funsVarTk | R Documentation |
Two functions: VarTk
and VarTkaij
.
Both functions compute the (finite sample) variance of Cuzick and Edwards T_k test statistic based on the
number of cases within k
NNs of the cases in the data under RL or CSR independence.
The common arguments for both functions are n1
, representing the number of cases and k
.
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 \insertCitecuzick: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
variance. N_s and N_t are defined on page 78 of (\insertCitecuzick:1990;textualnnspat) as follows.
N_s=∑_i∑_j a_{ij} a_{ji} (i.e., number of ordered pairs for which k
NN relation is symmetric)
and N_t= ∑ ∑_{i \ne l}∑ a_{ij} a_{lj} (i.e, number of triplets (i,j,l) i,j, and l distinct so that
j is among k
NNs of i and j is among k
NNs of l).
The function VarTkaij
uses Toshiro Tango's moments formulas based on the A=(a_{ij}) matrix
(and is equivalent to the function VarTk
, see \insertCitetango:2007;textualnnspat,
where a_{ij}(k) = 1 if z_j is among the k
NNs of z_i and 0 otherwise.
The function varTkaij
is equivalent to varTk
(with $var
extension).
See (\insertCitecuzick:1990,tango:2007;textualnnspat).
varTk(dat, n1, k, nonzero.mat = TRUE, ...) varTkaij(n1, k, a)
dat |
The data set in one or higher dimensions, each row corresponds to a data point, used in |
n1 |
Number of cases |
k |
Integer specifying the number of NNs (of subject i) |
nonzero.mat |
A logical argument (default is |
... |
are for further arguments, such as |
a |
The A=(a_{ij}) matrix, used in |
The function VarTk
returns a list
with the elements
var.Tk |
The (finite sample) variance of Cuzick and Edwards T_k test statistic for disease clustering |
Ns |
The N_s value standing for the number of ordered pairs for which |
Nt |
The N_t value standing for the number of triplets (i,j,l) i,j, and l distinct so that
j is among |
The function VarTkaij
returns only var.Tk
as above.
Elvan Ceyhan
Elvan Ceyhan
asyvarTk
n<-20 #or try sample(1:20,1) Y<-matrix(runif(3*n),ncol=3) cls<-sample(0:1,n,replace = TRUE) #or try cls<-rep(0:1,c(10,10)) n1<-sum(cls==1) k<-2 #try also 2,3 a<-aij.mat(Y,k) varTk(Y,n1,k) varTk(Y,n1,k,nonzero.mat=FALSE) varTk(Y,n1,k,method="max") n<-20 #or try sample(1:20,1) Y<-matrix(runif(3*n),ncol=3) cls<-sample(0:1,n,replace = TRUE) #or try cls<-rep(0:1,c(10,10)) n1<-sum(cls==1) k<-1 #try also 2,3, sample(1:5,1) a<-aij.mat(Y,k) varTkaij(n1,k,a) varTk(Y,n1,k)$var
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