# funs.auxcovtct: Auxiliary Functions for Computing Covariances Between Cell... In nnspat: Nearest Neighbor Methods for Spatial Patterns

## Description

Five functions: cov.2cells, cov.cell.col, covNijCk, cov2cols and covCiCj

These are auxiliary functions for computing covariances between entries in the TCT for the types I-IV cell-specific tests. The covariances between T_{ij} values for i,j=1,…,k in the TCT require covariances between two cells in the NNCT, between a cell and column sum, and between two column sums in the NNCT. cov.2cells computes the covariance between two cell counts N_{ij} and N_{kl} in an NNCT, cov.cell.col and covNijCk are equivalent and they compute the covariance between cell count N_{ij} and sum of column k, C_k, cov2cols and covCiCj are equivalent and they compute the covariance between sums of two columns, C_i and C_j. The index arguments refer to which entry or column sum is intended in the NNCT. The argument covN must be the covariance between N_{ij} values which are obtained from NNCT by row-wise vectorization. These covariances are valid under RL or conditional on Q and R under CSR.

## Usage

 1 2 3 4 5 6 7 8 9 cov.2cells(i, j, k, l, ct, covN) cov.cell.col(i, j, k, ct, covN) covNijCk(i, j, k, ct, covN) cov.2cols(i, j, ct, covN) covCiCj(i, j, ct, covN) 

## Arguments

 i, j, k, l Indices of the cell counts or column sums whose covariance is to be computed. All four are needed for cov.2cells referring to cells (i,j) and (k,l); only three indices i,j,k are needed for cov.cell.col and covNijCk referring to cell (i,j) and column k; only two indices i,j are needed for cov2cols and covCiCj referring to columns i and j. 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

cov.2cells returns the covariance between two cell counts N_{ij} and N_{kl} in an NNCT, cov.cell.col and covNijCk return the covariance between cell count N_{ij} and sum of column k, C_k, cov2cols and covCiCj return the covariance between sums of two columns, C_i and C_j.

## Author(s)

Elvan Ceyhan

cov.tct and cov.nnct
  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 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)$q Rv<-Rval(W) varN<-var.nnct(ct,Qv,Rv) covN<-cov.nnct(ct,varN,Qv,Rv) cov.2cells(1,1,1,2,ct,covN) cov.cell.col(2,2,1,ct,covN) covNijCk(2,2,1,ct,covN) cov.2cols(2,1,ct,covN) covCiCj(2,1,ct,covN) ############# n<-40 Y<-matrix(runif(3*n),ncol=3) ipd<-ipd.mat(Y) cls<-sample(1:4,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10)) ct<-nnct(ipd,cls) W<-Wmat(ipd) Qv<-Qvec(W)$q Rv<-Rval(W) varN<-var.nnct(ct,Qv,Rv) covN<-cov.nnct(ct,varN,Qv,Rv) cov.2cells(2,3,1,2,ct,covN) cov.cell.col(1,1,2,ct,covN) covNijCk(1,1,2,ct,covN) cov.2cols(3,4,ct,covN) covCiCj(3,4,ct,covN)