cov.tct: Covariance Matrix of the Entries of the Type I-IV TCTs

In nnspat: Nearest Neighbor Methods for Spatial Patterns

Covariance Matrix of the Entries of the Type I-IV TCTs

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.

See also (\insertCiteceyhan:jkss-posthoc-2017;textualnnspat).

Usage

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

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

cov.nnct and cov.nnsym

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.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)

nnspat documentation built on Aug. 30, 2022, 9:06 a.m.