# funs.covtct: Functions for Covariances of the Entries of the Types I, III... In nnspat: Nearest Neighbor Methods for Spatial Patterns

## Description

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

These functions return the covariances between 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.

## Usage

 1 2 3 4 5 6 7 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.

Elvan Ceyhan

## References

\insertAllCited

cov.tct and cov.nnct
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 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)