Nt.def

This function computes the $N_t$ value which is required in the computation of the asymptotic variance
of Cuzick and Edwards $T_k$ test. Nt is defined on page 78 of (cuzick:1990;textualnnspat) as follows.
$N_t= \sum \sum_{i \ne l}\sum a_{ij} a_{lj}$ (i.e, number of triplets $(i,j,l)$ $i,j$, and $l$ distinct so that
$j$ is among $k$NNs of $i$ and $j$ is among $k$NNs of $l$).
This function yields the same result as the <code>asyvarTk</code> and <code>varTk</code> functions with <code>$Nt</code> inserted at the
end.
See (cuzick:1990;textualnnspat) for more details.

Contains the functions for testing the spatial patterns (of segregation, spatial symmetry,
association, disease clustering, species correspondence, and reflexivity) based on nearest neighbor relations,
especially using contingency tables such as
nearest neighbor contingency tables (Ceyhan (2010) <doi:10.1007/s10651-008-0104-x> and
Ceyhan (2017) <doi:10.1016/j.jkss.2016.10.002> and references therein),
nearest neighbor symmetry contingency tables (Ceyhan (2014) <doi:10.1155/2014/698296>),
species correspondence contingency tables and reflexivity contingency tables (Ceyhan (2018)
<doi:10.2436/20.8080.02.72> for two (or higher) dimensional data.
The package also contains functions for generating patterns of segregation, association,
uniformity in a multi-class setting (Ceyhan (2014) <doi:10.1007/s00477-013-0824-9>),
and various non-random labeling patterns for disease clustering
in two dimensional cases (Ceyhan (2014)
<doi:10.1002/sim.6053>), and for visualization of all these patterns
for the two dimensional data.
The tests are usually (asymptotic) normal z-tests or chi-square tests.

Elvan Ceyhan

nnspat

Nearest Neighbor Methods for Spatial Patterns

Nt.def function

<dl><dt>a</dt>
<dd>The $A=(a_{ij})$ matrix. The argument <code>a</code> is the $A$ matrix, obtained as output fromm <code>aij.mat</code>.</dd></dl>

Arguments

Author

$N_t$ Value (found with the definition formula) — Nt.def

<dl>

<dt>a</dt>
<dd>The $A=(a_{ij})$ matrix. The argument <code>a</code> is the $A$ matrix, obtained as output fromm <code>aij.mat</code>.</dd>

</dl>

Nt.def: \(N_t\) Value (found with the definition formula)

Description

Usage

Value

Arguments

Author

References

See Also

Examples