funsZnnself.sum: Cumulative Species Correspondence Test with Normal Approximation

Description

Two functions: Znnself.sum.ct and Znnself.sum.

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 sum of the self entries (i.e. first column) in a species correspondence contingency table (SCCT) or the expected values of the sum of the diagonal entries \(N_{ii}\) in an NNCT to the one under RL or CSR. That is, each performs a cumulative species correspondence test which is appropriate (i.e., have the appropriate asymptotic sampling distribution) for completely mapped data. (See ceyhan:NNCorrespond2018;textualnnspat for more detail).

Each test is based on the normal approximation of the sum of the self entries (i.e., first column) in a species correspondence contingency table (SCCT) or the sum of the diagonal entries \(N_{ii}\) in an NNCT and are due to ceyhan:NNCorrespond2018nnspat.

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 sum of the self entries (i.e., first column) in a species correspondence contingency table (SCCT) or the sum of the diagonal entries \(N_{ii}\) in an NNCT, and method and name of the data set used.

The null hypothesis is that all \(E[S] = \sum_{i=1}^k n_i(n_i - 1)/(n - 1)\) where \(S\) is the sum of the self column in the SCCT, \(n_i\) is the size of class \(i\) and \(n\) is the data size.

The Znnself.sum functions (i.e., Znnself.sum.ct and Znnself.sum) are different from the Znnself functions (i.e., Znnself.ct and Znnself), and from the Znnref functions (i.e., Znnref.ct and Znnref) and also from Zself.ref functions (i.e., Zself.ref.ct and Zself.ref). Znnself.sum functions are testing the cumulative species correspondence using the sum of the self column (i.e., the first column) in the SCCT, while Znnself functions are testing the self reflexivity at a class-specific level (i.e., for each class) using the first column in the SCCT, while Zself.ref functions are for testing the self reflexivity for the entire data set using entry \((1,1)\) in RCT, and Znnref functions are for testing the self reflexivity and mixed non-reflexivity using the diagonal entries in the RCT.

Usage

Znnself.sum.ct(
  ct,
  covSC,
  nnct = FALSE,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95
)
Znnself.sum(
  dat,
  lab,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  ...
)

Value

A list with the elements

statistic: The \(Z\) test statistic for the overall species correspondence test
p.value: The \(p\)-value for the hypothesis test for the corresponding alternative
conf.int: Confidence interval for the sum of the self entries (i.e., first column) in a species correspondence contingency table (SCCT) or the sum of the diagonal entries \(N_{ii}\) in an NNCT at the given confidence level conf.level and depends on the type of alternative.
estimate: Estimate of the parameter, i.e., the observed sum of the self entries (i.e., first column) in a species correspondence contingency table (SCCT) or the sum of the diagonal entries \(N_{ii}\) in an NNCT.
null.value: Hypothesized null value for the sum of the self entries (i.e., first column) in a species correspondence contingency table (SCCT) or the sum of the diagonal entries \(N_{ii}\) in an NNCT which is \(E[S] = \sum_{i=1}^k n_i(n_i - 1)/(n - 1)\) where \(S\) is the sum of the self column in the SCCT, \(n_i\) is the size of class \(i\) and \(n\) is the data size.
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 Znnself.sum.ct only
data.name: Name of the data set, dat, returned by Znnself.sum only

Arguments

ct: The NNCT or SCCT, used in Znnself.sum.ct only
covSC: The covariance matrix for the self entries (i.e., first column) in the SCCT or the diagonal entries in the NNCT, used in Znnself.sum.ct only. Usually output of the functions covNii.ct or covNii.
nnct: A logical parameter (default=FALSE). If TRUE, x is taken to be the \(k \times k\) NNCT, and if FALSE, x is taken to be the IPD matrix, used in Znnself.sum.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 self entries in the SCCT or diagonal entries in the NNCT
dat: The data set in one or higher dimensions, each row corresponds to a data point, used in Znnself.sum only
lab: The vector of class labels (numerical or categorical), used in Znnself.sum only
...: are for further arguments, such as method and p, passed to the dist function. used in Znnself.sum 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<-scct(ipd,cls)
ct

W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)

vsq<-varNii.ct(ct,Qv,Rv)
cv<-covNii.ct(ct,vsq,Qv,Rv)

Znnself.sum(Y,cls)

Znnself.sum.ct(ct,cv)
Znnself.sum.ct(ct,cv,alt="g")

Znnself.sum(Y,cls,method="max")

ct<-nnct(ipd,cls)
Znnself.sum.ct(ct,cv,nnct = TRUE)

#############
n<-40
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(1:4,n,replace = TRUE)  #or try cls<-rep(1:2,c(10,10))
ipd<-ipd.mat(Y)
ct<-scct(ipd,cls)

W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)

vsq<-varNii.ct(ct,Qv,Rv)
cv<-covNii.ct(ct,vsq,Qv,Rv)

Znnself.sum(Y,cls)

Znnself.sum.ct(ct,cv)
Znnself.sum.ct(ct,cv,alt="g")

ct<-nnct(ipd,cls)
Znnself.sum.ct(ct,cv,nnct = TRUE)

Znnself.sum(Y,cls,alt="g")

Run the code above in your browser using DataLab