linearKcross

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).

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>.

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>.

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 \(r\).

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

correction

&#8230;

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 \(i\).

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()). 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

linearKcross function

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.

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

Description

Usage

Arguments

Value

Warnings

Details

References

See Also

Examples