For a multitype point pattern on a linear network,
 estimate the multitype \(K\) function
 which counts the expected number of points of type \(j\)
 within a given distance of a point of type \(i\).

linearKcross

Defines types of spatial data on a linear network
and provides functionality for geometrical operations,
data analysis and modelling of data on a linear network,
in the 'spatstat' family of packages.
Contains definitions and support for linear networks, including creation of networks, geometrical measurements, topological connectivity, geometrical operations such as inserting and deleting vertices, intersecting a network with another object, and interactive editing of networks.
Data types defined on a network include point patterns, pixel images, functions, and tessellations.
Exploratory methods include kernel estimation of intensity on a network, K-functions and pair correlation functions on a network, simulation envelopes, nearest neighbour distance and empty space distance, relative risk estimation with cross-validated bandwidth selection. Formal hypothesis tests of random pattern (chi-squared, Kolmogorov-Smirnov, Monte Carlo, Diggle-Cressie-Loosmore-Ford, Dao-Genton, two-stage Monte Carlo) and tests for covariate effects (Cox-Berman-Waller-Lawson, Kolmogorov-Smirnov, ANOVA) are also supported.
Parametric models can be fitted to point pattern data using the function lppm() similar to glm(). Only Poisson models are implemented so far. Models may involve dependence on covariates and dependence on marks. Models are fitted by maximum likelihood.
Fitted point process models can be simulated, automatically. Formal hypothesis tests of a fitted model are supported (likelihood ratio test, analysis of deviance, Monte Carlo tests) along with basic tools for model selection (stepwise(), AIC()) and variable selection (sdr). Tools for validating the fitted model include simulation envelopes, residuals, residual plots and Q-Q plots, leverage and influence diagnostics, partial residuals, and added variable plots.
Random point patterns on a network can be generated using a variety of models.

Adrian Baddeley

spatstat.linnet

Linear Networks Functionality of the 'spatstat' Family

Rolf Turner

Ege Rubak

Greg McSwiggan

Tilman Davies

Mehdi Moradi

Suman Rakshit

Ottmar Cronie

linearKcross function

Multitype K Function (Cross-type) for Linear Point Pattern — linearKcross

<dl>

 <dt>X</dt>
<dd>The observed point pattern, 
 from which an estimate of the cross type \(K\) function
 \(K_{ij}(r)\) will be computed.
 An object of class <code>"lpp"</code> which 
 must be a multitype point pattern (a marked point pattern
 whose marks are a factor).</dd>

 <dt>i</dt>
<dd>Number or character string identifying the type (mark value)
 of the points in <code>X</code> from which distances are measured.
 Defaults to the first level of <code>marks(X)</code>.</dd>

 <dt>j</dt>
<dd>Number or character string identifying the type (mark value)
 of the points in <code>X</code> to which distances are measured.
 Defaults to the second level of <code>marks(X)</code>.</dd>

 <dt>r</dt>
<dd>numeric vector. The values of the argument \(r\)
 at which the \(K\)-function
 \(K_{ij}(r)\) should be evaluated.
 There is a sensible default.
 First-time users are strongly advised not to specify this argument.
 See below for important conditions on \(r\).</dd>

 <dt>correction</dt>
<dd>Geometry correction.
 Either <code>"none"</code> or <code>"Ang"</code>. See Details.</dd>

 <dt>...</dt>
<dd>Ignored.</dd>

</dl>

Arguments

The arguments <code>i</code> and <code>j</code> are interpreted as
 levels of the factor <code>marks(X)</code>. Beware of the usual
 trap with factors: numerical values are not
 interpreted in the same way as character values.

Warnings

Adrian Baddeley <a href='mailto:Adrian.Baddeley@curtin.edu.au'>Adrian.Baddeley@curtin.edu.au</a>

linearKcross: Multitype K Function (Cross-type) for Linear Point Pattern

Description

Usage

Arguments

Value

Details

References

See Also

Examples