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

In elvanceyhan/nnspat: Nearest Neighbor Methods for Spatial Patterns

Covariance Matrix of the Cell Counts in an NNCT

Description

Returns the covariance matrix of cell counts N_{ij} for i,j=1,…,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 (\insertCitedixon:1994,dixon:NNCTEco2002,ceyhan:eest-2010,ceyhan:jkss-posthoc-2017;textualnnspat).

Usage

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

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.

Value

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

Author(s)

Elvan Ceyhan

References

\insertAllCited

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)

elvanceyhan/nnspat documentation built on Sept. 4, 2022, 10:28 a.m.