Spatial Autocorrelation¶

Spatial Lag
Global autocorrelation
Local autocorrelation
Exercises

In [1]:

%matplotlib inline

import geopandas
import numpy
import pandas
import matplotlib.pyplot as plt
from pysal.lib import weights
from pysal.explore import esda
from pysal.viz.splot import esda as esdaplot

db = geopandas.read_file("../data/lux_regions.gpkg")
w = weights.Queen.from_dataframe(db)
w.transform = "R"

Spatial Lag¶

In [2]:

ll_lag = weights.lag_spatial(w, db["light_level"])
pandas.Series(ll_lag).head()

Out[2]:

0    1639.250000
1    1016.857143
2    1386.000000
3    2495.000000
4     866.750000
dtype: float64

Global autocorrelation¶

Moran's I¶

In [3]:

mi = esda.Moran(db["light_level"], w)

Moran Plot¶

In [4]:

esdaplot.moran_scatterplot(mi);

Global inference¶

In [5]:

esdaplot.plot_moran_simulation(mi, aspect_equal=False);

Local autocorrelation¶

Local Moran's I¶

In [6]:

lisa = esda.Moran_Local(db["light_level"], w)

Clusters¶

In [7]:

esdaplot.lisa_cluster(lisa, db);

Putting everything together

In [8]:

esdaplot.plot_local_autocorrelation(lisa, db, "light_level");

Local inference¶

In [9]:

pandas.Series(lisa.p_sim).head()

Out[9]:

0    0.061
1    0.458
2    0.143
3    0.014
4    0.215
dtype: float64

In [10]:

f, axs = plt.subplots(1, 3, figsize=(16, 3))
for i, ax in zip([0.05, 0.01, 0.001], axs):
    esdaplot.lisa_cluster(lisa, db, p=i, ax=ax)
    ax.set_title(f"Confidence threshold = {i}")

Exercises¶

Plot the distribution of values for light_level and its spatial lag. How do they relate to each other? What can you say about the lag in comparison to the original variable?
Compare the results presented above with a similar analysis of POPULATION. What are the main similarities and differences?