nnspat (version 0.1.2)

covNrow2col: Conversion of the Covariance Matrix of the Row-wise Vectorized Cell Counts to Column-wise Vectorized Cell Counts in an NNCT

Description

Converts the \(k^2 \times k^2\) covariance matrix of row-wise vectorized cell counts \(N_{ij}\) for \(i,j=1,\ldots,k\) in the NNCT, ct to the covariance matrix of column-wise vectorized cell counts. In the output, the covariance matrix entries are \(cov(N_{ij},N_{kl})\) when \(N_{ij}\) values are corresponding to the column-wise vectorization of ct. 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

covNrow2col(covN)

Value

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

Arguments

covN

The \(k^2 \times k^2\) covariance matrix of row-wise vectorized cell counts of NNCT, ct.

Author

Elvan Ceyhan

References

See Also

cov.nnct

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)

covNrow<-cov.nnct(ct,varN,Qv,Rv)
covNcol1<-cov.nnct(ct,varN,Qv,Rv,byrow=FALSE)
covNcol2<-covNrow2col(covNrow)

covNrow
covNcol1
covNcol2

all.equal(covNcol1,covNcol2)

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

covNrow<-cov.nnct(ct,varN,Qv,Rv)
covNcol1<-cov.nnct(ct,varN,Qv,Rv,byrow=FALSE)
covNcol2<-covNrow2col(covNrow)

covNrow
covNcol1
covNcol2

all.equal(covNcol1,covNcol2)

#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)