Abstractspatstat is a package for analyzing spatial point pattern data. Its functionality includes exploratory data analysis, model-fitting, and simulation. It is designed to handle realistic datasets, including inhomogeneous point patterns, spatial sampling regions of arbitrary shape, extra covariate data, and 'marks' attached to the points of the point pattern.A unique feature of spatstat is its generic algorithm for fitting point process models to point pattern data. The interface to this algorithm is a function ppm that is strongly analogous to lm and glm.This paper is a general description of spatstat and an introduction for new users.

SUMMARY ‘Vertical’ sections are plane sections longitudinal to a fixed (but arbitrary) axial direction. Examples are sections of a cylinder parallel to the central axis; and sections of a flat slab normal to the plane of the slab. Vertical sections of any object can be generated by placing the object on a table and taking sections perpendicular to the plane of the table. The standard methods of stereology assume isotropic random sections, and are not applicable to this kind of biased sampling. However, by using specially designed test systems, one can obtain an unbiased estimate of surface area. General principles of stereology for vertical sections are outlined. No assumptions are necessary about the shape or orientation distribution of the structure. Vertical section stereology is valid on the same terms as standard stereological methods for isotropic random sections. The range of structural quantities that can be estimated from vertical sections includes Vv, Nv, Sv and the volume‐weighted mean particle volume v̄v, but not Lv. There is complete freedom to choose the vertical axis direction, which makes the sampling procedure simple and ‘natural’. Practical sampling procedures for implementation of the ideas are described, and illustrated by examples.

We develop methods for analysing the`interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely non-parametric study of interactions is possible using an analogue of the K -function. Alternatively one may assume a semi-parametric model in which a (parametrically speci®ed) homogeneous Markov point process is subjected to (non-parametric) inhomogeneous independent thinning. The effectiveness of these approaches is tested on datasets representing the positions of trees in forests.

Summary1. Presence-only data are widely used for species distribution modelling, and point process regression models are a flexible tool that has considerable potential for this problem, when data arise as point events. 2. In this paper, we review point process models, some of their advantages and some common methods of fitting them to presence-only data. 3. Advantages include (and are not limited to) clarification of what the response variable is that is modelled; a framework for choosing the number and location of quadrature points (commonly referred to as pseudoabsences or 'background points') objectively; clarity of model assumptions and tools for checking them; models to handle spatial dependence between points when it is present; and ways forward regarding difficult issues such as accounting for sampling bias. 4. Point process models are related to some common approaches to presence-only species distribution modelling, which means that a variety of different software tools can be used to fit these models, including MAXENT or generalised linear modelling software.

The clusters of young stars in massive star-forming regions show a wide range of sizes, morphologies, and numbers of stars. Their highly subclustered structures are revealed by the MYStIX project's sample of 31,754 young stars in nearby sites of star formation (regions at distances <3.6 kpc that contain at least one O-type star.) In 17 of the regions surveyed by MYStIX, we identify subclusters of young stars using finite mixture models -collections of isothermal ellipsoids that model individual subclusters. Maximum likelihood estimation is used to estimate the model parameters, and the Akaike Information Criterion is used to determine the number of subclusters. This procedure often successfully finds famous subclusters, such as the BN/KL complex behind the Orion Nebula Cluster and the KW-object complex in M 17. A catalog of 142 subclusters is presented, with 1 to 20 subclusters per region. The subcluster core radius distribution for this sample is peaked at 0.17 pc with a standard deviation of 0.43 dex, and subcluster core radius is negatively correlated with gas/dust absorption of the stars -a possible age effect. Based on the morphological arrangements of subclusters, we identify four classes of spatial structure: long chains of subclusters, clumpy structures, isolated clusters with a core-halo structure, and isolated clusters well fit by a single isothermal ellipsoid.Subject headings: methods: statistical; open clusters and associations: general; stars: formation; stars: pre-main sequence; H ii regions; ISM: structure 7 These libraries can be installed from the R session by install.packages ("spatstat",dependencies=T)

This paper describes a technique for computing approximate maximum pseudolikelihood estimates of the parameters of a spatial point process. The method is an extension of Berman & Turner's (1992) device for maximizing the likelihoods of inhomogeneous spatial Poisson processes. For a very wide class of spatial point process models the likelihood is intractable, while the pseudolikelihood is known explicitly, except for the computation of an integral over the sampling region. Approximation of this integral by a finite sum in a special way yields an approximate pseudolikelihood which is formally equivalent to the (weighted) likelihood of a loglinear model with Poisson responses. This can be maximized using standard statistical software for generalized linear or additive models, provided the conditional intensity of the process takes an 'exponential family' form. Using this approach a wide variety of spatial point process models of Gibbs type can be fitted rapidly, incorporating spatial trends, interaction between points, dependence on spatial covariates, and mark information.

Summary. We define residuals for point process models fitted to spatial point pattern data, and we propose diagnostic plots based on them.The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, kernel smoothed intensity and Berman's diagnostic) are recovered as special cases. Diagnostic tools are developed systematically, by using an analogy between our spatial residuals and the usual residuals for (non-spatial) generalized linear models. The conditional intensity λ plays the role of the mean response. This makes it possible to adapt existing knowledge about model validation for generalized linear models to the spatial point process context, giving recommendations for diagnostic plots. A plot of smoothed residuals against spatial location, or against a spatial covariate, is effective in diagnosing spatial trend or covariate effects. Q-Q-plots of the residuals are effective in diagnosing interpoint interaction.

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