funsZsegind: Z Tests for Segregation Indices

Description

Two functions: Zseg.ind.ct and Zseg.ind.

Both functions are objects of class "cellhtest" but with different arguments (see the parameter list below). Each one performs hypothesis tests of deviations of segregation indices from their expected values under RL or CSR for each segregation index in the NNCT. The test for each cell $i, j$ is based on the normal approximation of the corresponding segregation index.

Each function yields a contingency table of the test statistics, $p$ -values for the corresponding alternative, lower and upper confidence levels, sample estimates (i.e., observed values) and null value(s) (i.e., expected values) for the segregation indices and also names of the test statistics, estimates, null value, the description of the test, and the data set used.

The null hypothesis for each cell $i, j$ is that the corresponding segregation index equal to the expected value (which is 0) under RL or CSR.

See also (ceyhan:SiM-seg-ind2014;textualnnspat).

Usage

Zseg.ind.ct(
  ct,
  varN,
  inf.corr = FALSE,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95
)
Zseg.ind(
  dat,
  lab,
  inf.corr = FALSE,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  ...
)

Value

A list with the elements

statistic: The matrix of test statistics for the segregation indices
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 segregation indices at the given confidence level conf.level and depends on the type of alternative.
cnf.lvl: Level of the upper and lower confidence limits of the segregation indices, provided in conf.level.
estimate: Estimate of the parameter, i.e., matrix of the observed segregation indices
est.name,est.name2: Names of the estimates, both are same in this function
null.value: Hypothesized values for the parameters, i.e., the null values of the segregation indices, which are all 0 under RL or CSR.
null.name: Name of the null value
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 Zseg.ind.ct only
data.name: Name of the data set, dat, returned by Zseg.ind only

Arguments

ct: A nearest neighbor contingency table, used in Zseg.ind.ct only
varN: The variance matrix for cell counts in the NNCT, ct; used in Zseg.ind.ct only
inf.corr: A logical argument (default=FALSE). If TRUE, indices are modified so that they are finite and if FALSE the above definition in the description is used.
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 segregation indices
dat: The data set in one or higher dimensions, each row corresponds to a data point, used in Zseg.ind only
lab: The vector of class labels (numerical or categorical), used in Zseg.ind only
...: are for further arguments, such as method and p, passed to the dist function, used in Zseg.ind 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

seg.ind(ct)
seg.ind(ct,inf.corr=TRUE)
W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)
varN

Zseg.ind(Y,cls)
Zseg.ind(Y,cls,inf.corr=TRUE)
Zseg.ind.ct(ct,varN)

Zseg.ind(Y,cls,alt="g")
Zseg.ind.ct(ct,varN,alt="g")

Zseg.ind(Y,cls,method="max")

#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
Zseg.ind(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)
varN

Zseg.ind(Y,cls)
Zseg.ind(Y,cls,inf.corr = TRUE)

Zseg.ind.ct(ct,varN)
Zseg.ind.ct(ct,varN,inf.corr = TRUE)

#1D data points
n<-20  #or try sample(1:20,1)
X<-as.matrix(runif(n))# need to be entered as a matrix with one column
#(i.e., a column vector), hence X<-runif(n) would not work
ipd<-ipd.mat(X)
cls<-sample(1:2,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)

Zseg.ind(X,cls)
Zseg.ind.ct(ct,varN)
Zseg.ind.ct(ct,varN,inf.corr=TRUE)

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