| Xsq.nnsym {nnspat} | R Documentation |
Overall NN Symmetry Test with Chi-square Approximation
Description
An object of class "Chisqtest" performing the hypothesis test of equality of the expected
values of the off-diagonal cell counts (i.e., entries) under RL or CSR in the NNCT for k \ge 2 classes.
That is, the test performs Dixon's or Pielou's (first type of) overall NN symmetry test which is appropriate
(i.e., have the appropriate asymptotic sampling distribution)
for completely mapped data or for sparsely sample data, respectively.
(See Pielou (1961); Dixon (1994); Ceyhan (2014) for more detail).
The type="dixon" refers to Dixon's overall NN symmetry test and
type="pielou" refers to Pielou's first type of overall NN symmetry test.
The symmetry test is based on the chi-squared approximation of the corresponding quadratic form
and type="dixon" yields an extension of Dixon's NN symmetry test, which is extended by
Ceyhan (2014) and type="pielou" yields
Pielou's overall NN symmetry test.
The function yields the test statistic, p-value and df which is k(k-1)/2, description of the
alternative with the corresponding null values (i.e., expected values) of differences of the off-diagonal entries,(which is
0 for this function) and also the sample estimates (i.e., observed values) of absolute differences of the off-diagonal entries of
NNCT (in the upper-triangular form).
The functions also provide names of the test statistics, the description of the test and the data set used.
The null hypothesis is that all E(N_{ij})=E(N_{ji}) for i \ne j in the k \times k NNCT (i.e., symmetry in the
mixed NN structure) for k \ge 2.
In the output, if if type="pielou",
the test statistic, p-value and the df are valid only for (properly) sparsely sampled data.
See also (Pielou (1961); Dixon (1994); Ceyhan (2014)) and the references therein.
Usage
Xsq.nnsym(dat, lab, type = "dixon", ...)
Arguments
dat |
The data set in one or higher dimensions, each row corresponds to a data point. |
lab |
The |
type |
The type of the overall NN symmetry test with default= |
... |
are for further arguments, such as |
Value
A list with the elements
statistic |
The chi-squared test statistic for Dixon's or Pielou's (first type of) overall NN symmetry test |
stat.names |
Name of the test statistic |
p.value |
The |
df |
Degrees of freedom for the chi-squared test, which is |
estimate |
Estimates, i.e., absolute differences of the off-diagonal entries of NNCT (in the upper-triangular form). |
est.name, est.name2 |
Names of the estimates, former is a shorter description of the estimates than the latter. |
null.value |
Hypothesized null values for the differences between the expected values of the off-diagonal entries, which is 0 for this function. |
method |
Description of the hypothesis test |
data.name |
Name of the data set, |
Author(s)
Elvan Ceyhan
References
Ceyhan E (2014).
“Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations.”
The Scientific World Journal, Volume 2014, Article ID 698296.
Dixon PM (1994).
“Testing spatial segregation using a nearest-neighbor contingency table.”
Ecology, 75(7), 1940-1948.
Pielou EC (1961).
“Segregation and symmetry in two-species populations as studied by nearest-neighbor relationships.”
Journal of Ecology, 49(2), 255-269.
See Also
Znnsym.ss, Znnsym.dx and Znnsym2cl
Examples
n<-20 #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(1:2,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10))
Xsq.nnsym(Y,cls)
Xsq.nnsym(Y,cls,method="max")
Xsq.nnsym(Y,cls,type="pielou")
#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
Xsq.nnsym(Y,fcls)
Xsq.nnsym(Y,fcls,type="pielou")
#############
n<-40
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(1:4,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10))
Xsq.nnsym(Y,cls)
Xsq.nnsym(Y,cls,type="pielou")