funs.covtct {nnspat}

Functions for Covariances of the Entries of the Types I, III and IV TCTs

Description

Four functions: cov.tctI, cov.tctIII, cov.tct3, and cov.tctIV.

These functions return the covariances between entries in the TCT for the types I, III, and IV cell-specific tests in matrix form which is of dimension k^2 \times k^2. The covariance matrix entries are cov(T_{ij},T_{kl}) when T_{ij} values are by default corresponding to the row-wise vectorization of TCT. The argument CovN must be the covariance between N_{ij} values which are obtained from the NNCT by row-wise vectorization. The functions cov.tctIII and cov.tct3 are equivalent. These covariances are valid under RL or conditional on Q and R under CSR.

See also (Ceyhan (2017)).

Usage

cov.tctI(ct, CovN)

cov.tctIII(ct, CovN)

cov.tct3(ct, CovN)

cov.tctIV(ct, CovN)

Arguments

ct

A nearest neighbor contingency table

CovN

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

Value

Each of these functions returns a k^2 \times k^2 covariance matrix, whose entries are the covariances of the entries in the TCTs for the corresponding type I-IV cell-specific test. The row and column names are inherited from ct.

Author(s)

Elvan Ceyhan

References

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.

See Also

cov.tct and 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)
covN<-cov.nnct(ct,varN,Qv,Rv)

cov.tctI(ct,covN)
cov.tctIII(ct,covN)
cov.tctIV(ct,covN)