funsZdir.nnct.ss: Directional Segregation Test for Two Classes with Normal...

In nnspat: Nearest Neighbor Methods for Spatial Patterns

Directional Segregation Test for Two Classes with Normal Approximation (for Sparse Sampling)

Description

Two functions: Zdir.nnct.ss.ct and Zdir.nnct.ss.

Both functions are objects of class "htest" but with different arguments (see the parameter list below). Each one performs hypothesis tests of independence in the 2 \times 2 NNCT which implies Z_P=0 or equivalently N_{11}/n_1=N_{21}/n_2. Z_P=(N_{11}/n_1-N_{21}/n_2)√{n_1 n_2 n/(C_1 C_2)} where N_{ij} is the cell count in entry i,j, n_i is the sum of row i (i.e. size of class i), c_j is the sum of column j in the 2 \times 2 NNCT; N_{11}/n_1 and N_{21}/n_2 are also referred to as the phat estimates in row-wise binomial framework for 2 \times 2 NNCT (see \insertCiteceyhan:jnps-NNCT-2010;textualnnspat).

That is, each performs directional (i.e. one-sided) tests based on the 2 \times 2 NNCT and is appropriate (i.e. have the appropriate asymptotic sampling distribution) when that data is obtained by sparse sampling. (See \insertCiteceyhan:jnps-NNCT-2010;textualnnspat for more detail).

Each test is based on the normal approximation of Z_P which is the directional Z-tests for the chi-squared tests of independence for the contingency tables \insertCitebickel:1977nnspat.

Each function yields the test statistic, p-value for the corresponding alternative, the confidence interval, sample estimate (i.e. observed value) and null (i.e., expected) value for the difference in the phat values (which is 0 for this test) in an NNCT, and method and name of the data set used.

The null hypothesis is that E[Z_P] = 0 or equivalently N_{11}/n_1 = N_{21}/n_2.

Usage

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

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

Arguments

ct	The NNCT, used in Zdir.nnct.ss.ct only
alternative	Type of the alternative hypothesis in the test, one of "two.sided", "less" or "greater".
conf.level	Level of the confidence limits, default is 0.95, for the difference in phat values in the NNCT
dat	The data set in one or higher dimensions, each row corresponds to a data point, used in Zdir.nnct.ss only
lab	The vector of class labels (numerical or categorical), used in Zdir.nnct.ss only
...	are for further arguments, such as method and p, passed to the dist function. used in Zdir.nnct.ss only

Value

A list with the elements

statistic	The Z test statistic for the directional (i.e. one-sided) test of segregation based on the NNCT
p.value	The p-value for the hypothesis test for the corresponding alternative
conf.int	Confidence interval for the difference in phat values in the NNCT at the given confidence level conf.level and depends on the type of alternative.
estimate	Estimate of the parameter, i.e., the observed difference in phat values in the NNCT.
null.value	Hypothesized null value for the difference in phat values in the 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
ct.name	Name of the contingency table, ct, returned by Zdir.nnct.ss.ct only
data.name	Name of the data set, dat, returned by Zdir.nnct.ss only

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

Zdir.nnct.ct, Zdir.nnct, Pseg.ss.ct and Pseg.ss

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

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

Zdir.nnct.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)

Zdir.nnct.ss(Y,fcls)
Zdir.nnct.ss.ct(ct)

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

nnspat documentation built on Aug. 30, 2022, 9:06 a.m.