Tstat

The observed point pattern, 
 from which an estimate of \(T(r)\) 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=1.64-1" data-mini-rdoc="spatstat::as.ppp">as.ppp</a>()</code>.

&#8230;

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

Optional. Numeric. The maximum value of \(r\) for which
 \(T(r)\) should be estimated.

rmax

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

correction

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. If <code>TRUE</code>, an estimate of the computation time
 is printed.

verbose

Computes the third order summary statistic \(T(r)\)
 of a spatial point pattern.

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

Tstat function

If the number of points is large, the algorithm can take a very long time
 to inspect all possible triangles. A rough estimate
 of the total computation time will be printed at the beginning
 of the calculation. If this estimate seems very large,
 stop the calculation using the user interrupt signal, and
 call <code>Tstat</code> again, using <code>rmax</code> to restrict the
 range of <code>r</code> values,
 thus reducing the number of triangles to be inspected.

Computation time

The observed point pattern, 
 from which an estimate of \(T(r)\) 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>.

Tstat: Third order summary statistic

Description

Usage

Arguments

Value

Computation time

Details

References

See Also

Examples