funsZcell.nnct: 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 dixon: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 (dixon: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,
  ...
)

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

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

Author

Elvan Ceyhan

References

Examples

Run this code

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)

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