nnspat (version 0.1.2)

cov.nnct: Covariance Matrix of the Cell Counts in an NNCT

Description

Returns the covariance matrix of cell counts \(N_{ij}\) for \(i,j=1,\ldots,k\) in the NNCT, ct. The covariance matrix is of dimension \(k^2 \times k^2\) and its entries are \(cov(N_{ij},N_{kl})\) when \(N_{ij}\) values are by default corresponding to the row-wise vectorization of ct. If byrow=FALSE, the column-wise vectorization of ct is used. These covariances are valid under RL or conditional on \(Q\) and \(R\) under CSR.

See also (dixon:1994,dixon:NNCTEco2002,ceyhan:eest-2010,ceyhan:jkss-posthoc-2017;textualnnspat).

Usage

cov.nnct(ct, varN, Q, R, byrow = TRUE)

Value

The \(k^2 \times k^2\) covariance matrix of cell counts \(N_{ij}\) for \(i,j=1,\ldots,k\) in the NNCT, ct

Arguments

ct

A nearest neighbor contingency table

varN

The \(k \times k\) variance matrix of cell counts of NNCT, ct.

Q

The number of shared NNs

R

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

byrow

A logical argument (default=TRUE). If TRUE, rows of ct are appended to obtain the vector and if FALSE columns of ct are appended to obtain the vector.

Author

Elvan Ceyhan

References

See Also

covNrow2col, cov.tct, and cov.nnsym

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)

W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)

cov.nnct(ct,varN,Qv,Rv)
cov.nnct(ct,varN,Qv,Rv,byrow=FALSE)

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

W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)

cov.nnct(ct,varN,Qv,Rv)
cov.nnct(ct,varN,Qv,Rv,byrow=FALSE)

#1D data points
n<-20  #or try sample(1:20,1)
X<-as.matrix(runif(n))# need to be entered as a matrix with one column
#(i.e., a column vector), hence X<-runif(n) would not work
ipd<-ipd.mat(X)
cls<-sample(1:2,n,replace = TRUE)  #or try cls<-rep(1:2,c(10,10))
ct<-nnct(ipd,cls)

W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)
cov.nnct(ct,varN,Qv,Rv)