square

unit.square

spatial

datagen

A package for analysing spatial data, mainly Spatial Point
        Patterns, including multitype/marked points and spatial
        covariates, in any two-dimensional spatial region. Also
        supports three-dimensional point patterns, and space-time point
        patterns in any number of dimensions. Contains 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 and
        tessellations. Point process models can be fitted to point
        pattern data. Cluster type models are fitted by the method of
        minimum contrast. Very general Gibbs point process models can
        be fitted to point pattern data using a function ppm similar to
        lm or glm. Models may include dependence on covariates,
        interpoint interaction and dependence on marks. Fitted models
        can be simulated automatically. Also provides facilities for
        formal inference (such as chi-squared tests) and model
        diagnostics (including simulation envelopes, residuals,
        residual plots and Q-Q plots).

Adrian Baddeley

spatstat

Spatial Point Pattern analysis, model-fitting, simulation, tests

square function

Square Window

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.

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

square: Square Window

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Examples