D Scatter Plot
10.3 3-D Scatter Plot
The final technique we consider to explore multivariate associations consists of a three dimensional scatter plot (or cube). Clear the conditional plot and start up the 3D scatter plot interface by clicking on the toolbar icon or selecting Explore > 3D Scatter Plot from the menu (Figure 10.7 on p. 74).
This starts the variable selection dialog, shown in Figure 10.8 on p. 74. Select the variable CRIME in the drop down list for the X Variable, UNEMP for the Y Variable and POLICE for the Z Variable, as in Figure 10.9 on p. 74. Note that the order of the variables does not really matter, since the data cube can easily be rotated (for example, switching the x-axis from horizontal to vertical). Finally, click the OK button to generate the initial 3D view, shown in Figure 10.10 on p. 74.
Figure 10.7: Three dimensional scatter plot function.
Figure 10.8: 3D scatter plot Figure 10.9: Variables selected variable selection.
in 3D scatter plot.
Figure 10.10: Three dimensional scatter plot (police, crime, unemp).
Figure 10.11: 3D scatter plot rotated with 2D projection on the zy panel.
Figure 10.12: Setting the se- Figure 10.13: Moving the se- lection shape in 3D plot.
lection shape in 3D plot. The 3D plot can be further manipulated in a number of ways. For
example, click anywhere in the plot and move the mouse to rotate the plot. Right click to zoom in and out. More importantly, a number of options are available in the left hand panel of the window. At the top of the panel are three check boxes to toggle projection of the 3D point cloud on the side panels. For example, in Figure 10.11 the cube has been rotated and the projection on the z-y panel turned on.
The options in the bottom half of the left hand panel define the selection shape and control brushing. Check the Select box and a red outline of a cube will appear in the graph. Now move the slider to the right and below each variable name in the panel to change the size of the selection box along that dimension. For example, in Figure 10.12, the side of the box along the X dimension (CRIME) is increased as the slider is moved to the right. Manipulate the sliders for each of the three variables until the box has a
Figure 10.14: Brushing the 3D scatter plot.
sizeable dimension. You can rotate the cube to get a better feel of where in the 3D space your selection box is situated.
The slider to the left and below each variable in the left panel of the graph is used to move the selection box along the corresponding dimension. As shown in Figure 10.13 on p. 75, dragging the bottom left slider will move the selection box along the Z axis, which corresponds to the POLICE variable. Selected observations are shown as yellow.
Experiment with changing the selection shape and moving the box around. You may find it helpful to rotate the cube often, so that you can see where the box is in relation to the point cloud. Also, you can move the selection box directly by holding down the Control key while clicking with the left mouse button.
The 3D scatter plot is linked to all the other maps and graphs. How- ever, the update of the selection is implemented slightly differently from the two dimensional case. In contrast to the standard situation, where the updating is continous, the selection in the 3D plot is updated each time the mouse stops moving. The yellow points in the cloud plot will be matched to the corrresponding observations in all the other graphs. For example, in Figure 10.14, the selected points in the cloud plot are highlighted on the Mississippi county map. In all other respect, brushing is similar to the two dimensional case, although it takes some practice to realize where the selection box is in the three dimensional space.
Brushing also works in the other direction, but only with the Select check box turned off. To see this, create a brush in the county map and start moving it around. Each time the brush stops, the matching selection
Figure 10.15: Brushing a map linked to the 3D scatter plot. in the 3D plot will be shown as yellow points, as shown in Figure 10.15. In
practice, you may find that it often helps to zoom in and out and rotate the cube frequently.
10.4 Practice
Apply the conditional plots and the 3D scatter plot in an exploration of the relation between median house value (CMEDV) and other variables in the BOSTON sample data set (boston.shp with ID as the Key). For example, consider the relation between house value and air quality (NOX) conditioned by geographical location (X and Y) in a conditional scatter plot. Also, explore the associations between house value, air quality and crime (CRIM) in a 3D scatter plot. Experiment with brushing on a Thiessen polygon map created from the tract centroids.