cov.nnsym: Covariance Matrix of the Differences of the Off-Diagonal Cell...

In nnspat: Nearest Neighbor Methods for Spatial Patterns

Covariance Matrix of the Differences of the Off-Diagonal Cell Counts in an NNCT

Description

Returns the covariance matrix of the differences of the cell counts, N_{ij}-N_{ji} for i,j=1,\ldots,k and i \ne j, in the NNCT, ct. The covariance matrix is of dimension k(k-1)/2 \times k(k-1)/2 and its entries are cov(N_{ij}-N_{ji}, N_{kl}-N_{lk}) where the order of i,j for N_{ij}-N_{ji} is as in the output of ind.nnsym(k). These covariances are valid under RL or conditional on Q and R under CSR.

The argument covN is the covariance matrix of N_{ij} (concatenated rowwise).

See also (\insertCitedixon:1994,ceyhan:SWJ-spat-sym2014;textualnnspat).

Usage

cov.nnsym(covN)

Arguments

covN	The k^2 \times k^2 covariance matrix of row-wise vectorized entries of NNCT

Value

The k(k-1)/2 \times k(k-1)/2 covariance matrix of the differences of the off-diagonal cell counts N_{ij}-N_{ji} for i,j=1,\ldots,k and i \ne j in the NNCT, ct

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

var.nnsym, cov.tct, cov.nnct and cov.seg.coeff

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

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

cov.nnsym(covN)

#############
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)
covN<-cov.nnct(ct,varN,Qv,Rv)

cov.nnsym(covN)

nnspat documentation built on May 29, 2024, 10:03 a.m.