funs.overall.nnct: Dixon's Overall Test of Segregation for NNCT In nnspat: Nearest Neighbor Methods for Spatial Patterns

Description

Two functions: overall.nnct.ct and overall.nnct.

Both functions are objects of class "Chisqtest" but with different arguments (see the parameter list below). Each one performs hypothesis tests of deviations of cell counts from the expected values under RL or CSR for all cells (i.e., entries) combined in the NNCT. That is, each test is Dixon's overall test of segregation based on NNCTs for k ≥ 2 classes. This overall test is based on the chi-squared approximation of the corresponding quadratic form and are due to \insertCitedixon:1994,dixon:NNCTEco2002;textualnnspat. Both functions exclude the last column of the NNCT (in fact any column will do and last column is chosen without loss of generality), to avoid ill-conditioning of the covariance matrix (for its inversion in the quadratic form).

Each function yields the test statistic, p-value and df which is k(k-1), description of the alternative with the corresponding null values (i.e. expected values) of NNCT entries, sample estimates (i.e. observed values) of the entries in NNCT. The functions also provide names of the test statistics, the method and the data set used.

The null hypothesis is that all N_{ij} entries are equal to their expected values under RL or CSR.

See also (\insertCitedixon:1994,dixon:NNCTEco2002,ceyhan:eest-2010,ceyhan:jkss-posthoc-2017;textualnnspat) and the references therein.

Usage

 1 2 3 overall.nnct.ct(ct, covN) overall.nnct(dat, lab, ...) 

Arguments

 ct A nearest neighbor contingency table, used in overall.nnct.ct only covN The k^2 \times k^2 covariance matrix of row-wise vectorized entries of NNCT, ct ; used in overall.nnct.ct only. dat The data set in one or higher dimensions, each row corresponds to a data point, used in overall.nnct only lab The vector of class labels (numerical or categorical), used in overall.nnct only ... are for further arguments, such as method and p, passed to the dist function. used in overall.nnct only

Value

A list with the elements

 statistic The overall chi-squared statistic stat.names Name of the test statistic p.value The p-value for the hypothesis test df Degrees of freedom for the chi-squared test, which is k(k-1) for this function. estimate Estimates of the parameters, NNCT, i.e., matrix of the observed N_{ij} values which is the NNCT. est.name,est.name2 Names of the estimates, former is a longer description of the estimates than the latter. null.value Matrix of hypothesized null values for the parameters which are expected values of the the N_{ij} values in the NNCT. null.name Name of the null values method Description of the hypothesis test ct.name Name of the contingency table, ct, returned by overall.nnct.ct only data.name Name of the data set, dat, returned by overall.nnct only

Elvan Ceyhan

References

\insertAllCited

overall.seg.ct, overall.seg, overall.tct.ct and overall.tct
  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)$q Rv<-Rval(W) varN<-var.nnct(ct,Qv,Rv) covN<-cov.nnct(ct,varN,Qv,Rv) #default is byrow overall.nnct(Y,cls) overall.nnct.ct(ct,covN) overall.nnct(Y,cls,method="max") #cls as a factor na<-floor(n/2); nb<-n-na fcls<-rep(c("a","b"),c(na,nb)) ct<-nnct(ipd,fcls) overall.nnct(Y,fcls) overall.nnct.ct(ct,covN) ############# n<-40 Y<-matrix(runif(3*n),ncol=3) ipd<-ipd.mat(Y) cls<-sample(1:4,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10)) ct<-nnct(ipd,cls) W<-Wmat(ipd) Qv<-Qvec(W)$q Rv<-Rval(W) varN<-var.nnct(ct,Qv,Rv) covN<-cov.nnct(ct,varN,Qv,Rv) overall.nnct(Y,cls) overall.nnct.ct(ct,covN)