funs.cell.spec.ss: Pielou's Cell-specific Segregation Test with Normal Approximation (for Sparse Sampling)

Description

Two functions: cell.spec.ss.ct and cell.spec.ss.

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 cell counts (i.e., entries) in the NNCT for \(k \ge 2\) classes. Each test is appropriate (i.e., have the appropriate asymptotic sampling distribution) when that data is obtained by sparse sampling.

Each cell-specific segregation test is based on the normal approximation of the entries in the NNCT and are due to pielou:1961;textualnnspat.

Each function yields a contingency table of the test statistics, \(p\)-values for the corresponding alternative, expected values, lower and upper confidence levels, sample estimates (i.e., observed values) and null value(s) (i.e., expected values) for the \(N_{ij}\) values for \(i,j=1,2,\ldots,k\) 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 \(E(N_{ij})=n_i c_j /n\) where \(n_i\) is the sum of row \(i\) (i.e., size of class \(i\)) \(c_j\) is the sum of column \(j\) in the \(k \times k\) NNCT for \(k \ge 2\). In the output, the test statistic, \(p\)-value and the lower and upper confidence limits are valid only for (properly) sparsely sampled data.

See also (pielou:1961,ceyhan:eest-2010;textualnnspat) and the references therein.

Usage

cell.spec.ss.ct(
  ct,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95
)
cell.spec.ss(
  dat,
  lab,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  ...
)

Value

A list with the elements

statistic: The matrix of \(Z\) test statistics for cell-specific tests
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 entries \(N_{ij}\) in the NNCT 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 (i.e., conf.level) of the NNCT entries.
estimate: Estimates of the parameters, i.e., matrix of the NNCT entries of the \(k \times k\) NNCT, Nij for i,j=1,2,...,k.
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 values of the NNCT entries, E(Nij) for i,j=1,2,...,k.
null.name: Name of the null values
alternative: Type of the alternative hypothesis in the test, one of "two.sided", "less", "greater"
method: Description of the hypothesis test
ct.name: Name of the contingency table, ct, returned by cell.spec.ss.ct only
data.name: Name of the data set, dat, returned by cell.spec.ss only

Arguments

ct: A nearest neighbor contingency table, used in cell.spec.ss.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 entries, \(N_{ij}\) in the NNCT
dat: The data set in one or higher dimensions, each row corresponds to a data point, used in cell.spec.ss only
lab: The vector of class labels (numerical or categorical), used in cell.spec.ss only
...: are for further arguments, such as method and p, passed to the dist function. used in cell.spec.ss 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)

cell.spec.ss(Y,cls)
cell.spec.ss.ct(ct)
cell.spec.ss.ct(ct,alt="g")

cell.spec.ss(Y,cls,method="max")

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

cell.spec.ss(Y,fcls)
cell.spec.ss.ct(ct)

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

cell.spec.ss(Y,cls,alt="l")
cell.spec.ss.ct(ct)
cell.spec.ss.ct(ct,alt="l")

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