# cov.nnct: Covariance Matrix of the Cell Counts in an NNCT In nnspat: Nearest Neighbor Methods for Spatial Patterns

 cov.nnct R Documentation

## 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.

### 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

Elvan Ceyhan

### References

\insertAllCited

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)



nnspat documentation built on Aug. 30, 2022, 9:06 a.m.