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Automated interpretation of the spatial distribution of socio-economic conditions
Contour maps and perspective views
Is the spatial distribution of a socio-economic condition characterized best by a 2-dimensional or by a 3-dimensional graphic? This is not an easy question to answer so, as argued, let us first agree that the spatial distribution of a socio-economic condition is continuous. Now let us agree that at least at the macro level the landform of the surface of the earth is continuous; and, how would I characterize the landform of the surface of the earth? I could use a contour map (a 2-dimensional graphic), and to provide an immediate impression of the mountains, valleys and plains I could use a perspective view (a 3-dimensional graphic in a 2-dimensional space – the surface of the paper). Can I not do the same with Italian born as a percentage of the total population? After all it is just another continuous distribution. The answer is yes.  Fig. 3: A contour map of Burnside Figure 3. provides an example of a contour map. The black indicates virtually no Italian born and the red patch indicates a lot of Italian born relative to the total population. While I do not find contour maps aesthetically pleasing at least they go part of the way to characterising the continuous nature of the spatial distribution of a socio-economic condition. Regardless, similar to choropleth maps, interpreting reality from a contour map is a long and tortuous journey. There are many contour mapping options, and a change in any one will modify, often dramatically, the characterisation of the spatial distribution. Also, the contour map provides a strong visual statement suggesting the result of hypothesis testing, not what it really is – the starting point of an investigation, a vehicle for hypothesis generation. Finally, there are many methods of contour interpolation (or extrapolation) and smoothing, and these and their implications are considered briefly in the following discussion of perspective views. A perspective view looking from the southwest at Burnside and showing Italian born as a percentage of the total population is presented in figure 4. It gives a good – even exciting - idea of the spatial distribution of this socio-economic condition. There is a “mountain” of Italian born in the northeast corner and this mountain will be the subject of considerable analysis in my ongoing research. As with most things there is good news and bad news; let us deal with the bad news about perspective views first. Using the census data for Burnside you prepare to generate a perspective view by building a centroid set containing 80 subsets (one for each CCD) with each subset being an {x,y,z}-tuple. The x and y elements are the easting and northing respectively of the centroid for one of the CCDs and the associated z element is the percentage datum for that CCD. Notwithstanding the fact that the locations of the centroids are usually not determined with anything approaching the rigor of applied plane geometry, thus far the investigator has little to worry about. But that is about to change. The centroid set is used to build a matrix or “grid” with rows and columns. The intersection of a row and column is a cell containing a number which is an interpolated (or extrapolated) and smoothed datum. The grid data will be used to generate the perspective view so the nature of the view is dependent completely on the method used for interpolation (or extrapolation) and smoothing; the same statement applies to the generation of a contour map, as discussed. The selection of this method is anything but straightforward, since even after the method has been selected usually its application can be “tuned” by adjusting several parameters. Kriging is the method used to build the grid data that, in turn, were used to generate the perspective views presented in this paper. But other methods include minimum curvature, polynomial regression, and triangulation with linear interpolation. There are many others and the application of each results in a grid containing very different interpolated (or extrapolated) and smoothed data and, hence, will result in the generation of very different looking perspective views (and contour maps). The question is: Which one is the best perspective view? But wait, there is more. Given the grid data, the technology of generating a perspective view is very involved with a vast array of options. For example, view point and distance from the view are but two of the choices to be made by the investigator, and they are perhaps the easiest to make. More subtle is the application of colour, the nature of shading and the aspect ratio.  Fig. 4: A perspective view of Burnside – Italian born The most unsettling aspect of perspective views is related to exactly what is so engaging about them in the first instance: they give a good – even exciting – idea of the spatial distribution of a socio-economic condition. But this, apparently, is where it stops. After looking at the view from several different points and distances and changing the colors and aspect ratio and adjusting a number of other parameters, you are drawn to the conclusion that the perspective view is only just a qualitative characterisation of the spatial distribution of the socio-economic condition. It cannot be analysed quantitatively. |