GeoWorld

GeoWorld March 2013

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Dependency Issues The other type of spatial dependency, spatial correlation, provides the foundation for analyzing spatial relationships among map layers. It involves spatially evaluating traditional statistical procedures using one of four ways to access georegistered data: local, focal, zonal and global (see Figure 3 and "Author's Notes 3 and 4"). After the spatially coincident data are collected and compatibly formatted, they can be directly passed to standard multivariate statistics packages or more-advanced statistical engines (e.g., CART, induction or neural net). Also, a growing number of GISs have incorporated many of the most frequently used statistical operations. Most statistical-analysis operations simply repackage map values for processing by traditional statistics procedures. For example, local processing of map layers is analogous to when two maps are overlaid on a light table. As your eye moves around, you note the spatial coincidence at each spot. In grid-based map analysis, the cell-by-cell collection of data for two or more grid layers accomplishes the same thing by spearing the map values at a location, creating a summary (e.g., simple or weighted average), storing the new value and repeating the process for the next location. Figure 2. Surface modeling involves generating map surfaces that portray the continuous spatial distribution implied in a set of discrete point data. More Processing Another technique, focal processing, funnels the maplayer data surrounding a location (roving window), creates a summary (e.g., correlation coefficient), stores the new value and then repeats the process. Note that local and focal procedures store the results on a cell-by-cell basis. The other two techniques (right side of Figure 3) generate entirely different summary results. Zonal processing uses a predefined template (i.e., map region) to lace together the map values for a regionwide summary. For example, a wildlife habitat unit may serve as a template map to retrieve slope values from a data map of terrain steepness, compute the average of the values and then store the result for all locations defining the region. Or maps of animal activity for two time periods could be accessed and a paired t-test performed to determine if a significant difference exists within the habitat unit. The interpretation of the resultant map value assigned to all template locations is that each cell is an "element of a spatial entity having that overall summary statistic." Global processing isn't much different from the other techniques in terms of mechanics, but it's radically different in terms of the numerical rigor implied. In map-wide statistical analysis, the entire map is considered a variable, each cell a case and each value a measurement (or instance) in mathematical/ statistical modeling terminology. Figure 3. Statistical analysis of mapped data involves repackaging mapped data for processing by standard multivariate statistics or more-advanced statistical operations. Within this context, the processing has "all the rights, privileges and responsibilities" afforded nonspatial quantitative analysis. For example, a regression could be spatially evaluated by "plunging" the equation through a set of independent map variables to generate a dependent-variable map on a cell-by-cell basis or reported as an overall map-wide value. So what's the take-home from all this discussion? It's that maps are "numbers first, pictures later," and we can spatially discover and subsequently evaluate the spatial relationships inherent in sets of grid-based mapped data as true "map-ematical" expressions. All that's needed is a new perspective of what a map is (and isn't). Author's Note: In the online book Beyond Mapping III at www. innovativegis.com/basis/MapAnalysis, see 1) Topic 9, "Analyzing Landscape Patterns"; 2) Topic 2, "Spatial Interpolation Procedures and Assessment," and 8, "Investigating Spatial Dependency"; 3) Topic 22, "Reclassifying and Overlaying Maps," Section 2, "Getting the Numbers Right"; and 4) a reference to C. Dana Tomlin's four data-acquisition classes. M A R C H 2 O 1 3 / W W W . G E O P L A C E . C O M 11

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