# cov.tct: Covariance Matrix of the Entries of the Type I-IV TCTs In nnspat: Nearest Neighbor Methods for Spatial Patterns

## Description

Returns the covariance matrix of the entries T_{ij} for i,j=1,…,k in the TCT for the types I, III, and IV cell-specific tests. The covariance matrix is of dimension k^2 \times k^2 and its 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 matrix of 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.

## Usage

 1 cov.tct(ct, covN, type = "III") 

## 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. type The type of the cell-specific test, default="III". Takes on values "I"-"IV" (or equivalently 1-4, respectively.

## Value

The k^2 \times k^2 covariance matrix of the entries T_{ij} for i,j=1,…,k in the Type I-IV TCTs

Elvan Ceyhan

## References

\insertAllCited

cov.nnct and cov.nnsym
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 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)$q Rv<-Rval(W) varN<-var.nnct(ct,Qv,Rv) covN<-cov.nnct(ct,varN,Qv,Rv) cov.tct(ct,covN,type=1) cov.tct(ct,covN,type="I") cov.tct(ct,covN,type="II") cov.tct(ct,covN,type="III") cov.tct(ct,covN,type="IV") cov.tctI(ct,covN) cov.tct(ct,covN) cov.tctIII(ct,covN) cov.tct3(ct,covN) ############# n<-40 Y<-matrix(runif(3*n),ncol=3) ipd<-ipd.mat(Y) cls<-sample(1:4,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10)) ct<-nnct(ipd,cls) W<-Wmat(ipd) Qv<-Qvec(W)$q Rv<-Rval(W) varN<-var.nnct(ct,Qv,Rv) covN<-cov.nnct(ct,varN,Qv,Rv) cov.tct(ct,covN,type=3) cov.tct(ct,covN,type="III") cov.tctIII(ct,covN) cov.tct3(ct,covN)