R and geographical information systems , especially

The paper starts by sketching the key modes of spatial data analysis (point pattern, continuous surface, areal/lattice), and how they fit into legacy GIS data models. Based on development work with the GRASS release 5 team (GRASS 5 is GPL), status is reported for using R in the analysis of sites (point) data and for raster data, as well as using R as an intermediate analytical environment for interpolating from sites data to discretised continuous surfaces. Indications are given for broader interfacing using the GDAL library for GIS raster data and remote sensing data for other GIS than GRASS. So far, there are few vector data results, although again, interesting open source possibilities seem to be emerging. 1 Spatial data analysis Spatial data analysis ranges from the visualization and exploration of spatial data, through spatial statistics to spatial econometrics. The techniques involved are intended to explore for and demonstrate the presence of dependence between observations in space. Typically, observations are classified into three broad types: fields or surfaces with values at least theoretically observable over the whole study area, as in geostatistics, point patterns representing the occurrence of a phenomenon, such as reported cases in epidemiology, and finally lattice observations, where attribute values adhere to a tesselation of the study area. This last form has much in common with time series studies, and shares a number of key testing techniques with econometrics. ∗Economic Geography Section, Department of Economics, Norwegian School of Economics and Business Administration, Bergen, Norway Proceedings of DSC 2001 2 Since observations of spatial data are as unlikely to be independent as observations on time series, it is perhaps surprising that not more use has been made of this source of information. With an adequate choice of explanatory variables, this spatial dependence may be readily drawn into a model. The literature on spatial statistics is substantial (see for example [7, 8, 21, 24, 15, 1, 16], and more recently [9, 3, 13]). Attention has also been given to the potentials for integrating Geographical Information Systems (GIS) with modelling and analysis tools, for instance in [14, 10, 19], and [20]. Some of the analytical tools are available in the SPLUS spatial statistics module [17], and links between the ARC-INFO GIS and the ArcView desktop GIS are available for SPLUS. Special numbers of journals have been devoted to exploratory spatial data analisis (The Statistician, 1998, number 3), and computing environments for spatial data analysis (Journal of Geographical Systems, 2000, number 3), among others. Within R, a range of packages are designed for use with spatial data of various kinds, or can be used for such data as well as for non-spatial data. A survey dating from 1998 can be found in [5], written with Albrecht Gebhardt of the University of Klagenfurt, one of the people who has contributed most to repackaging and releasing tools for spatial data analysis. For the analysis of spatially continuous data, he is maintaining the sgeostat package, and is working on compiled functions to increase its speed to that of the functions in spatial; he also maintains akima, ash, and tripack. A promising package in development is Paulo Ribeiro and Peter Diggle’s geoR. For point pattern data, spatial and splancs are available, and other tools are under development. So far no code has been posted for area data analysis, where the clear benchmark is Luc Anselin’s GAUSS-based closed source SpaceStat. Some mapping functionality is available from work by Ray Brownrigg, discussed in [6]. A starting point for spatial data analysis is that positional information for the observations matters. For point pattern analysis, all we have is where the points are located, given most often as coordinates in two dimensions. The only realistic analogy in data analysis is with time series, in which either local position relative to an arbitrary origin, or absolute position in for example UTC is given. However, spatial data vary a great deal both in the ways in which their position attributes are recorded, and in the adequacy of documentation of how position has been determined. This applies both to secondary data and to data capture by remote sensing, Global Positioning System input, or data capture from analogue maps. This also constitutes a specific difference from the analysis say of medical imagery, which only requires a local coordinate system. Knowledge about the spatial reference system is needed to establish the positional coordinates’ units of measurement, obviously needed for calculating distances between observations, and/or for describing the network topology of their relative positions. 1http://www.math.lancs.ac.uk/∼ribeiro/geoS.html 2Adrian Baddeley and Rolf Turner have made a beta of spatstat available on http://www.maths.uwa.edu.au/∼adrian/spatstat.html 3http://www.spacestat.com 4ftp://ftp.mcs.vuw.ac.nz/pub/statistics/map Proceedings of DSC 2001 3