funsQandR | R Documentation |

Four functions: `Qval`

, `Qvec`

, `sharedNN`

and `Rval`

.

`Qval`

returns the *Q* value, the number of points with shared nearest neighbors (NNs), which occurs when two or
more points share a NN, for data in any dimension.

`Qvec`

returns the Q-value and also yields the Qv vector *Qv=(Q_0,Q_1,…)* as well for data in any
dimension, where *Q_j* is the number of points shared as a NN by *j* other points.

`sharedNN`

returns the `vector`

of number of points with shared NNs, *Q=(Q_0,Q_1,…)* where *Q_i* is
the number of points that are NN to *i* points, and if a point is a NN of *i* points, then there are *i(i-1)*
points that share a NN. So *Q=∑_{i>1} i(i-1)Q_i*.

`Rval`

returns the number of reflexive NNs, R (i.e., twice the number of reflexive NN pairs).

These quantities are used, e.g., in computing the variances and covariances of the entries of the
nearest neighbor contingency tables used for Dixon's tests and other NNCT tests.
The input must be the incidence matrix, *W*, of the NN digraph.

Qval(W) Qvec(W) sharedNN(W) Rval(W)

`W` |
The incidence matrix, |

`Qval`

returns the *Q* value
`Qvec`

returns a `list`

with two elements

`q` |
the |

`qvec` |
the |

`sharedNN`

returns a `matrix`

with 2 rows, where first row is the *j* values and second row is
the corresponding vector of *Q_j* values
`Rval`

the *R* value, the number of reflexive NNs

See the description above for the details of these quantities.

Elvan Ceyhan

`Tval`

, `QRval`

, `sharedNNmc`

and `Ninv`

#Examples for Qval #3D data points n<-10 Y<-matrix(runif(3*n),ncol=3) ipd<-ipd.mat(Y) W<-Wmat(ipd) Qval(W) #1D data points X<-as.matrix(runif(10)) # need to be entered as a matrix with one column #(i.e., a column vector), hence X<-runif(10) would not work ipd<-ipd.mat(X) W<-Wmat(ipd) Qval(W) #with ties=TRUE in the data Y<-matrix(round(runif(15)*10),ncol=3) ipd<-ipd.mat(Y) W<-Wmat(ipd,ties=TRUE) Qval(W) #with ties=TRUE in the data Y<-matrix(round(runif(15)*10),ncol=3) ipd<-ipd.mat(Y) W<-Wmat(ipd,ties=TRUE) Qval(W) #Examples for Qvec #3D data points n<-10 Y<-matrix(runif(3*n),ncol=3) ipd<-ipd.mat(Y) W<-Wmat(ipd) Qvec(W) #2D data points n<-15 Y<-matrix(runif(2*n),ncol=2) ipd<-ipd.mat(Y) W<-Wmat(ipd) Qvec(W) #1D data points X<-as.matrix(runif(15)) # need to be entered as a matrix with one column #(i.e., a column vector), hence X<-runif(15) would not work ipd<-ipd.mat(X) W<-Wmat(ipd) Qvec(W) #with ties=TRUE in the data Y<-matrix(round(runif(15)*10),ncol=3) ipd<-ipd.mat(Y) W<-Wmat(ipd,ties=TRUE) Qvec(W) #Examples for sharedNN #3D data points n<-10 Y<-matrix(runif(3*n),ncol=3) ipd<-ipd.mat(Y) W<-Wmat(ipd) sharedNN(W) Qvec(W) #1D data points X<-as.matrix(runif(15)) # need to be entered as a matrix with one column #(i.e., a column vector), hence X<-runif(5) would not work ipd<-ipd.mat(X) W<-Wmat(ipd) sharedNN(W) Qvec(W) #2D data points n<-15 Y<-matrix(runif(2*n),ncol=2) ipd<-ipd.mat(Y) W<-Wmat(ipd) sharedNN(W) Qvec(W) #with ties=TRUE in the data Y<-matrix(round(runif(30)*10),ncol=3) ipd<-ipd.mat(Y) W<-Wmat(ipd,ties=TRUE) sharedNN(W) #Examples for Rval #3D data points n<-10 Y<-matrix(runif(3*n),ncol=3) ipd<-ipd.mat(Y) W<-Wmat(ipd) Rval(W) #1D data points X<-as.matrix(runif(15)) # need to be entered as a matrix with one column #(i.e., a column vector), hence X<-runif(5) would not work ipd<-ipd.mat(X) W<-Wmat(ipd) Rval(W) #with ties=TRUE in the data Y<-matrix(round(runif(30)*10),ncol=3) ipd<-ipd.mat(Y) W<-Wmat(ipd,ties=TRUE) Rval(W)

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