funsZcell.nnct: Dixon's Cell-specific Z Tests of Segregation for NNCT

In nnspat: Nearest Neighbor Methods for Spatial Patterns

Dixon's Cell-specific Z Tests of Segregation for NNCT

Description

Two functions: Zcell.nnct.ct and Zcell.nnct.

Both functions are objects of class "cellhtest" but with different arguments (see the parameter list below). Each one performs hypothesis tests of deviations of cell counts from the expected values under RL or CSR for each cell (i.e., entry) in the NNCT. The test for each cell i,j is based on the normal approximation of the corresponding cell count, N_{ij} and are due to \insertCitedixon:1994,dixon:NNCTEco2002;textualnnspat.

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, sample estimates (i.e., observed values) for the cell counts and also names of the test statistics, estimates, null values, the description of the test, and the data set used.

The null hypothesis for each cell i,j is that the corresponding cell count is equal to the expected value under RL or CSR, that is E[N_{ii}] = n_i(n_i - 1)/(n - 1) and E[N_{ij}] = n_i n_j/(n - 1) where n_i is the size of class i and n is the size of the data set.

See also (\insertCitedixon:1994,dixon:NNCTEco2002,ceyhan:eest-2010;textualnnspat).

Usage

Zcell.nnct.ct(
  ct,
  varN,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95
)

Zcell.nnct(
  dat,
  lab,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  ...
)

Arguments

ct	A nearest neighbor contingency table, used in Zcell.nnct.ct only
varN	The variance matrix for cell counts in the NNCT, ct; used in Zcell.nnct.ct only
alternative	Type of the alternative hypothesis in the test, one of "two.sided", "less" or "greater".
conf.level	Level of the upper and lower confidence limits, default is 0.95, for the cell counts, i.e. N_{ij} values
dat	The data set in one or higher dimensions, each row corresponds to a data point, used in Zcell.nnct only
lab	The vector of class labels (numerical or categorical), used in Zcell.nnct only
...	are for further arguments, such as method and p, passed to the dist function, used in Zcell.nnct only

Value

A list with the elements

statistic	The matrix of Dixon's cell-specific test statistics
stat.names	Name of the test statistics
p.value	The matrix of p-values for the hypothesis test for the corresponding alternative
LCL, UCL	Matrix of lower and upper confidence levels for the cell counts at the given confidence level conf.level and depends on the type of alternative.
conf.int	The confidence interval for the estimates, it is NULL here, since we provide the UCL and LCL in matrix form.
cnf.lvl	Level of the upper and lower confidence limits of the cell counts, provided in conf.level.
estimate	Estimates of the parameters, i.e., matrix of the observed cell counts which is the NNCT
est.name, est.name2	Names of the estimates, both are same in this function
null.value	Matrix of hypothesized null values for the parameters which are expected values of the cell counts.
null.name	Name of the null values
alternative	Type of the alternative hypothesis in the test, one of "two.sided", "less" or "greater"
method	Description of the hypothesis test
ct.name	Name of the contingency table, ct, returned by Zcell.nnct.ct only
data.name	Name of the data set, dat, returned by Zcell.nnct only

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

Zcell.nnct.2s, Zcell.nnct.rs, Zcell.nnct.ls, Zcell.nnct.pval, and Zcell.tct

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)
varN

Zcell.nnct(Y,cls)
Zcell.nnct(Y,cls,alt="g")

Zcell.nnct.ct(ct,varN)
Zcell.nnct.ct(ct,varN,alt="g")

Zcell.nnct(Y,cls,method="max")

#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
Zcell.nnct(Y,cls)

#############
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)

Zcell.nnct(Y,cls)
Zcell.nnct.ct(ct,varN)

nnspat documentation built on May 29, 2024, 10:03 a.m.