funsXsq.nnsym.ss: Pielou's First Type of NN Symmetry Test with Chi-square Approximation for multiple classes (for Sparse Sampling)

Description

Two functions: Xsq.nnsym.ss.ct and Xsq.nnsym.ss.

Both functions are objects of class "Chisqtest" but with different arguments (see the parameter list below). Each one performs the hypothesis test of equality of the expected value of the off-diagonal cell counts (i.e., entries) under RL or CSR in the NNCT for \(k \ge 2\) classes. That is, each performs Pielou's first type of NN symmetry test which is also equivalent to McNemar's test on the NNCT. The test 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 chi-squared approximation of the corresponding quadratic form and are due to pielou:1961;textualnnspat.

The argument cont.corr is a logical argument (default=TRUE) for continuity correction to this test. If TRUE the continuity correction to McNemar's test is implemented, and if FALSE such a correction is not implemented.

Each function yields the test statistic, \(p\)-value and df which is \(k(k-1)/2\), description of the alternative with the corresponding null values (i.e., expected values) of differences of the off-diagonal entries,(which is 0 for this function) and also the sample estimates (i.e., observed values) of absolute differences of th off-diagonal entries of NNCT (in the upper-triangular form). The functions also provide names of the test statistics, the description of the test and the data set used.

The null hypothesis is that \(E(N_{ij})=E(N_{ji})\) for all entries for \(i \ne j\) (i.e., symmetry in the mixed NN structure). In the output, the test statistic, \(p\)-value and df are valid only for (properly) sparsely sampled data.

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

Usage

Xsq.nnsym.ss.ct(ct, cont.corr = TRUE)
Xsq.nnsym.ss(dat, lab, cont.corr = TRUE, ...)

Value

A list with the elements

statistic: The chi-squared test statistic for Pielou's first type of NN symmetry test
stat.names: Name of the test statistic
p.value: The \(p\)-value for the hypothesis test
df: Degrees of freedom for the chi-squared test, which is \(k(k-1)/2\) for this function.
estimate: Estimates, i.e., absolute differences of the off-diagonal entries of NNCT (in the upper-triangular form).
est.name,est.name2: Names of the estimates, former is a shorter description of the estimates than the latter.
null.value: Hypothesized null values for the differences between the expected values of the off-diagonal entries, which is 0 for this function.
method: Description of the hypothesis test
ct.name: Name of the contingency table, ct, returned by Xsq.nnsym.ss.ct only
data.name: Name of the data set, dat, returned by Xsq.nnsym.ss only

Arguments

ct: A nearest neighbor contingency table, used in Xsq.nnsym.ss.ct only
cont.corr: A logical argument (default=TRUE). If TRUE the continuity correction to McNemar's test is implemented, and if FALSE such a correction is not implemented.
dat: The data set in one or higher dimensions, each row corresponds to a data point, used in Xsq.nnsym.ss only
lab: The vector of class labels (numerical or categorical), used in Xsq.nnsym.ss only
...: are for further arguments, such as method and p, passed to the dist function. used in Xsq.nnsym.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

Xsq.nnsym.ss(Y,cls)
Xsq.nnsym.ss.ct(ct)

Xsq.nnsym.ss(Y,cls,method="max")

Xsq.nnsym.ss(Y,cls,cont.corr=FALSE)
Xsq.nnsym.ss.ct(ct,cont.corr=FALSE)

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

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

Xsq.nnsym.ss(Y,cls)
Xsq.nnsym.ss.ct(ct)
Xsq.nnsym.ss.ct(ct,cont.corr = FALSE)

Run the code above in your browser using DataLab