Estimates the intensity of a point process on a linear network
 using a two-dimensional smoothing kernel.

densityQuick.lpp

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

densityQuick.lpp function

Kernel Estimation of Intensity on a Network using a 2D Kernel — densityQuick.lpp

<dl>

 <dt>x</dt>
<dd>Point pattern on a linear network (object of class <code>"lpp"</code>).</dd>

 <dt>sigma</dt>
<dd>Smoothing bandwidth. A single numeric value,
 in the same units as the coordinates of <code>x</code>.
 Alternatively <code>sigma</code> may be a function which selects a
 bandwidth when applied to <code>x</code>,
 for example, <code>bw.scott.iso</code> or <code>bw.lppl</code>.
 There is a sensible default.</dd>

 <dt>...</dt>
<dd>Additional arguments passed to <code>as.mask</code>
 to determine the pixel resolution, or arguments passed to
 <code>sigma</code> if it is a function.</dd>

 <dt>kernel</dt>
<dd>String (partially matched) specifying the smoothing kernel.
 Current options are <code>"gaussian"</code>, <code>"epanechnikov"</code>,
 <code>"quartic"</code> or <code>"disc"</code>.</dd>

 <dt>at</dt>
<dd>String (partially matched)
 specifying whether to compute the intensity values
 at a fine grid of locations on the network
 (<code>at="pixels"</code>, the default) or
 only at the points of <code>x</code> (<code>at="points"</code>).</dd>

 <dt>what</dt>
<dd>String (partially matched)
 specifying whether to calculate the intensity estimate,
 or its estimated standard error, or its estimated variance.</dd>

 <dt>leaveoneout</dt>
<dd>Logical value indicating whether to compute a leave-one-out
 estimator. Applicable only when <code>at="points"</code>.</dd>

 <dt>diggle</dt>
<dd>Logical value specifying whether to use the &#8216;Diggle&#8217;
 correction.</dd>

 <dt>edge2D</dt>
<dd>Logical value specifying whether to apply the usual
 two-dimensional edge correction procedure to the numerator and
 denominator of the estimate.</dd>

 <dt>weights</dt>
<dd>Optional weights to be attached to the points.
 A numeric vector, an <code>expression</code>, or a pixel image.</dd>

 <dt>positive</dt>
<dd>Logical value indicating whether to force the resulting values to be
 positive. Default is <code>FALSE</code> for the sake of speed.</dd>

</dl>

Arguments

If <code>sigma=Inf</code>, the resulting density estimate is 
 constant over all locations,
 and is equal to the average density of points per unit length.
 (If the network is not connected, then this rule
 is applied separately to each connected component of the network).

Infinite bandwidth

Adrian Baddeley, Suman Rakshit and Tilman Davies

densityQuick.lpp: Kernel Estimation of Intensity on a Network using a 2D Kernel

Description

Usage

Arguments

Value

Details

References

See Also

Examples