page_title: GeoDa
section_title: Anselin's Moran scatter plot
hierarchical_section_title: GeoDa / Functionality / Anselin's Moran scatter plot
caption_attribution_description: English: Moran Scatter Plot of crime in Columbus, created in GeoDA.
context_page_description: GeoDa is a free software package that conducts spatial data analysis, geovisualization, spatial autocorrelation and spatial modeling.
  OpenGeoDa is the cross-platform, open source version of Legacy GeoDa. While Legacy GeoDa only runs on Windows XP, OpenGeoDa runs on different versions of Windows, Mac OS, and Linux. The package was initially developed by the Spatial Analysis Laboratory of the University of Illinois at Urbana-Champaign under the direction of Luc Anselin. From 2016 development continues at the Center for Spatial Data Science at the University of Chicago.
  GeoDa has powerful capabilities to perform spatial analysis, multivariate exploratory data analysis, and global and local spatial autocorrelation. It also performs basic linear regression. As for spatial models, both the spatial lag model and the spatial error model, both estimated by maximum likelihood, are included.
  OpenGeoDa is released under the GNU GPL version 3.0.
context_section_description: A very interesting device available in GeoDa to explore global patterns of autocorrelation in space is Anselin's Moran scatterplot. This graph depicts a standardized variable in the x-axis versus the spatial lag of that standardized variable. The spatial lag is nothing but a summary of the effects of the neighboring spatial units. That summary is obtained by means of a spatial weights matrix, which can take various forms, but a very commonly used is the contiguity matrix. The contiguity matrix is an array that has a value of one in the position (i, j) whenever the spatial unit j is contiguous to the unit i. For convenience that matrix is standardized in such a way that the rows sum to one by dividing each value by the row sum of the original matrix.
  In essence, Anselin's Moran scatterplot presents the relation of the variable in the location i with respect to the values of that variable in the neighboring locations. By construction, the slope of the line in the scatter plot is equivalent to the Moran's I coefficient. The latter is a well-known statistic that accounts for the Global spatial autocorrelation. If that slope is positive it means that there is positive spatial autocorrelation: high values of the variable in location i tend to be clustered with high values of the same variable in locations that are neighbors of i, and vice versa. If the slope in the scatter plot is negative that means that we have a sort of checkerboard pattern or a sort of spatial competition in which high values in a variable in location i tend to be co-located with lower values in the neighboring locations.
  In Anselin's Moran scatter plot, the slope of the curve is calculated and displayed on top of the graph. In this case, this value is positive, which means that areas with a high rate of criminality tend to have neighbors with high rates as well, and vice versa.
caption: Moran scatter plot of crime in Columbus
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