Computer software for spatial statistical analysis

Prepared by: Rodrigo Tapia-McClung

Last revision: November 22, 2005

• GeoDa (WIN) - Freewarehttps://www.geoda.uiuc.edu/default.php

– Spatial Data Manipulation: create point shape files from text files, centroids for polygons, Thiessenpolygons from points, contiguity based spatial weights for polygons, distance based spatial weightsfor points and polygons.

– Data Transformation: variable transformation (log, exp, etc.), queries, dummy variables (regimevariables), variable algebra (addition, multiplication, etc.), spatial lag variable construction, ratecalculation and rate smoothing.

– Mapping: quantile choropleth and standard deviational maps, outlier maps (box map), percentilemap, circular cartogram, conditional maps, smoothed rate map, excess rate map.

– Exploratory Data Analysis: histogram, box plot, scatter plot, parallel coordinate plot, 3D-scatterplot, conditional plot.

– Spatial Autocorrelation: spatial weights creation (rook, queen, distance, k-nearest), higher orderspatial weights, spatial weights characteristics (connectedness histogram), Moran scatterplot withinference, bivariate Moran scatterplot with inference, Moran scatterplot for rates (Empirical Bayes-EB- standardization), Local Moran significance map, Local Moran cluster map, bivariate LocalMoran, Local Moran for rates (EB standardization).

– Spatial Regression: Ordinary Least Squares (OLS) with diagnostics (e.g., LM test, Moran’s I)Maximum Likelihood spatial lag model, Maximum Likelihood spatial error model, predicted valuemap, residual map

• PASSAGE (WIN) - Freewarehttp://www.passagesoftware.net/

– Calculate geographic distances and angles (Euclidean and Spherical).

– Calculate distance matrices from univariate or multivariate data.

– Calculate distance classes/bins.

– Calculate connections among point locations: Distances, Nearest Neighbors, Minimum SpanningTrees, Relative Neighborhood Networks, Gabriel Graphs, Delaunay/Dirichlet Tessellations, LeastDiagonal Networks.

– Random point patterns.

– Convert point values into grids.

– Point Analyses: Dispersion indices, Second-Order Analyses (i.e., Ripley’s K function), JoinCounts.

– Transect Analyses: Quadrat Variance, Spectral Analysis, Fractal Dimension, Lacunarity Analysis,Wavelet

– Surface Analyses: Quadrat Variance, Lacunarity Analysis, Wavelet.

– Scattered Data Analyses: Correlograms (Moran’s I, Geary’s c and Mantel’s correlation), Bearing,Angular Correlation.

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– Miscellaneous Analyses: Modified t-test for correlation, Mantel tests (including partial Manteltests).

– Graphical Analyses: Coordinate plots (including connections, tessellations, superimposed maps,etc.), Surface plots, Post plots, Transect plots.

• Rookcase (An Excel 97/2000 Visual Basic (VB) Add-in) - Freewarehttp://www.lpc.uottawa.ca/ orhttp://www.lpc.uottawa.ca/data/scripts/index.html

– Regular datset (lattice): Moran’s I, Geary’s c, Join-Count Statistics.

– Irregular dataset (lattice): Moran’s I, Geary’s c, LISA functions (local Moran’s I, Geary’s c andGetis-Ord Gi and G∗

i .

– Monte-Carlo simulations: create random distributions of Moran’s I, Geary’s c or Joint-CountStatistics.

– Import an IDRISI image into Excel.

• SpPack (An Excel Visual Basic (VB) Add-in) - FreewareAvailable by request to the author: george.perry@kcl.ac.ukPerry, G.L.W. 2004. SpPack: spatial point pattern analysis in Excel using Visual Basic for Applications(VBA). Environmental Modelling & Software 19:559-569 (Issue 6, June 2004).Can perform tests in three broad classes: (1) nearest-neighbour derived (first-order) analyses; (2)second-order analyses; and (3) simple grid-based analyses (with an ecological bias).Tests can be performed on univariate and bivariate event sets, and can be performed on specificsubgroups of that data (e.g. if the data were divided into different species or size-classes, etc.).Can also generate event sets (univariate or bivariate) for analysis or comparison; these artificial sets mayconform to complete spatial randomness (CSR), or be aggregated or over-dispersed at a user-specifiedscale, or scales. Tests available in the program include:

– Ripley’s K;

– Diggle’s G and F ;

– k − th order nearest neighbours;

– Local PPA: Fotheringham-Zhan placement method, Getis-Franklin Local Second-Order;

– Neighbourhood Density Function;

– Grid-based and Spatial Autocorrelation: Simple Quadrat Based Mean (variance analysis), GlobalMoran’s I and Geary’s c, Dispersion Indices.

• CrimeStat, version 3.0 (WIN) - Freewarehttp://www.icpsr.umich.edu/NACJD/crimestat.html

– Spatial distribution: statistics for describing the spatial distribution of incidents, such as the meancenter, center of minimum distance, standard deviational ellipse, Moran’s I spatial autocorrelationindex, or directional mean, Moran correlogram that calculates Moran’s I for different distanceseparations.

– Distance analysis: statistics for describing properties of distances between incidents includingnearest neighbor analysis, linear nearest neighbor analysis, and Ripley’s K statistic.

– ‘Hot spot’ analysis: routines for conducting ’hot spot’ analysis including the mode, the fuzzymode, hierarchical nearest neighbor clustering, and risk-adjusted nearest neighbor hierarchicalclustering. The hierarchical nearest neighbor hot spots can be output as ellipses or convex hulls.Also has routines for conducting hot spot analysis including the Spatial and Temporal Analysisof Crime (STAC), K-means clustering, and Anselin’s Local Moran statistics. The STAC andK-means hot spots can be output as ellipses or convex hulls.

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– Interpolation: single-variable kernel density estimation routine for producing a surface or contourestimate of the density of incidents (e.g., burglaries) and a dual-variable kernel density estimationroutine for comparing the density of incidents to the density of an underlying baseline (e.g.,burglaries relative to the number of households).

– Space-time analysis: tools for analyzing clustering in time and in space. These include the Knoxand Mantel indices and the Correlated Walk Analysis module, which analyzes and predicts thebehavior of a serial offender.

• spdep: Spatial Dependence (for use with R - WIN, MacOS, Linux) - Freewarehttp://cran.r-project.org/src/contrib/Descriptions/spdep.html orhttp://spatial.nhh.no/R/spdep/

A collection of functions that run in the R language to:

– Create spatial weights matrix objects from polygon contiguities, from point patterns by distanceand tesselations, for summarising these objects, and for permitting their use in spatial dataanalysis.

– Tests for spatial autocorrelation, including global Moran’s I, Geary’s c, Hubert/Mantel generalcross product statistic, Empirical Bayes estimates and Assuncao/Reis Index, Getis/Ord G andmulticoloured join count statistics, local Moran’s I and Getis/Ord G, saddlepoint approximationsfor global and local Moran’s I.

– Estimate spatial simultaneous autoregressive (SAR) models.

• SAGE for Sun workstation only (running Solaris), for use with ARC/INFO - Freewareftp://ftp.shef.ac.uk/pub/uni/academic/D-H/g/sage/sagehtm/sage.htm orhttp://www.shef.ac.uk/∼scgisa/newscgisa/research.htm

– Computing distribution statistics of attributes.

– Correlation analysis for every selected pair of attributes and cross-tabulated analysis on categoricaldata.

– Local Getis and Moran I indicators and their significant values, and saving these results as newattributes.

– Computing the relative risks for objects based on observed and expected counts by means ofempirical Bayesian and kernel estimations. Two models - Gamma and log-normal, are supportedfor empirical Bayesian estimations.

– Fitting a classical linear regression model and the models with spatial error term and spatialindependent term as well as performing tests on the goodness-of-fit of the models, coefficients andspatial dependence, and saving results such as residuals, fitted values and leverages as attributes.

– Fitting a generalised linear regression model.

• IDRISI (Win) - Licensedhttp://www.clarklabs.org/

– Summary statistics of raster images.

– Produce Thiessen polygons around a set of irregularly distributed points.

– Spatial Autocorrelation of an image (Moran’s I).

– Triangulated Irregular Network, Kriging.

– Surface Interpolation and Spatial Trend on surfaces.

– Quadrat analysis.

– Measure the similarity between two images or maps.

– Create a random image with random values that obey either a rectilinear, normal, or lognormaldistribution, according to a user-specified mean and standard deviation.

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– Variograms using Gstat (a program for geostatistical modeling, prediction and simulation).

• ArcGIS 9 (Win, UNIX, Solaris) - Licensedhttp://www.esri.com/

– TIN creation and manipulation

– Statistics for tables

– Kernel, Line and Point Density Functions

– Calculate distances

– Surface interpolation: Inverse Distance Weighting, Kriging, Trends.

– Cell statistics

– Map Algebra

– Block, Focal, Line and Point Statistics

– Raster creation

– Nearest Neighbors, Getis-Ord G and G∗, Global and Local Moran’s I

– Measures for Geographic Distributions: central feature, standard deviational ellipse, linear direc-tional mean, mean center, standard distance.

• Spacestat, version 1.91 and ArcView 3.x extension (WIN) - Licensedhttp://www.terraseer.com/products/spacestat.html

– Creation and manipulation of spatial weights matrices

– Exploratory spatial data analysis (ESDA): descriptive statistics, join count statistics, Moran’s I(global and local), Geary’s c (global), G-statistics (global and local Gi and G∗

i ).

– Visualization: Box, Percentile, Spatial Lag Bar Chart and Spatial Lag Pie Chart maps. MoranScatterplot, LISA Local Moran, Moran Significance, G-Stat, Residual and Predicted Maps.

– Spatial regressions: Generic, Trend surface, Spatial regimes, Spatial expansion, Spatial analysisof variance (ANOVA).

– Includes techniques to describe and visualize spatial distributions, identify atypical locations (spa-tial outliers), discover patterns of spatial association (spatial clusters) and suggest different spatialregimes and other forms of spatial non-stationarity.

• S-Plus (S+SpatialStats and ArcView GIS extension), version 7 (WIN, Linux, UNIX) - Licensedhttp://www.insightful.com/products/splus/ orhttp://www.insightful.com/products/spatial/default.asp orhttp://www.insightful.com/products/arcview/default.asp

– Geostatistical data: Contour plots, 3D point clouds, Variogram plots and box plots Directionalvariograms and correlograms, Empirical variogram estimation, Variogram models including spher-ical and exponential, Ordinary and universal kriging, Block and Point Kriging prediction at arbi-trary locations with standard errors, Parametric and nonparametric trend surface.

– Point Patterns: Point maps that include region boundaries, Spatial randomness tests, Ripley’sK-functions, Simulation of spatial random processes, Local intensity estimation.

– Lattice Data:“Binning” of high density data into a regular lattice of counts, Geary and Moran spa-tial autocorrelation coefficients, Spatial regression models including conditional and simultaneousautoregressive models, Nearest neighbor search, Visualization of neighbor structures.

• A list of software, ordered by category/functionality, and listing the platform (WIN, Linux, etc.), thetype of GIS (Raster/Vector) and whether they contain geostatistical functions or not can be found at:http://www.ai-geostats.org/.

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