Moran Scatter Plot

The Moran scatter plot provides a tool for visual exploration of spatial autocorrelation (Anselin 1996, 2002). It is produced when you perform a univariate or bivariate local Moran analysis. Anselin (2002) describes this as "the spatial lag of the variable on the vertical axis and the original variable on the horizontal axis" --the spatial lag refers to the values of a location's neighbors.

You can obtain two different kinds of Moran scatter plots:

Univariate (the same variable is plotted for the objects and their neighbors).
Bivariate (one variable is plotted for the objects while another is plotted for neighbors).

The Moran scatter plot displays standardized variables, not the raw data. Standardization is denoted by a (Z), for z-score, after the variable name. The Moran scatter plot uses the same color scheme for representing statistical values for each point as is described for locations in Univariate Local Moran maps: see "Interpreting Local Moran statistics". In this example, there are many points reprsenting high-high clusters (red, upper right quadrant) and low-low clusters (medium blue, lower left quadrant), and only a few low-high (light blue, upper left quadrant) and high-low (pink, lower right quadrant) clusters.

Click on the image below for more information.

Plot features

x-axis	standardized value for each geographic object
y-axis	mean standardized neighbor value
points	points for various locations are colored based on the "high-high/low low" classification scheme (e.g., red is high-high, gray is not significant, dark blue is low- low).
origin	because the data are z-scores, the raw data has been standardized so that its mean value is zero. (0,0) is the value at the cross-hairs of the graph.
units	the values in the graph correspond to standard deviations
slope	the slope of the best-fit (regression) line through the points is proportional to the global Moran's I for the dataset. The Moran's I value and significance can also be found in the log output.

Graph statistics for Moran scatter plots

In addition to the plot, the Moran scatter plot view includes a Graph Statistics window that shows the mean and standard deviation of each data set at the time shown in the animation toolbar. Recall that when data are Z-transformed, the goal is a mean of zero and a standard deviation of 1, but actual values may be slightly different (as in the image above, where the mean is a very small number, but not zero). This window also shows two coefficients that measure the correlation between variables, the simple correlation coefficient, and Spearman's rank correlation coefficient. When the Graph Statistics window is open, the best fit (regression) line also appears in the scatter plot. By default, the statistics shown in this window are for all of the points in the scatter plot, but you can select a subset of points with the cursor, and then choose to show statistics calculated for this subset -- under "Show statistics for:", click on the open circle next to "Selection." You can hide or undock the Graph Statistics window using the buttons in the upper right corner of the window, and can bring back the window after hiding it by clicking on "Graph Statistics" in the Graph pull-down menu.

Animation and linkage

Like most views in SpaceStat, Moran scatter plots can be animated; use the animation toolbar to scroll through the temporal range of your data. You can also synchronize the animation with animation in other views, such as maps. Moran scatter plot views are by default linked to other visualization tools, so that areas selected in one plot, map, or table, are also selected in other visible views.

The animation and graph toolbars

The far left pull-down menu in the Moran scatter plot window allows you to hide or show the Animation (shown by default) and Graph (hidden by default) toolbars. Note that if you wish to change the time step size for animations, this option is available from the Animation pull-down menu, but not from the toolbar.

From the Graph pull-down menu or toolbar, or the right-click menu, you have the following options:

You can alter the look of your Moran scatter plot by changing its properties. Options here range from changes to the title and way things are selected, to changes in the fill, size, and symbols used for points. You can use options within scatter plot properties to show variation in a covariate data set, as is shown here in the description of "regular" scatter plots.
You can print a Moran scatterplot by choosing "Print" from the same menu,
You can copy an image of your plot to the clipboard, so it is ready to paste into other applications, or
You can export an animated Moran scatter plot as an .avi file.