# funsC_MI_II: Correction Matrices for the Covariance Matrix of NNCT entries In nnspat: Nearest Neighbor Methods for Spatial Patterns

## 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 (\insertCiteceyhan:SJScorrected2010;textualnnspat) or Sections 3.5.1 and 3.5.2 in (\insertCiteECarXivCorrected:2008;textualnnspat) for more details.

## Usage

 ```1 2 3``` ```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.

Elvan Ceyhan

## References

\insertAllCited

`nnct.cr1` and `nnct.cr2`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```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 ```