funsC_MI_II {nnspat}

Correction Matrices for the Covariance Matrix of NNCT entries

Description

Two functions: correct.cf1 and correct.cf1.

Each function yields matrices which are used in obtaining covariance matrices of T_{ij} values for types I and II tests from the usual Chi-Square test of contingency tables (i.e., Pielou's test) applied on NNCTs. The output matrices are to be term-by-term multiplied with the covariance matrix of the entries of NNCT. See Sections 3.1 and 3.2 in (Ceyhan (2010)) or Sections 3.5.1 and 3.5.2 in (Ceyhan (2008)) for more details.

Usage

correct.cf1(ct)

correct.cf2(ct)

Arguments

ct

A nearest neighbor contingency table

Value

Both functions return a correction matrix which is to be multiplied with the covariance matrix of entries of the NNCT so as to obtain types I and II overall tests from Pielou's test of segregation. See the description above for further detail.

Author(s)

Elvan Ceyhan

References

Ceyhan E (2008). “New Tests for Spatial Segregation Based on Nearest Neighbor Contingency Tables.” https://arxiv.org/abs/0808.1409v3 [stat.ME]. Technical Report # KU-EC-08-6, Koç University, Istanbul, Turkey.

Ceyhan E (2010). “New Tests of Spatial Segregation Based on Nearest Neighbor Contingency Tables.” Scandinavian Journal of Statistics, 37(1), 147-165.

See Also

nnct.cr1 and nnct.cr2

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)

#correction type 1
CM1<-correct.cf1(ct)
CovN.cf1<-covN*CM1

#correction type 2
CM2<-correct.cf2(ct)
CovN.cf2<-covN*CM2

covN
CovN.cf1
CovN.cf2