cov.nnct {nnspat}

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, 2002); Ceyhan (2010, 2017)).

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,\ldots,k in the NNCT, ct

Author(s)

Elvan Ceyhan

References

Ceyhan E (2010). “On the use of nearest neighbor contingency tables for testing spatial segregation.” Environmental and Ecological Statistics, 17(3), 247-282.

Ceyhan E (2017). “Cell-Specific and Post-hoc Spatial Clustering Tests Based on Nearest Neighbor Contingency Tables.” Journal of the Korean Statistical Society, 46(2), 219-245.

Dixon PM (1994). “Testing spatial segregation using a nearest-neighbor contingency table.” Ecology, 75(7), 1940-1948.

Dixon PM (2002). “Nearest-neighbor contingency table analysis of spatial segregation for several species.” Ecoscience, 9(2), 142-151.

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)