Spatial data analysis

Wikipedia, the free to: navigation, has been suggested that geospatial analysis be merged into this article. This was one of the first uses of map-based spatial l analysis or spatial statistics includes any of the formal techniques which study entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic x issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research. The most fundamental of these is the problem of defining the spatial location of the entities being fication of the techniques of spatial analysis is difficult because of the large number of different fields of research involved, the different fundamental approaches which can be chosen, and the many forms the data can take. Analysis can perhaps be considered to have arisen with early attempts at cartography and surveying but many fields have contributed to its rise in modern form. Biology contributed through botanical studies of global plant distributions and local plant locations, ethological studies of animal movement, landscape ecological studies of vegetation blocks, ecological studies of spatial population dynamics, and the study of biogeography. Mathematics continues to provide the fundamental tools for analysis and to reveal the complexity of the spatial realm, for example, with recent work on fractals and scale invariance. Analysis confronts many fundamental issues in the definition of its objects of study, in the construction of the analytic operations to be used, in the use of computers for analysis, in the limitations and particularities of the analyses which are known, and in the presentation of analytic results. Many of these issues are active subjects of modern errors often arise in spatial analysis, some due to the mathematics of space, some due to the particular ways data are presented spatially, some due to the tools which are available. Census data, because it protects individual privacy by aggregating data into local units, raises a number of statistical issues. However these straight lines may have no inherent meaning in the real world, as was shown for the coastline of problems represent a challenge in spatial analysis because of the power of maps as media of presentation. When results are presented as maps, the presentation combines spatial data which are generally accurate with analytic results which may be inaccurate, leading to an impression that analytic results are more accurate than the data would indicate. Citation needed] the colors indicate the spatial distribution of plague outbreaks over definition of the spatial presence of an entity constrains the possible analysis which can be applied to that entity and influences the final conclusions that can be reached. While this property is fundamentally true of all analysis, it is particularly important in spatial analysis because the tools to define and study entities favor specific characterizations of the entities being studied. Statistical techniques favor the spatial definition of objects as points because there are very few statistical techniques which operate directly on line, area, or volume elements. Computer tools favor the spatial definition of objects as homogeneous and separate elements because of the limited number of database elements and computational structures available, and the ease with which these primitive structures can be l dependency or auto-correlation[edit]. Also: spatial l dependency is the co-variation of properties within geographic space: characteristics at proximal locations appear to be correlated, either positively or negatively. Spatial dependency leads to the spatial autocorrelation problem in statistics since, like temporal autocorrelation, this violates standard statistical techniques that assume independence among observations. For example, regression analyses that do not compensate for spatial dependency can have unstable parameter estimates and yield unreliable significance tests. Spatial regression models (see below) capture these relationships and do not suffer from these weaknesses.

It is also appropriate to view spatial dependency as a source of information rather than something to be corrected. Effects also manifest as spatial heterogeneity, or the apparent variation in a process with respect to location in geographic space. Spatial heterogeneity means that overall parameters estimated for the entire system may not adequately describe the process at any given l measurement scale is a persistent issue in spatial analysis; more detail is available at the modifiable areal unit problem (maup) topic entry. 3] in more general terms, no scale independent method of analysis is widely agreed upon for spatial l sampling involves determining a limited number of locations in geographic space for faithfully measuring phenomena that are subject to dependency and heterogeneity. These basic schemes can be applied at multiple levels in a designated spatial hierarchy (e. It is also possible to exploit ancillary data, for example, using property values as a guide in a spatial sampling scheme to measure educational attainment and income. Spatial models such as autocorrelation statistics, regression and interpolation (see below) can also dictate sample design. Fundamental issues in spatial analysis lead to numerous problems in analysis including bias, distortion and outright errors in the conclusions reached. A paper by benoit mandelbrot on the coastline of britain it was shown that it is inherently nonsensical to discuss certain spatial concepts despite an inherent presumption of the validity of the concept. Locational fallacy refers to error due to the particular spatial characterization chosen for the elements of study, in particular choice of placement for the spatial presence of the l characterizations may be simplistic or even wrong. Studies of humans often reduce the spatial existence of humans to a single point, for instance their home address. This can easily lead to poor analysis, for example, when considering disease transmission which can happen at work or at school and therefore far from the spatial characterization may implicitly limit the subject of study. For example, the spatial analysis of crime data has recently become popular but these studies can only describe the particular kinds of crime which can be described spatially. Ecological fallacy describes errors due to performing analyses on aggregate data when trying to reach conclusions on the individual units. However, in spatial analysis, we are concerned with specific types of mathematical spaces, namely, geographic space. In geographic space, the observations correspond to locations in a spatial measurement framework that capture their proximity in the real world. The locations in a spatial measurement framework often represent locations on the surface of the earth, but this is not strictly necessary. A spatial measurement framework can also capture proximity with respect to, say, interstellar space or within a biological entity such as a liver. The fundamental tenet is tobler's first law of geography: if the interrelation between entities increases with proximity in the real world, then representation in geographic space and assessment using spatial analysis techniques are euclidean distance between locations often represents their proximity, although this is only one possibility. There are an infinite number of distances in addition to euclidean that can support quantitative analysis. It is also possible to compute minimal cost paths across a cost surface; for example, this can represent proximity among locations when travel must occur across rugged of spatial analysis[edit].

Data comes in many varieties and it is not easy to arrive at a system of classification that is simultaneously exclusive, exhaustive, imaginative, and satisfying. And regional studies deal with large tables of spatial data obtained from censuses and surveys. Multivariable analysis (or factor analysis, fa) allows a change of variables, transforming the many variables of the census, usually correlated between themselves, into fewer independent "factors" or "principal components" which are, actually, the eigenvectors of the data correlation matrix weighted by the inverse of their eigenvalues. Since factors are not-correlated, other smaller processes than social status, which would have remained hidden otherwise, appear on the second, third, … analysis depends on measuring distances between observations : the choice of a significant metric is crucial. The euclidean metric (principal component analysis), the chi-square distance (correspondence analysis) or the generalized mahalanobis distance (discriminant analysis ) are among the more widely used. Multivariate methods in spatial analysis began really in the 1950s (although some examples go back to the beginning of the century) and culminated in the 1970s, with the increasing power and accessibility of computers. 12] the use of factor analysis in geography, made so easy by modern computers, has been very wide but not always very wise. The vectors extracted are determined by the data matrix, it is not possible to compare factors obtained from different censuses. A better solution, proposed by psychometricians,[14] groups the data in a « cubic matrix », with three entries (for instance, locations, variables, time periods). A three-way factor analysis produces then three groups of factors related by a small cubic « core matrix ». 15] this method, which exhibits data evolution over time, has not been widely used in geography. These statistics require measuring a spatial weights matrix that reflects the intensity of the geographic relationship between observations in a neighborhood, e. Classic spatial autocorrelation statistics compare the spatial weights to the covariance relationship at pairs of locations. Spatial autocorrelation that is more positive than expected from random indicate the clustering of similar values across geographic space, while significant negative spatial autocorrelation indicates that neighboring values are more dissimilar than expected by chance, suggesting a spatial pattern similar to a chess l autocorrelation statistics such as moran' global in the sense that they estimate the overall degree of spatial autocorrelation for a dataset. The possibility of spatial heterogeneity suggests that the estimated degree of autocorrelation may vary significantly across geographic space. Local spatial autocorrelation statistics provide estimates disaggregated to the level of the spatial analysis units, allowing assessment of the dependency relationships across tics compare neighborhoods to a global average and identify local regions of strong autocorrelation. Spatial stratified heterogeneity reflects the essence of nature, implies potential distinct mechanisms by strata, suggests possible determinants of the observed process, allows the representativeness of observations of the earth, and enforces the applicability of statistical inferences. The value of q is within [0, 1], 0 indicates no spatial stratified heterogeneity, 1 indicates perfect spatial stratified value of q indicates the percent of the variance of an attribute explained by the q follows a noncentral f probability density function. Kriging is a more sophisticated method that interpolates across space according to a spatial lag relationship that has both systematic and random components. This can accommodate a wide range of spatial relationships for the hidden values between observed locations. Kriging provides optimal estimates given the hypothesized lag relationship, and error estimates can be mapped to determine if spatial patterns l regression[edit].

Also: local regression and l regression methods capture spatial dependency in regression analysis, avoiding statistical problems such as unstable parameters and unreliable significance tests, as well as providing information on spatial relationships among the variables involved. Depending on the specific technique, spatial dependency can enter the regression model as relationships between the independent variables and the dependent, between the dependent variables and a spatial lag of itself, or in the error terms. Geographically weighted regression (gwr) is a local version of spatial regression that generates parameters disaggregated by the spatial units of analysis. 19] this allows assessment of the spatial heterogeneity in the estimated relationships between the independent and dependent variables. Spatial stochastic processes, such as gaussian processes are also increasingly being deployed in spatial regression analysis. Model-based versions of gwr, known as spatially varying coefficient models have been applied to conduct bayesian inference. 20] spatial stochastic process can become computationally effective and scalable gaussian process models, such as gaussian predictive processes[21] and nearest neighbor gaussian processes (nngp). In addition, the topological, or connective, relationships between areas must be identified, particularly considering the often conflicting relationship between distance and topology; for example, two spatially close neighborhoods may not display any significant interaction if they are separated by a highway. After specifying the functional forms of these relationships, the analyst can estimate model parameters using observed flow data and standard estimation techniques such as ordinary least squares or maximum likelihood. Competing destinations versions of spatial interaction models include the proximity among the destinations (or origins) in addition to the origin-destination proximity; this captures the effects of destination (origin) clustering on flows. Computational methods such as artificial neural networks can also estimate spatial interaction relationships among locations and can handle noisy and qualitative data. Adaptive systems theory as applied to spatial analysis suggests that simple interactions among proximal entities can lead to intricate, persistent and functional spatial entities at aggregate levels. Cellular automata modeling imposes a fixed spatial framework such as grid cells and specifies rules that dictate the state of a cell based on the states of its neighboring cells. As time progresses, spatial patterns emerge as cells change states based on their neighbors; this alters the conditions for future time periods. The method analyzes the spatial statistics of the geological model, called the training image, and generates realizations of the phenomena that honor those input multiple-point statistics. Together, several realizations may be used to quantify spatial of the recent methods is presented by tahmasebi et al. Furthermore, the method is not sensitive to any type of data and is able to simulate both categorical and continuous scenarios. Information: geographic information systems § spatial phic information systems (gis) and the underlying geographic information science that advances these technologies have a strong influence on spatial analysis. The increasing ability to capture and handle geographic data means that spatial analysis is occurring within increasingly data-rich environments. Geographic data capture systems include remotely sensed imagery, environmental monitoring systems such as intelligent transportation systems, and location-aware technologies such as mobile devices that can report location in near-real time. Gis provide platforms for managing these data, computing spatial relationships such as distance, connectivity and directional relationships between spatial units, and visualizing both the raw data and spatial analytic results within a cartographic flow map of napoleon's ill-fated march on moscow is an early and celebrated example of geovisualization.

Projection transformation theory is the foundation of spatial object l distribution: the similar spatial object groups positioning information, including distribution, trends, contrast etc.. Form: the geometric shape of the spatial l space: the space objects' approaching l relationship: relationship between spatial objects, including topological, orientation, similarity, etc.. Gvis) combines scientific visualization with digital cartography to support the exploration and analysis of geographic data and information, including the results of spatial analysis or simulation. Gvis leverages the human orientation towards visual information processing in the exploration, analysis and communication of geographic data and information. In contrast with traditional cartography, gvis is typically three- or four-dimensional (the latter including time) and phic knowledge discovery (gkd) is the human-centered process of applying efficient computational tools for exploring massive spatial databases. Gkd includes geographic data mining, but also encompasses related activities such as data selection, data cleaning and pre-processing, and interpretation of results. Gkd is based on the premise that massive databases contain interesting (valid, novel, useful and understandable) patterns that standard analytical techniques cannot find. Gkd can serve as a hypothesis-generating process for spatial analysis, producing tentative patterns and relationships that should be confirmed using spatial analytical l decision support systems (sdss) take existing spatial data and use a variety of mathematical models to make projections into the future. Information atical able areal unit l of spatial analysis ic phic information ographic architectural spatial olation domain ry problem (in spatial analysis). Upton & bernard fingelton: spatial data analysis by example volume 1: point pattern and quantitative data john wiley & sons, new york. Tucker l r (1964) « the extension of factor analysis to three-dimensional matrices », in frederiksen n & h gulliksen eds, contributions to mathematical psychology, holt, rinehart and winston, ny. Changes in the location of manufacturing in new zealand 1957-1968: an application of three-mode factor analysis". 2014), hierarchical modeling and analysis for spatial data, second edition, monographs on statistics and applied probability (2nd ed. Geostatistical simulation and reconstruction of porous media by a cross-correlation function and integration of hard and soft data". Dia commons has media related to spatial data commission on geospatial analysis and educational resource about spatial statistics and geostatistics. Comprehensive guide to principles, techniques & software and spatial al center for geographic information and analysis (ncgia). Cartographic association (ica), the world body for mapping and giscience ization of technical ical data ional ation atical t ific re interface cal opher r. Ries: geographygeostatisticsstatistical data typesspatial data analysiscartographygeographic data and informationmathematical and quantitative methods (economics)hidden categories: articles to be merged from july 2016all articles to be mergedall articles with unsourced statementsarticles with unsourced statements from february 2013articles with unsourced statements from december 2010articles with unsourced statements from november 2015articles with unsourced statements from august 2014wikipedia spam cleanup from june 2014wikipedia further reading cleanupcommons category without a link on logged intalkcontributionscreate accountlog pagecontentsfeatured contentcurrent eventsrandom articledonate to wikipediawikipedia out wikipediacommunity portalrecent changescontact links hererelated changesupload filespecial pagespermanent linkpage informationwikidata itemcite this a bookdownload as pdfprintable version. A non-profit l data analysis and modeling with l data analysis and modeling with r¶. R is a widely used programming language and software environment that for data analysis and graphics. Also has advanced capabilities for dealing with spatial, and spatio-temporal, data; and it provides unparalleled opportunities for analyzing such here if you have never used r, or if you need a refresher.

Spatial data manipulation with this to learn about the basics if reading, writing, and manipulating spatial data. Spatial l simulation models with l data analysis and modeling with l data analysis and modeling with r¶. The results of spatial analysis are dependent on the locations of the objects being analyzed. Software that implements spatial analysis techniques requires access to both the locations of objects and their attributes. Of white by census blocks, hed by census ons of the visualization s two different visualization us no task view: analysis of spatial iner:roger t: at r includes many functions that can be used for reading,Visualising, and analysing spatial data. Geographical" spatial data, where observations can be geographical locations, and where additional information locations may be retrieved if the location is recorded . Active development contributed packages address two broad areas: moving spatial and out of r, and analysing spatial data in g-list is a good place to begin for obtaining discussing questions about both accessing data, and analysing mailing list is a good place to search for information nt courses. If you some package is missing from the list, please let me s for spatial data. Because many of es importing and using spatial data have had to s of storing data and functions for visualising it,An initiative is in progress to construct shared plotting functions for spatial e is discussed in a note now on cran, and is ly developed ing simple features for r. It provides simple features vector data, and as such is a modern implementation of parts other packages have become dependent on e provides an interface to topology es a "spatiallinesnetwork" class based routing analysis within r. Another network package t spatial objects, facilitate handling and reporting of and geometry validity issues. It claims to provide a r that will fix all geometry problems, and eliminate (at ) the likelihood of having issues when doing spatial e is a major extension of spatial s to virtualise access to large rasters, permitting s to be analysed, and extending the analytical tools both raster and vector data. E contains spatial functions meant e the core functionality of ing a parallel processing engine for use with e provides linked micromaps e provides rams with rectangle sizes reflecting for example population; es a simpler binning approach to us s the shared classes defined -temporal data (-temporal data in l object from class spatialgriddataframe ative approach to some of these issues is implemented ing support. In addition,Facilities directed to meet the needs of geologists, and uses ng spatial data. Uces many gis methods that now permit much to be done l data without having to use gis in addition to r. It may nce, which provided distances and routes on geographic s computations of distance and be carried out on spatial data in geographical e provides an interface to dggrid g with discrete global grids, using hexagons, triangles, ds to overcome the issue that every bin have the same of sampling functions. S to permit the accessing and manipulating of spatial data e provides osition of entropy for categorical map comparisons. E permits interactive graphical l data es spatial ng and random sampling from compact geographical a data class for perability working with spatial-temporal data together ponding functions and methods (conversions, basic basic data manipulation). The class distinguishes between spatial,Temporal and other dimensions to facilitate the development perability of tools build for it. Additional features -based addressing of data and internal consistency checks (ng for the right data order in calculations). Uscensus2000 suite of packages (uscensus2000cdp,Uscensus2000tract) makes of data from the 2000 us census more convenient.

An set, guerry's "moral statistics of france", has been e, which provides maps and examples designed to contribute to the multivariate and spatial e is designed for downloading, manipulating bathymetric and topographic data in query the etopo1 bathymetry and topography database hosted by , use simple latitude-longitude-depth data in ascii format, and age of the advanced plotting tools available in r to ation-quality bathymetric maps (see ). Modern country boundaries ed at 2 resolutions ons to join and map tabular data referenced by or codes. Higher resolution s are available from the linked ical country boundaries (1946-2012) can be obtained from e along with functions for ce matrices (g and measuring country e with for exploring and developing correction tools for a collection of utility ience functions, and some interesting spatial e provides wrappers for the abstraction library (gdal) bed a geojson-centred approach to reading wkt data. And similarity transformations on sp objects may be functions in windows and mac osx cran binaries e subsets of possible data source drivers; if needed, use other conversion utilities, or install from t a version of gdal with the required e provides functions g and writing well-known text (wkt) geometry, and e provides functions for reading and -known binary (wkb) g and writing spatial data - other of other packages for accessing vector data on cran:Provides access to the same kinds of geographical databases as s -. E gives a simple interface between -making software and access to open street map raster images,Provides infrastructure to access from different sources, to work with the data in common r manner,And to convert data into available infrastructure provided e provides additional functions to the. Rpostgresql' package to interface r with a 'postgis'-enabled database,As well as convenient wrappers to common 'postgresql' queries. E provides functions to convert 'hstore' data types from 'postgresql' into standard r objects,As well as to simplify the import of r data frames (including frames) into 'postgresql'. E provides methods spatial objects interactively, usually on a web mapping es a simple method to visualize 'sp' and 'raster' objects,Allows for basic zooming, panning, identifying, and labeling l objects, and does not require that the data be in e allows raphic representations such as proportional symbols,Choropleth, typology, flows or discontinuities. North arrows and scales for such e provides methods for isation of spatial and spatio-temporal objects in google maps a package providing methods visualisation of spatial and spatio-temporal objects in . A further option tr, which provides -mapping functionality to combine vector data files and tiles from different pattern e is a recommended package shipped with base r, and l core functions, including an implementation of its author, prof. In addition,Allows freedom in defining the region(s) of interest, and ions to marked processes and spatial covariates. Ths are model-fitting and simulation, and it has a e that will enable the user to fit inhomogeneous point with interpoint e provides graphs, graph visualisation and graph ies to be used with spatial point pattern analysis. E also allows point data to be a polygonal region of interest, and covers many methods,Including 2d kernel densities. S statistical methods for analyzing case-control point methods available closely follow those in chapter 6 of l statistics for public health data by waller and rs, functions and data for spatial point pattern analysis,Used in the book on spatial ecology of the ecespa/aeet. Second-order multi-scale analyses derived from ripley'e is a collection ons for estimating centrographic statistics and ries from spatial point ns functions for spatial distance sampling data es segregation measures for multitype spatial the grieg-smith method on. Computation of a full set of spatial statistic functions ce, including classical ones (ripley's k and others) and ones used by spatial economists (duranton and overman's kd,Marcon and puech's m). It relies on spatstat for ns functions that lattice-based density estimator of barry and mcintyre, ts for point processes in two-dimensional regions lar boundaries and es a wide range of functions for univariate and tistics, also for larger datasets, n functions for tistics. Besides,It includes functions for the design of optimal spatial ks based on geostatistical e to offer functions to optimize sample configurations, l simulated annealing. Non-gaussian models are inla, and gaussian geostatistical models use maximum e is a tool l/spatio-temporal modelling and prediction with large approach, discussed in cressie and johannesson (2008), field, and hence the covariance function, using a fixed set of functions, where n is typically much smaller than the number points (or polygons) e provides functions simulation and analysis of random fields, and descriptions can be passed es several approaches for spatial extremes fields. E is able to fit, spatially predict ally forecast large amounts of space-time data using [1]. Provides functions geostatistical interpolation of data with irregular t such as runoff related data or data from e provides functions for models with spatially correlated errors by robust and cted maximum likelihood and for computing robust and and block kriging predictions, along with utility functions -validation and for unbiased back-transformation of tions of log-transformed data.

Geostatistical methods in a clean, straightforward, , and is said to be a quasi reboot e implements spatial error permutation-based spatial variable importance using l cross-validation and spatial block bootstrap e provides functions for hybrid machine learning methods for spatial predictive modelling. In addition,Supports the computation of spatial covariance data on rectangles, lcovariance, and the estimation of the parameters of a using the em algorithm, and the estimation of ter standard errors using a spatio-temporal another random tions package. Mapping and other graphical functions es functions o erenced point data via inverse path distance weighting. Coastal marine applications where barriers in the de interpolation with euclidean be used as a processing program for buted data, and is capable of error corrections and e mapping and areal data a package for the detection l clusters of diseases. It extends and depends on e, which provides basic functions ng neighbour lists and spatial weights, tests for rrelation for areal data like moran's i, and functions g spatial regression models, such as sar and car models. Assume that the spatial dependence can be described by ons provide moran fitting, as do more modern functions in e provides implementations r detection and disease mapping functions, including r detection, and supports strata. E offers the formatting of population and case data, standardized incidence ratios, and fitting the bym model . E provides researchers and educators with easy-to-learn ly tools for calculating key spatial statistics and to as well as advanced methods of spatial analysis in real include: local pearson and geographically weighted ation coefficients, spatial inequality measures (gini, , lq, focal lq), spatial autocorrelation (global and 's i), several geographically weighted regression techniques spatial analysis tools (other geographically weighted statistics). Models the spatial correlation is modelled by a set of s, which are assigned a conditional autoregressive (car) bution. Examples of the models included are the bym model as a recently developed localised spatial smoothing e is a helpful way of passing out to winbugs. E fits spatial glmms,Using the matern correlation function as the basic model for e is for sion, which is a dirichlet process bayesian clustering model;. Provides a spatial car term that can be included in the s (which are global, ie. Account for any spatial correlation in the e provides tools uct and exploit spatially weighted context data, and combining the resulting spatially weighted context data dual-level predictor and outcome variables, for the multilevel ce matrices from shape files and represents spatially evel analysis results. Bayesian inference for parametric s spatial survival models - ng and analysis of spatially correlated survival data - e provides modelling functions based d stepwise regression, incremental forward stagewise regression,Least angle regression (lars), and lasso models for selecting l scale of covariates in regression choice of function for spatial regression will depend on t available. If the data are characterised by point the spatial process is continuous, geostatistical methods may , or functions in e. If the areal, and the spatial process is not being treated as continuous,Functions provided in package can also be seen as providing spatial ons, and, as noted above, provides basic functions ng neighbour lists and spatial weights, tests for rrelation for areal data like moran's i, and functions g spatial regression models. It provides the full range indicators of spatial association, such as local moran's i stic tools for fitted linear models, including lier tests. Spatial regression models that can be fitted m likelihood include spatial lag models, spatial error models,And spatial durbin models. For larger data sets, sparse ques can be used for maximum likelihood fits, while spatial least squares and generalised method of moments estimators alternative. Regression is provided using custom locally weighted regression, semiparametric and tric regression, fourier and cubic spline functions, gmm ized spatial logit and probit, k-density functions rfactuals, nonparametric quantile regression and y functions, machado-mata decomposition for sions, spatial ar model, repeat sales models, ionally parametric logit and e provides methods g spatial panel data by maximum likelihood and gm. They exploratory and euclidean methods in nmental sciences, the analysis of habitat selection by tion, decomposition and analysis of space-time series,For ordination methods and other ons for community and vegetation ecologists, and functions in other contributed packages.

One such timation, basing on the classes provided entered cran recently, es a range of spatial nonparametric covariance e provides functions for spatial on generalized estimating equations (gee) and s (wrm), functions for scaling by wavelet sion (wmrr), conducting multi-model inference, and stepwise a package to manipulate species range. E is a platform for experimenting lly explicit individual-based vegetation on other packages to create underlying gis data. S for watersheds aggregation and spatial drainage spatial analysis of plant disease es tools for analyzing spatial data, especially data. It supports the sparse spatial generalized linear of hughes and haran (2013) and the centered autologistic caragea and kaiser (2009).