Ksector

The observed point pattern, 
 from which an estimate of \(K(r)\) will be computed.
 An object of class <code>"ppp"</code>, or data
 in any format acceptable to <code><a rd-options="" href="/link/as.ppp?package=spatstat&version=1.56-1" data-mini-rdoc="spatstat::as.ppp">as.ppp</a>()</code>.

Numeric values giving the range of angles inside which
 points will be counted. Angles are measured in degrees
 (if <code>units="degrees"</code>, the default) or radians
 (if <code>units="radians"</code>) anti-clockwise from the positive \(x\)-axis.

begin,end

&#8230;

Units in which the angles <code>begin</code> and <code>end</code> are expressed.

units

Optional. Vector of values for the argument \(r\) at which \(K(r)\) 
 should be evaluated. Users are advised not to specify this
 argument; there is a sensible default.

This argument is for internal use only.

breaks

Optional. A character vector containing any selection of the
 options <code>"none"</code>, <code>"border"</code>, <code>"bord.modif"</code>,
 <code>"isotropic"</code>, <code>"Ripley"</code>, <code>"translate"</code>,
 <code>"translation"</code>, <code>"none"</code>, <code>"good"</code> or <code>"best"</code>.
 It specifies the edge correction(s) to be applied.
 Alternatively <code>correction="all"</code> selects all options.

correction

Optional window. The first point \(x_i\) of each pair of points
 will be constrained to lie in <code>domain</code>.

domain

Logical. 
 If <code>TRUE</code>, the numerator and denominator of
 each edge-corrected estimate will also be saved,
 for use in analysing replicated point patterns.

ratio

Logical value indicating whether to print progress reports
 and warnings.

verbose

A directional counterpart of Ripley's \(K\) function,
 in which pairs of points are counted only when the
 vector joining the pair happens to
 lie in a particular range of angles.

spatial

nonparametric

Comprehensive open-source toolbox for analysing Spatial Point Patterns. Focused mainly on two-dimensional point patterns, including multitype/marked points, in any spatial region. Also supports three-dimensional point patterns, space-time point patterns in any number of dimensions, point patterns on a linear network, and patterns of other geometrical objects. Supports spatial covariate data such as pixel images.
Contains over 2000 functions for plotting spatial data, exploratory data analysis, model-fitting, simulation, spatial sampling, model diagnostics, and formal inference.
Data types include point patterns, line segment patterns, spatial windows, pixel images, tessellations, and linear networks.
Exploratory methods include quadrat counts, K-functions and their simulation envelopes, nearest neighbour distance and empty space statistics, Fry plots, pair correlation function, kernel smoothed intensity, relative risk estimation with cross-validated bandwidth selection, mark correlation functions, segregation indices, mark dependence diagnostics, and kernel estimates of covariate effects. 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 functions ppm(), kppm(), slrm(), dppm() similar to glm(). Types of models include Poisson, Gibbs and Cox point processes, Neyman-Scott cluster processes, and determinantal point processes. Models may involve dependence on covariates, inter-point interaction, cluster formation and dependence on marks. Models are fitted by maximum likelihood, logistic regression, minimum contrast, and composite likelihood methods.
A model can be fitted to a list of point patterns (replicated point pattern data) using the function mppm(). The model can include random effects and fixed effects depending on the experimental design, in addition to all the features listed above.
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.

Adrian Baddeley

spatstat

Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests

Ksector function

The observed point pattern, 
 from which an estimate of \(K(r)\) will be computed.
 An object of class <code>"ppp"</code>, or data
 in any format acceptable to <code><a rd-options='' href='as.ppp'>as.ppp</a>()</code>.

Ksector: Sector K-function

Description

Usage

Arguments

Value

Details

See Also

Examples