Exploratory Analysis of spatial data – Visualising Spatial Autocorrelation
Maps can be powerful tools to analyze attribute patterns in space. You could for example ask the questions: If you are likely to donate money for a good cause, is your neighbor as well? Or where are the greediest people living? Is there a connection between the willingness to donate money for a good cause and the geographical space you live in? Or is it just all random if people donate or not? Lastly, you would like your neighbors to have the same intrinsic ideas to share their wealth with others, so where should you move to, to make sure you end up in the right place? Thanks to GSoC the PySAL development team and I were able to create a visualization package called splot, that helps us to answer these questions.
A visual inspection of a Choropleth map (a map with the containing polygons colored according to their attribute value), showing how much money people in France donated for a good cause on a yearly average in the 1830s, allows us to already see spatial structure (data: Guerry). If the values would be completely random, we would see no dark or light clusters on the map:
# imports you will need: import matplotlib.pyplot as plt from bokeh.io import show, output_notebook import libpysal.api as lp import geopandas as gpd import esda from libpysal import examples # load example data link_to_data = examples.get_path('Guerry.shp') df = gpd.read_file(link_to_data) # calculate Local Moran Statistics for 'Donatns' y = df['Donatns'].values w = lp.Queen.from_dataframe(df) # Queen weights w.transform = 'r' moran_loc = esda.moran.Moran_Local(y, w) # load Splot Choropleth functionality and plot from splot.bk import plot_choropleth fig = plot_choropleth(df, 'Donatns', reverse_colors=True) show(fig)
Your brains can hereby help us identify these clusters. But careful, sometimes we tend to detect patterns where there is no statistical correlation between the values of neighboring polygons. This can especially be the case when these polygons are of different shapes and sizes. In order to make it a bit easier for our brain to detect clusters where there are statistically significant clusters, we can use Local Spatial Autocorrelation Statistics to identify so called hot and cold-spots on the map. There are many different methods of Local Spatial Autocorrelation Statistics. However, they all combine the idea of calculating two similarities: The similarity of space and the similarity of a certain attribute. (Note: we won’t dive too deep into Spatial Autocorrelation, but if you are interested in it I can highly recommend to check out the geopython tutorial offered by PySAL’s development team.)
In our case we can simply use PySAL and Esda to calculate Local Moran values. With Splot we can now plot the resulting Moran Scatterplot in combination with a LISA cluster map, indicating hot and cold spots as well as outliers, and the original Choropleth showcasing the values:
# Load splot plot_local_autocorrelation() functionality and plot from splot.mpl import plot_local_autocorrelation fig = plot_local_autocorrelation(moran_loc, df, "Donatns", legend=True) plt.show()
Let’s assume further, you have now picked a particular region you have heard has beautiful nature and you would like to check locally, if people there are statistically more likely to donate larger sums. You can simply use two masking options in splot and the
plot_local_autocorrelation() function in order to find out how your favorite Region “Ain” is doing (region-masking) and where all other regions with similar statistical values can be found (quadrant-masking):
# use plot_local_autocorrelation() with mask options fig = plot_local_autocorrelation(moran_loc, df, "Donatns", legend=True, region_column='Dprtmnt', mask=['Rhone', 'Ain', 'Hautes-Alpes'], quadrant=3) plt.show()
Lastly, you have discovered it is actually way more important to you if your neighbors are likely to share a glass of good French red wine with you in the evening instead of how much they donate. No problem, you can use any other geopandas dataframe, e.g. containing information about the wine consumption per year per region, and repeat the analysis.
The code above uses Matplotlib as the main plotting library, you can however also use our interactive Bokeh version.