nnspat (version 0.1.2)

asyvarTk: Asymptotic Variance of Cuzick and Edwards \(T_k\) Test statistic

Description

This function computes the asymptotic variance of Cuzick and Edwards \(T_k\) test statistic based on the number of cases within kNNs of the cases in the data.

The argument, \(n_1\), is the number of cases (denoted as n1 as an argument). The number of cases are denoted as \(n_1\) and number of controls as \(n_0\) in this function to match the case-control class labeling, which is just the reverse of the labeling in cuzick:1990;textualnnspat.

The logical argument nonzero.mat (default=TRUE) is for using the \(A\) matrix if FALSE or just the matrix of nonzero locations in the \(A\) matrix (if TRUE) for computing \(N_s\) and \(N_t\), which are required in the computation of the asymptotic variance. \(N_s\) and \(N_t\) are defined on page 78 of (cuzick:1990;textualnnspat) as follows. \(N_s=\sum_i\sum_j a_{ij} a_{ji}\) (i.e., number of ordered pairs for which kNN relation is symmetric) and \(N_t= \sum \sum_{i \ne l}\sum a_{ij} a_{lj}\) (i.e, number of triplets \((i,j,l)\) \(i,j\), and \(l\) distinct so that \(j\) is among kNNs of \(i\) and \(j\) is among kNNs of \(l\)). For the \(A\) matrix, see the description of the functions aij.mat and aij.nonzero.

See (cuzick:1990;textualnnspat) for more details.

Usage

asyvarTk(dat, n1, k, nonzero.mat = TRUE, ...)

Value

A list with the elements

asy.var

The asymptotic variance of Cuzick and Edwards \(T_k\) test statistic for disease clustering

Ns

The \(N_s\) value standing for the number of ordered pairs for which kNN relation is symmetric, see the description.

Nt

The \(N_t\) value standing for the number of triplets \((i,j,l)\) \(i,j\), and \(l\) distinct so that \(j\) is among kNNs of \(i\) and \(j\) is among kNNs of \(l\) see the description.

Arguments

dat

The data set in one or higher dimensions, each row corresponds to a data point.

n1

Number of cases

k

Integer specifying the number of NNs (of subject \(i\))

nonzero.mat

A logical argument (default is TRUE) to determine whether the \(A\) matrix or the matrix of nonzero locations of the \(A\) matrix will be used in the computation of \(N_s\) and \(N_t\). If TRUE the nonzero location matrix is used, otherwise the \(A\) matrix itself is used.

...

are for further arguments, such as method and p, passed to the dist function.

Author

Elvan Ceyhan

References

See Also

ceTk, varTk, and varTkaij

Examples

n<-20  #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(0:1,n,replace = TRUE)  #or try cls<-rep(0:1,c(10,10))
n1<-sum(cls==1)
k<-3 #try also 2,3

asyvarTk(Y,n1,k)
asyvarTk(Y,n1,k,nonzero.mat=FALSE)
asyvarTk(Y,n1,k,method="max")