# cov.nnsym: Covariance Matrix of the Differences of the Off-Diagonal Cell... In nnspat: Nearest Neighbor Methods for Spatial Patterns

## Description

Returns the covariance matrix of the differences of the cell counts, N_{ij}-N_{ji} for i,j=1,…,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).

## Usage

 1 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,…,k and i \ne j in the NNCT, ct

Elvan Ceyhan

## References

\insertAllCited

var.nnsym, cov.tct, cov.nnct and cov.seg.coeff
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 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)