funs.auxcovtct: Auxiliary Functions for Computing Covariances Between Cell...

Description Usage Arguments Value Author(s) See Also Examples

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

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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

See Also

cov.tct and cov.nnct

Examples

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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)

nnspat documentation built on May 10, 2021, 9:06 a.m.