funsZnnsym.dx {nnspat} | R Documentation |
Dixon's Pairwise NN Symmetry Test with Normal Approximation
Description
Two functions: Znnsym.dx.ct
and Znnsym.dx
.
Both functions are objects of class "cellhtest"
but with different arguments (see the parameter list below).
Each one performs hypothesis tests of equality of the expected values of the off-diagonal
cell counts (i.e., entries) for each pair i,j
of classes under RL or CSR in the NNCT for k \ge 2
classes.
That is, each performs Dixon's NN symmetry test which is appropriate
(i.e., have the appropriate asymptotic sampling distribution)
for completely mapped data.
(See Dixon (1994); Ceyhan (2014) for more detail).
Each symmetry test is based on the normal approximation of the difference of the off-diagonal entries in the NNCT and are due to Dixon (1994).
Each function yields a contingency table of the test statistics, p
-values for the corresponding
alternative, expected values (i.e., null value(s)), lower and upper confidence levels and sample estimates (i.e., observed values)
for the N_{ij}-N_{ji}
values for i \ne j
(all in the upper-triangular form except for the null value, which is 0
for all pairs) and also names of the test statistics, estimates, null values, 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, the test statistic, p
-value and the lower and upper confidence limits are valid
for completely mapped data.
See also (Dixon (1994); Ceyhan (2014)) and the references therein.
Usage
Znnsym.dx.ct(
ct,
varS,
alternative = c("two.sided", "less", "greater"),
conf.level = 0.95
)
Znnsym.dx(
dat,
lab,
alternative = c("two.sided", "less", "greater"),
conf.level = 0.95,
...
)
Arguments
ct |
A nearest neighbor contingency table, used in |
varS |
The variance vector of differences of off-diagonal cell counts in NNCT, |
alternative |
Type of the alternative hypothesis in the test, one of |
conf.level |
Level of the upper and lower confidence limits, default is |
dat |
The data set in one or higher dimensions, each row corresponds to a data point,
used in |
lab |
The |
... |
are for further arguments, such as |
Value
A list
with the elements
statistic |
The |
stat.names |
Name of the test statistics |
p.value |
The |
LCL , UCL |
Matrix of Lower and Upper Confidence Levels (in the upper-triangular form) for the |
conf.int |
The confidence interval for the estimates, it is |
cnf.lvl |
Level of the upper and lower confidence limits (i.e., conf.level) of the differences of the off-diagonal entries. |
estimate |
Estimates of the parameters, i.e., matrix of the difference of the off-diagonal entries
(in the upper-triangular form) of the |
est.name , est.name2 |
Names of the estimates, former is a shorter description of the estimates than the latter. |
null.value |
Hypothesized null value for the expected difference between the off-diagonal entries,
|
null.name |
Name of the null values |
alternative |
Type of the alternative hypothesis in the test, one of |
method |
Description of the hypothesis test |
ct.name |
Name of the contingency table, |
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.
See Also
Znnsym2cl.dx.ct
, Znnsym2cl.dx
, Znnsym.ss.ct
,
Znnsym.ss
, Xsq.nnsym.dx.ct
and Xsq.nnsym.dx
Examples
n<-20 #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
cls<-sample(1:2,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10))
ct<-nnct(ipd,cls)
ct
W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)
covN<-cov.nnct(ct,varN,Qv,Rv) #default is byrow
varS<-var.nnsym(covN)
Znnsym.dx(Y,cls)
Znnsym.dx.ct(ct,varS)
Znnsym.dx(Y,cls,method="max")
Znnsym.dx(Y,cls,alt="g")
Znnsym.dx.ct(ct,varS,alt="g")
#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
Znnsym.dx(Y,fcls)
#############
n<-40
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
cls<-sample(1:4,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10))
ct<-nnct(ipd,cls)
W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)
covN<-cov.nnct(ct,varN,Qv,Rv) #default is byrow
varS<-var.nnsym(covN)
Znnsym.dx(Y,cls)
Znnsym.dx.ct(ct,varS)