Understanding Dynamic Data
In the New Orleans examples described previously, we were able to use information over time to gain insight into how the changes that occur over time can help us to better understand our current problems and needs. In this example, we examine a more formal mathematical approach to change over time, in this case concerning the spread of innovation in public policy and organizations among American states.
Example: Diffusion of Innovation in the United States (3D map)
The establishment of colleges to train teachers, called normal schools in nineteenth-century America, or the date by which a state required school age children to attend school are examples of the kind of innovation that organizational researchers study (Jensen, 2004). Using data from a study by Walker (1973), Jensen (2004: 3) examines a number of hypotheses that might explain the overall path of diffusion across 27 different types of organizational and policy innovation including the two educational-oriented adoptions we will examine. One of the interesting features of data on diffusion is that measures of diffusion combine both time and space. Diffusion happens across these two dimensions, and the degree to which one process dominates the other can impact the process of diffusion and the adaptation of innovative forms and policies. Imagine a situation where two relatively small political units share a common border and the reaches of both areas are well within a day’s travel time. If one unit adopts a new organization or a new practice that is reasonably visible and judged by the people in the unit to be successful and to contribute to the greater good, people who reside in the other unit traveling back and forth will begin to wonder if this innovation would be good for them to adopt as well. So innovation can spread via diffusion over space. The length of time may vary by how far away the innovation is from the potential adopters and by how much communication, travel, contact, and so on there is between them as well as by how fast such activities occur. If we were to map such a process, we would see a small area where the innovation begins, and then over time we would see a gradual seeping out from that center, almost like water flowing downhill, faster (shorter time frame) or slower depending on how steep the terrain was from the high spot (first place the form was adopted).
On the other hand, diffusion can also skip the surrounding areas and appear to jump across space in a relatively short time. Suppose one of the influential founders of the innovation were to relocate several units away; this innovator may convince new fellow residents to adopt the innovation quickly, even though many of the new units’ residents have not seen the new form in action as in the first example. Either way, mapping the adoption of these new forms and practices can help us to understand the process, the factors that might influence it, and the differences to be seen when comparing one innovation to another.
One way to proceed is to construct a thematic map of the places that adopt the innovation and the time frame involved. In the case of the opening of teacher training colleges, Figure 2.64 shows the time frames in which U.S. states adopted this organizational innovation.
Figure 2.64 The adoption of teaching colleges among the U.S. states, 1839-1911
Several interesting patterns jump out from the map. These colleges were founded initially in the Northeastern states, such as New York, New Jersey, Connecticut, Massachusetts, and a couple of innovative Midwestern states, Iowa and Michigan. A second wave of adoptions seems to have occurred in a spatial diffusion pattern starting from New York and Massachusetts going north to Upper New England and south to Pennsylvania and Delaware; West Virginia only became a state during the Civil War but seems to have immediately adopted this innovation. A second wave of spatial diffusion emanates from Iowa, reaching most of the states that border on Iowa by 1870; a couple of distant western states also adopt in this period. Most of the Western U.S. states, along with Louisiana and Arkansas, founded these colleges in the period from 1871 to 1895, but there is a curious band of holdouts from Ohio to Kentucky, Tennessee, Alabama, and Mississippi that are the last, along with Maryland, to adopt this organizational form. Mapping these data show the patterns of diffusion clearly and suggest many possible explanations. For example, the southern states that resisted so long may have had problems with poverty and racial inequality that held back the adoption of teacher training colleges in the post-Civil War period.
Another way to look at these data is to take a more formal approach to the diffusion process. Walker (1973) calculates an innovation score for each of the 27 forms or policies his data cover to relate how each state’s adoption of the innovation related to the entire process of adoption across all the states. Walker gave a score of 0 on this measure to the first state that adopted, and then gave subsequent states a score proportional to the length of time after the initial adoption that it took for later adapters to create the new form or organization or policy innovation. If Massachusetts adopted the first teacher training school in 1839, and Mississippi was the last state to do so in 1910, the latter gets a score of 1 and the former 0. If Indiana adopts this organization in 1865, the score for innovation is the time since the first one divided by the entire time it takes for all states to adopt, or 1865-1839/1910-1839, or 26/71, for a score of 0.3661. This measure is a kind of reverse innovation score, as the lower the score the more "innovative" the state is on this measure.
Although flat maps like the ones we have used thus far in this topic can be very informative, the recently enhanced power of software and hardware available to the everyday GIS practitioner has meant that a powerful visual alternative, three-dimensional or 3D maps can now be constructed using software such as ArcGIS. Using height or elevation as a metaphor in the case of innovation and diffusion research is a potentially powerful tool for gaining new insight into these processes and the factors that influence new policy practices and organizational forms.
Constructing a 3D map of the reverse innovation score for the adoption of teacher training colleges reveals some very interesting new information, as shown in Figure 2.65. You can immediately see the differences in innovation and diffusion in the different regions of the country in the 3D display: the valleys of light gray (blue) where teachers colleges first were organized, the light gray (blue) of the first wave of diffusion spreading north into New England and south to Pennsylvania, and the spherical pattern of diffusion around Iowa, with distant western imitators California and Utah. Finally, the dark gray (red) mountain range of holdout states in the middle of the country, from Ohio to Mississippi and Alabama, are seen clearly in the 3D representation.
FIGURE 2.65 3D map of innovation index, teacher training colleges, U.S. states, 1839-1911
Making 3D maps is somewhat complicated, but the results may justify the difficulties. First, your license for ArcGIS must include the 3D Analyst extension (go to www.esri.com for further information on extensions). Second, you need to activate the extension by clicking on Tools on the main tool bar and clicking on Extensions; this will bring up the Extensions submenu, as in Figure 2.66.
FIGURE 2.66 Extensions submenu
Usually if the extension is licensed, it will already be checked, but if it is licensed and not activated, simply check the box and click close to activate. Next you need to activate the 3D Analyst tool bar, by clicking on View, toolbars, 3D Analyst. You can drag the tool bar around the screen to place it in a convenient location.
To get a standard map ready for conversion to a 3D map, you need to add two fields to the attribute table of the map, one for the X coordinate and the other for the Y coordinate. In a geographic-based map like those used in the topic, the X and Y coordinates are the familiar latitude and longitude. If you run your cursor across a map like the one in Figure 2.65, at the bottom of the ArcMap screen you will see the X and Y coordinates displayed; all these maps are based on these coordinates. Although the coordinates are in that sense built in to these maps, the 3D functions of ArcGIS need to have those coordinates listed for each point or polygon you use in your mapping process. For a 3D map, you need a third dimension, of course, but here is where you can use height or elevation as a metaphor, to be based on a variable of interest to you. In this case, we can look at the reverse innovation score as providing the source of the elevation data for the 3D representation. To get started on the process, first add the coordinates to the attribute table.
Step 1 Open the attribute table of the map you wish to convert to 3D by right-clicking on the layer and selecting Open Attribute Table from the popup menu.
Step 2 Click on Options, and select Add Field; if you have been editing, Add Field will not be selectable, so be sure to save any previous edits and stop editing before proceeding further.
Step 3 Create two new fields in this way called "Point_X" and "Point_Y"; select double as the precision for these fields.
Step 4 Minimize the attribute table, and click on Edit, and click on Start Editing. This is necessary for the next step of actually calculating the X and Y coordinates.
Step 5 Highlight the name field at the top of the column for "Point_X" and right-click to bring up the field submenu; click on Calculate Values to open the Field Calculator submenu.
Step 6 Check the Advanced box in the middle of the menu; this will bring up the label on the bottom box to become "Pre-Logic VBA Script Code," and move the Point_X = box down to new location at the bottom of the Field Calculator submenu.
Step 7 Click on Help. This will bring up a window that contains some very useful information about Pre-Logic VBA Script codes, and some examples you can use for the task at hand. What you want to do is to create an XY coordinate for the centroid or center point of a polygon and add that to the attribute table. Find the example labeled, "To add the X coordinate of Polygon Centroids," highlight the entire four-line script, press and hold the control key (Ctrl) and hit the letter c while holding the control key to copy what you have highlighted. Close the Help dialog box, move the cursor into the Pre-Logic VBA Script Code box, and paste the text from the Help dialog into the box.
Step 8 Type pArea.Centriod.X in the box under Point_X = so that the result of your calculation gets assigned to your coordinate field; make sure that the field in your original attribute table that describes the shape of the units you are using, usually polygon, is called Shape. If not, type the name of that field into the third line of the script where the word Shape appears between brackets. Your submenu should look like that in Figure 2.67.
FIGURE 2.67 Calculate fields submenu for XY coordinates in polygons
Step 9 Click OK, and the X coordinates should appear in the attribute table.
Step 10 Open the Field Calculator submenu for Point_Y and the submenu reappears with the Pre-Logic VBA Script Code box and the code as it was in Figure 2.67; change the X to Y in the fourth line of the script and in the box now labeled Point_Y = and click OK; coordinates for the Point_Y now appear in the attribute table.
Step 11 Minimize the attribute table, click on the Editor button, click on Save edits, and click on Stop editing. Now you can close the attribute table.
Now you are ready to convert your two-dimensional map to a three-dimensional map using an attribute at height or elevation, and the XY coordinates you have already added to create the 3D effects. To do this, follow these steps.
Step 1 Click on the 3D Analyst tool bar, select Convert, and select Features to 3D, as in Figure 2.68.
FIGURE 2.68 3D Analyst and submenus
Step 2 The Features to 3D submenu appears as in Figure 2.69; select the layer name for the map you want to convert, and select Input feature attribute as the source of heights. Select the field you wish to use—here we are looking at the reverse innovation measure for normal schools, which is called normal2 in this table. Under output features, type a name for the 3D layer file; click OK.
FIGURE 2.69 Features to 3D conversion submenu
The new layer will appear in the display contents at the top and will be displayed on the map. Do not be alarmed that the map does not look any different; you are still viewing it in the two-dimensional world of ArcMap. To see the new features, you need to move the map into the 3D viewer that comes with ArcGIS, ArcScene, which can be activated by pressing the ArcScene button on the 3D Analyst tool bar. This will open the ArcScene window, as in Figure 2.70. The ArcScene window is very similar to the ArcMap window with many of the same commands, although it has additional commands and tool bars to handle the 3D viewing capabilities.
FIGURE 2.70 ArcScene window
To fully convert your map to 3D, follow these steps.
Step 1 Return to the ArcMap window and right-click on the new 3D layer; click on Copy when the popup menu appears. Step 2 Return to the ArcScene window, and right-click on Scene layers in the Display contents window. Click on Paste layers, and your new map will appear in the window, as shown in Figure 2.71. The map now gives hints of having some elevation, but again do not be concerned that the 3D aspect is not very visible. More steps are required to give the proper aspect to the map for 3D viewing.
FIGURE 2.71 Newly converted 3D map
Step 3 Right-click on the Scene layers line again; this time select Scene Properties as in Figure 2.72. Under the General tab, click on the button labeled, Calculate From Extent. This feature provides a scaling of the 3D heights you have provided that makes it possible to see the three-dimensional structure of the map. Click on Apply and then OK, and the map will start to appear to have a third dimension. However, this is still hard to see. More steps will enhance and show the full potential of this approach to mapping.
FIGURE 2.72 Scene Properties submenu
To really visualize the third dimension, you need to give your map some more realistic 3D characteristics, like depth and shadow, as if the sun were shining on this map from a particular angle. You realize through this process that a great deal of what we see when we view the three-dimensional world is the product of depth and shadow/light as well as the actual width, height, and length of objects we view.
Step 4 Click on the 3D Analyst tool, select Create/Modify TIN and select Create TIN From Features as shown in Figure 2.73.
FIGURE 2.73 Creating a TIN (triangulated irregular network)
A triangulated irregular network (TIN) is basically a representation of a three-dimensional feature using a series of interconnected vertices of triangles to model the physical aspects of the feature—its height, the slope up or down to the height of the adjacent features, the shadows and valleys that are created by the ups and downs of the terrain, and so on. Figure 2.74 shows some of the aspects of a TIN taken from the ArcGIS help file.
FIGURE 2.74 The structure of a TIN surface
The mountain on the right is built from a series of intersecting triangles that interpret or model what the actual surface might look like given the three coordinates that describe the mountain peak and the surrounding areas as the mountain declines down to the valley surrounding it. In the map we are using, the states are each represented by three dimensions, and the TIN structure models what the surfaces connecting each state look like given that each state has an elevation based on the attribute of interest, in this case the reverse innovation score. The TIN creates depth and shadow more realistically to represent a three-dimensional surface and thus highlight the trends, differences, and similarities exhibited by the states on the attribute providing the elevation or height to the map.
Clicking on the final command in Figure 2.73 creates the TIN structure, as seen in Figure 2.75. You can now really start to see some of the three-dimensional aspects. For example, notice how the California coast seems to be very low and dramatically rise up to the next set of states—Nevada and Oregon, which form the beginning of a high plateau. This plateau goes up even higher as we pass into Idaho and Montana. These differences reflect the reverse innovation scores, but they are still not too clearly visible.
FIGURE 2.75 Initial view of TIN map
Step 5 Open the Layer Properties submenu (Figure 2.76), and click on the Symbology tab. You will see in the left-hand side two boxes checked next to the words, "Edge Types" and "Faces." Uncheck the Faces box, and click Add right below this area of the menu. A popup menu with a list of choices will appear (the Add Renderer submenu): select "Face elevation with graduated color ramp." Click on Add and then Dismiss to close the window.
FIGURE 2.76 Layer Properties menu and the Add Renderer submenu
Step 6 Since the innovation score varies between 0 and 1, drop the number of classifications down to 4, and select an appropriate color ramp; change the colors if you wish to. The result will start to look much more interesting; you can manipulate the 3D image—rotate it, tilt it, even look upside down at it, with the tool on the ArcScene tool bar. Interesting perspectives can be gained in this manner, as Figure 2.77 demonstrates.
FIGURE 2.77 3D map of normal school innovation score, U.S. states, 1839-1911
Now you can start to see the peaks and valleys that represent the diffusion of this innovation, and the possibilities for close-ups and magnification and different angles of view are potentially limitless. These kinds of manipulations and the insights that can be found in them are only possible with the power of the three-dimensional approach to GIS.
Another of the technical aspects of this example involves the power of Arc-Map’s database management. To bring together the basic map data for the U.S. states and the data from Walker’s (1973) study of innovation, some database manipulations had to be conducted to put the data from both sources into one attribute table so it could be mapped in the 2D and 3D forms. After saving the Walker data in a .dbf format file using Microsoft Excel, we had to add a field to the Walker data that would be a match to a field in the attribute table for the U.S. states map, as shown in Figure 2.78.
Figure 2.78 Attribute table for the U.S. states layer
There is a code in the very first column called FID, which is simply a numeric identification code that ArcMap places into attribute tables. Since the states in the Walker file were in a different order than the states in the map layer, entering the FID code from the Attribute table of the map layer for each state in the Walker file would also allow us to sort the Walker file so that the states would be in the same order for joining with the map attribute table. This was done in Microsoft Excel as well and saved into a .dbf format. Using the Add data command in ArcMap, the Walker data were than added to the display contents (Figure 2.79).
FIGURE 2.79 File "state2" diffusion study (Walker, 1973) added to the display contents
Opening the attribute table of state2 shows the variables and the common field, FID1, as shown in Figure 2.80.
FIGURE 2.80 Attribute table for state2, diffusion data file with FID1 field
Step 1 To join the two tables, right-click on the map layer and select Joins and Relates; from the submenu select Join. Step 2 Indicate the field in the map layer you want to base the join on, that is, the field that the other table also contains, in this case FID. Step 3 Select the Table to join to the map layer, in this case state2. Step 4 Select the field in the second table, state2, to base the join on, in this case FID1; your Join submenu should look like that in Figure 2.81.
FIGURE 2.81 Join submenu
Step 5 Click OK and the join will occur. Open the attribute table for the map layer, and you will notice that all the new variables from state2 are now part of the table, with variables names like "state2.fid1" showing that they came from the state2 file originally. The variables in the map attribute table are also newly labeled as "state.fid" to show their origin. Now the Walker study variables are available to map and visualize in three dimensions.
