2D points which constitute the vertices of the CS-PCD.
Yp	A set of 2D points which constitute the vertices of the Delaunay triangles.
t	A positive real number which serves as the expansion parameter in CS proximity region.
ch.cor	A logical argument for convex hull correction, default ch.cor=FALSE, recommended when both Xp and Yp have the same rectangular support.
alternative	Type of the alternative hypothesis in the test, one of "two.sided", "less", "greater".
conf.level	Level of the confidence interval, default is 0.95, for the arc density of CS-PCD based on the 2D data set Xp.

Value

A list with the elements

statistic	Test statistic
p.value	The p-value for the hypothesis test for the corresponding alternative
conf.int	Confidence interval for the arc density at the given confidence level conf.level and depends on the type of alternative.
estimate	Estimate of the parameter, i.e., arc density
null.value	Hypothesized value for the parameter, i.e., the null arc density, which is usually the mean arc density under uniform distribution.
alternative	Type of the alternative hypothesis in the test, one of "two.sided", "less", "greater"
method	Description of the hypothesis test
data.name	Name of the data set

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

PEarc.dens.test and CSarc.dens.test1D

Examples

#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-100; ny<-5;  #try also nx<-40; ny<-10 or nx<-1000; ny<-10;

set.seed(1)
Xp<-cbind(runif(nx),runif(nx))
Yp<-cbind(runif(ny,0,.25),runif(ny,0,.25))+cbind(c(0,0,0.5,1,1),c(0,1,.5,0,1))
#try also Yp<-cbind(runif(ny,0,1),runif(ny,0,1))

plotDelaunay.tri(Xp,Yp,xlab="",ylab = "")

CSarc.dens.test(Xp,Yp,t=.5)
CSarc.dens.test(Xp,Yp,t=.5,ch=TRUE)
#try also t=1.0 and 1.5 above

pcds documentation built on May 29, 2024, 9:36 a.m.