nnspat (version 0.1.2)

Tval: \(T\) value in NN structure

Description

Returns the \(T\) value, which is the number of triplets \((z_i, z_j, z_k)\) with "\(NN(z_i) = NN(z_j) = z_k\) and \(NN(z_k) = z_j\)" where \(NN(\cdot)\) is the nearest neighbor function. Note that in the NN digraph, \(T+R\) is the sum of the indegrees of the points in the reflexive pairs.

This quantity (together with \(Q\) and \(R\)) is used in computing the variances and covariances of the entries of the reflexivity contingency table. See (ceyhan:NNreflexivity2017;textualnnspat) for further details.

Usage

Tval(W, R)

Value

Returns the \(T\) value. See the description above for the details of this quantity.

Arguments

W

The incidence matrix, \(W\), for the NN digraph

R

The number of reflexive NNs (i.e., twice the number of reflexive NN pairs)

Author

Elvan Ceyhan

See Also

Qval, Qvec, sharedNN, and Rval

Examples

#3D data points
n<-10
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd)
R<-Rval(W)
Tval(W,R)

#1D data points
X<-as.matrix(runif(15)) # need to be entered as a matrix with one column
#(i.e., a column vector), hence X<-runif(5) would not work
ipd<-ipd.mat(X)
W<-Wmat(ipd)
R<-Rval(W)
Tval(W,R)

#with ties=TRUE in the data
Y<-matrix(round(runif(30)*10),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd,ties=TRUE)
R<-Rval(W)
Tval(W,R)