funsZnnsym2cl.ss: Pielou's First Type of NN Symmetry Test with Normal Approximation for Two Classes (for Sparse Sampling)

Description

Two functions: Znnsym2cl.ss.ct and Znnsym2cl.ss.

Both functions are objects of class "htest" but with different arguments (see the parameter list below). Each one performs hypothesis tests of equality of the expected value of the off-diagonal cell counts (i.e., entries) under RL or CSR in the NNCT for $k = 2$ classes. That is, each performs Pielou's first type of NN symmetry test which is appropriate (i.e., have the appropriate asymptotic sampling distribution) provided that data is obtained by sparse sampling. (See ceyhan:SWJ-spat-sym2014;textualnnspat 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 pielou:1961;textualnnspat.

Each function yields the test statistic, $p$ -value for the corresponding alternative, the confidence interval, estimate and null value for the parameter of interest (which is the difference of the off-diagonal entries in the NNCT), and method and name of the data set used.

The null hypothesis is that $E (N_{12}) = E (N_{21})$ in the $2 \times 2$ NNCT (i.e., symmetry in the mixed NN structure). In the output, the test statistic, $p$ -value and the confidence interval are valid only for (properly) sparsely sampled data.

See also (pielou:1961,ceyhan:SWJ-spat-sym2014;textualnnspat) and the references therein.

Usage

Znnsym2cl.ss.ct(
  ct,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95
)
Znnsym2cl.ss(
  dat,
  lab,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  ...
)

Value

A list with the elements

statistic: The $Z$ test statistic for Pielou's first type of NN symmetry test
p.value: The $p$ -value for the hypothesis test for the corresponding alternative
conf.int: Confidence interval for the difference of the off-diagonal entries, $N_{12} - N_{21}$ in the $2 \times 2$ NNCT at the given confidence level conf.level and depends on the type of alternative.
estimate: Estimate, i.e., the difference of the off-diagonal entries of the $2 \times 2$ NNCT, $N_{12} - N_{21}$ .
null.value: Hypothesized null value for the expected difference between the off-diagonal entries, $E (N_{12}) - E (N_{21})$ in the $2 \times 2$ NNCT, which is 0 for this function.
alternative: Type of the alternative hypothesis in the test, one of "two.sided", "less", "greater"
method: Description of the hypothesis test
data.name: Name of the data set, dat, or name of the contingency table, ct

Arguments

ct: A nearest neighbor contingency table, used in Znnsym2cl.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 difference of the off-diagonal entries, $N_{12} - N_{21}$
dat: The data set in one or higher dimensions, each row corresponds to a data point, used in Znnsym2cl.ss only
lab: The vector of class labels (numerical or categorical), used in Znnsym2cl.ss only
...: are for further arguments, such as method and p, passed to the dist function. used in Znnsym2cl.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)
ct

Znnsym2cl.ss(Y,cls)
Znnsym2cl.ss.ct(ct)

Znnsym2cl.ss(Y,cls,method="max")

Znnsym.ss.ct(ct)

Znnsym2cl.ss(Y,cls,alt="g")
Znnsym2cl.ss.ct(ct,alt="g")

#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
Znnsym2cl.ss(Y,fcls)

#############
ct<-matrix(sample(1:20,4),ncol=2)
Znnsym2cl.ss.ct(ct) #gives an error message if ct<-matrix(sample(1:20,9),ncol=3)

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