funsNNclass.spec {nnspat}

NN Class-specific Chi-square Tests based on NNCTs

Description

Two functions: NN.class.spec.ct and NN.class.spec.

Both functions are objects of class "classhtest" but with different arguments (see the parameter list below). Each one performs class specific segregation tests for the columns, i.e., NN categories for k \ge 2 classes. That is, each one performs hypothesis tests of deviations of entries in each column of NNCT from the expected values under RL or CSR for each column. Recall that column labels in the NNCT are NN class labels. The test for each column i is based on the chi-squared approximation of the corresponding quadratic form and are due to Ceyhan (2009).

The argument covN must be covariance of column-wise vectorization of NNCT if the logical argument byrow=FALSE otherwise the function converts covN (which is done row-wise) to columnwise version with covNrow2col function.

Each function yields the test statistic, p-value and df for each base class i, description of the alternative with the corresponding null values (i.e., expected values) for the column i, estimates for the entries in column i for i=1,\ldots,k. The functions also provide names of the test statistics, the description of the test and the data set used.

The null hypothesis for each column is that the corresponding N_{ij} entries in column i are equal to their expected values under RL or CSR.

See also (Dixon (2002); Ceyhan (2009)) and the references therein.

Usage

NN.class.spec.ct(ct, covN, byrow = TRUE)

NN.class.spec(dat, lab, ...)

Arguments

ct

A nearest neighbor contingency table, used in NN.class.spec.ct only

covN

The k^2 \times k^2 covariance matrix of column-wise vectorized entries of NNCT, ct; used in NN.class.spec.ct only.

byrow

A logical argument (default=TRUE). If TRUE, rows of ct are appended to obtain the vector of N_{ij} values and covN is the covariance matrix for this vector and if FALSE columns of ct are appended to obtain the N_{ij} vector and covN is converted to the row-wise version by covNrow2col function;used in NN.class.spec.ct only.

dat

The data set in one or higher dimensions, each row corresponds to a data point, used in NN.class.spec only

lab

The vector of class labels (numerical or categorical), used in NN.class.spec only

...

are for further arguments, such as method and p, passed to the dist function. used in NN.class.spec only

Value

A list with the elements

type

Type of the class-specific test, which is "NN" for this function

statistic

The vector of NN class-specific test statistics

stat.names

Name of the test statistics

p.value

The vector of p-values for the hypothesis test

df

Degrees of freedom for the chi-squared test, which is k for this function.

estimate

Estimates of the parameters, transpose of the NNCT, i.e., transpose of the matrix of the observed N_{ij} values which is the transpose of NNCT.

null.value

Transpose of the matrix of hypothesized null values for the parameters which are expected values of 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 NN.class.spec.ct only

data.name

Name of the data set, dat, returned by NN.class.spec only

Author(s)

Elvan Ceyhan

References

Ceyhan E (2009). “Class-Specific Tests of Segregation Based on Nearest Neighbor Contingency Tables.” Statistica Neerlandica, 63(2), 149-182.

Dixon PM (2002). “Nearest-neighbor contingency table analysis of spatial segregation for several species.” Ecoscience, 9(2), 142-151.

See Also

base.class.spec.ct, base.class.spec, class.spec.ct and class.spec

Examples

n<-20
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)
covNrow<-cov.nnct(ct,varN,Qv,Rv)
covNcol<-covNrow2col(covNrow)

NN.class.spec(Y,cls)
NN.class.spec(Y,cls,method="max")

NN.class.spec.ct(ct,covNrow)
NN.class.spec.ct(ct,covNcol,byrow = FALSE)

#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
ct<-nnct(ipd,fcls)

NN.class.spec(Y,fcls)
NN.class.spec.ct(ct,covNrow)

#############
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)
covNrow<-cov.nnct(ct,varN,Qv,Rv)
covNcol<-covNrow2col(covNrow)

NN.class.spec(Y,cls)

NN.class.spec.ct(ct,covNrow)
NN.class.spec.ct(ct,covNcol,byrow = FALSE)