import matplotlib.pyplot as plt
import matplotlib as mpl
import geopandas as gpd
import numpy as np
from libpysal.weights.contiguity import Queen
from libpysal.weights.spatial_lag import lag_spatial
import seaborn as sbn
from esda.moran import (Moran_Local, Moran_Local_BV,
Moran, Moran_BV)
import warnings
from spreg import OLS
from matplotlib import patches, colors
from ._viz_utils import (mask_local_auto, moran_hot_cold_spots,
splot_colors)
"""
Lightweight visualizations for esda using Matplotlib and Geopandas
TODO
* geopandas plotting, change round shapes in legends to boxes
* prototype moran_facet using `seaborn.FacetGrid`
"""
__author__ = ("Stefanie Lumnitz <stefanie.lumitz@gmail.com>")
def _create_moran_fig_ax(ax, figsize, aspect_equal):
"""
Creates matplotlib figure and axes instances
for plotting moran visualizations. Adds common viz design.
"""
if ax is None:
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(111)
else:
fig = ax.get_figure()
ax.spines['left'].set_position(('axes', -0.05))
ax.spines['right'].set_color('none')
ax.spines['bottom'].set_position(('axes', -0.05))
ax.spines['top'].set_color('none')
if aspect_equal is True:
ax.set_aspect('equal')
else:
ax.spines['left'].set_smart_bounds(True)
ax.spines['bottom'].set_smart_bounds(True)
return fig, ax
[docs]def moran_scatterplot(moran, zstandard=True, p=None,
aspect_equal=True, ax=None,
scatter_kwds=None, fitline_kwds=None):
"""
Moran Scatterplot
Parameters
----------
moran : esda.moran instance
Values of Moran's I Global, Bivariate and Local
Autocorrelation Statistics
zstandard : bool, optional
If True, Moran Scatterplot will show z-standardized attribute and
spatial lag values. Default =True.
p : float, optional
If given, the p-value threshold for significance
for Local Autocorrelation analysis. Points will be colored by
significance. By default it will not be colored.
Default =None.
aspect_equal : bool, optional
If True, Axes will show the same aspect or visual proportions
for Moran Scatterplot.
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline.
Default =None.
Returns
-------
fig : Matplotlib Figure instance
Moran scatterplot figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import (Moran, Moran_BV,
... Moran_Local, Moran_Local_BV)
>>> from splot.esda import moran_scatterplot
Load data and calculate weights
>>> link_to_data = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link_to_data)
>>> x = gdf['Suicids'].values
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
Calculate esda.moran Objects
>>> moran = Moran(y, w)
>>> moran_bv = Moran_BV(y, x, w)
>>> moran_loc = Moran_Local(y, w)
>>> moran_loc_bv = Moran_Local_BV(y, x, w)
Plot
>>> fig, axs = plt.subplots(2, 2, figsize=(10,10),
... subplot_kw={'aspect': 'equal'})
>>> moran_scatterplot(moran, p=0.05, ax=axs[0,0])
>>> moran_scatterplot(moran_loc, p=0.05, ax=axs[1,0])
>>> moran_scatterplot(moran_bv, p=0.05, ax=axs[0,1])
>>> moran_scatterplot(moran_loc_bv, p=0.05, ax=axs[1,1])
>>> plt.show()
"""
if isinstance(moran, Moran):
if p is not None:
warnings.warn('`p` is only used for plotting `esda.moran.Moran_Local`\n'
'or `Moran_Local_BV` objects')
fig, ax = _moran_global_scatterplot(moran=moran, zstandard=zstandard,
ax=ax, aspect_equal=aspect_equal,
scatter_kwds=scatter_kwds,
fitline_kwds=fitline_kwds)
elif isinstance(moran, Moran_BV):
if p is not None:
warnings.warn('`p` is only used for plotting `esda.moran.Moran_Local`\n'
'or `Moran_Local_BV` objects')
fig, ax = _moran_bv_scatterplot(moran_bv=moran, ax=ax,
aspect_equal=aspect_equal,
scatter_kwds=scatter_kwds,
fitline_kwds=fitline_kwds)
elif isinstance(moran, Moran_Local):
fig, ax = _moran_loc_scatterplot(moran_loc=moran, zstandard=zstandard,
ax=ax, p=p, aspect_equal=aspect_equal,
scatter_kwds=scatter_kwds,
fitline_kwds=fitline_kwds)
elif isinstance(moran, Moran_Local_BV):
fig, ax = _moran_loc_bv_scatterplot(moran_loc_bv=moran, ax=ax,
p=p, aspect_equal=aspect_equal,
scatter_kwds=scatter_kwds,
fitline_kwds=fitline_kwds)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
return fig, ax
def _moran_global_scatterplot(moran, zstandard=True,
aspect_equal=True, ax=None,
scatter_kwds=None, fitline_kwds=None):
"""
Global Moran's I Scatterplot.
Parameters
----------
moran : esda.moran.Moran instance
Values of Moran's I Global Autocorrelation Statistics
zstandard : bool, optional
If True, Moran Scatterplot will show z-standardized attribute and
spatial lag values. Default =True.
aspect_equal : bool, optional
If True, Axes will show the same aspect or visual proportions.
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline.
Default =None.
Returns
-------
fig : Matplotlib Figure instance
Moran scatterplot figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran
>>> from splot.esda import moran_scatterplot
Load data and calculate weights
>>> link_to_data = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link_to_data)
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
Calculate Global Moran
>>> moran = Moran(y, w)
plot
>>> moran_scatterplot(moran)
>>> plt.show()
customize plot
>>> fig, ax = moran_scatterplot(moran, zstandard=False,
... fitline_kwds=dict(color='#4393c3'))
>>> ax.set_xlabel('Donations')
>>> plt.show()
"""
# to set default as an empty dictionary that is later filled with defaults
if scatter_kwds is None:
scatter_kwds = dict()
if fitline_kwds is None:
fitline_kwds = dict()
# define customization defaults
scatter_kwds.setdefault('alpha', 0.6)
scatter_kwds.setdefault('color', splot_colors['moran_base'])
scatter_kwds.setdefault('s', 40)
fitline_kwds.setdefault('alpha', 0.9)
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
# get fig and ax
fig, ax = _create_moran_fig_ax(ax, figsize=(7, 7),
aspect_equal=aspect_equal)
# set labels
ax.set_xlabel('Attribute')
ax.set_ylabel('Spatial Lag')
ax.set_title('Moran Scatterplot' +
' (' + str(round(moran.I, 2)) + ')')
# plot and set standards
if zstandard is True:
lag = lag_spatial(moran.w, moran.z)
fit = OLS(moran.z[:, None], lag[:, None])
# plot
ax.scatter(moran.z, lag, **scatter_kwds)
ax.plot(lag, fit.predy, **fitline_kwds)
# v- and hlines
ax.axvline(0, alpha=0.5, color='k', linestyle='--')
ax.axhline(0, alpha=0.5, color='k', linestyle='--')
else:
lag = lag_spatial(moran.w, moran.y)
b, a = np.polyfit(moran.y, lag, 1)
# plot
ax.scatter(moran.y, lag, **scatter_kwds)
ax.plot(moran.y, a + b*moran.y, **fitline_kwds)
# dashed vert at mean of the attribute
ax.vlines(moran.y.mean(), lag.min(), lag.max(), alpha=0.5,
linestyle='--')
# dashed horizontal at mean of lagged attribute
ax.hlines(lag.mean(), moran.y.min(), moran.y.max(), alpha=0.5,
linestyle='--')
return fig, ax
[docs]def plot_moran_simulation(moran, aspect_equal=True,
ax=None, fitline_kwds=None,
**kwargs):
"""
Global Moran's I simulated reference distribution.
Parameters
----------
moran : esda.moran.Moran instance
Values of Moran's I Global Autocorrelation Statistics
aspect_equal : bool, optional
If True, Axes of Moran Scatterplot will show the same
aspect or visual proportions.
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the
vertical moran fitline. Default =None.
**kwargs : keyword arguments, optional
Keywords used for creating and designing the figure,
passed to seaborn.kdeplot.
Returns
-------
fig : Matplotlib Figure instance
Simulated reference distribution figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran
>>> from splot.esda import plot_moran_simulation
Load data and calculate weights
>>> link_to_data = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link_to_data)
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
Calculate Global Moran
>>> moran = Moran(y, w)
plot
>>> plot_moran_simulation(moran)
>>> plt.show()
customize plot
>>> plot_moran_simulation(moran, fitline_kwds=dict(color='#4393c3'))
>>> plt.show()
"""
# to set default as an empty dictionary that is later filled with defaults
if fitline_kwds is None:
fitline_kwds = dict()
figsize = kwargs.pop('figsize', (7, 7))
# get fig and ax
fig, ax = _create_moran_fig_ax(ax, figsize,
aspect_equal=aspect_equal)
# plot distribution
shade = kwargs.pop('shade', True)
color = kwargs.pop('color', splot_colors['moran_base'])
sbn.kdeplot(moran.sim, shade=shade, color=color, ax=ax, **kwargs)
# customize plot
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
ax.vlines(moran.I, 0, 1, **fitline_kwds)
ax.vlines(moran.EI, 0, 1)
ax.set_title('Reference Distribution')
ax.set_xlabel('Moran I: ' + str(round(moran.I, 2)))
return fig, ax
[docs]def plot_moran(moran, zstandard=True, aspect_equal=True,
scatter_kwds=None, fitline_kwds=None, **kwargs):
"""
Global Moran's I simulated reference distribution and scatterplot.
Parameters
----------
moran : esda.moran.Moran instance
Values of Moran's I Global Autocorrelation Statistics
zstandard : bool, optional
If True, Moran Scatterplot will show z-standardized attribute and
spatial lag values. Default =True.
aspect_equal : bool, optional
If True, Axes of Moran Scatterplot will show the same
aspect or visual proportions.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline
and vertical fitline. Default =None.
**kwargs : keyword arguments, optional
Keywords used for creating and designing the figure,
passed to seaborne.kdeplot.
Returns
-------
fig : Matplotlib Figure instance
Moran scatterplot and reference distribution figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran
>>> from splot.esda import plot_moran
Load data and calculate weights
>>> link_to_data = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link_to_data)
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
Calculate Global Moran
>>> moran = Moran(y, w)
plot
>>> plot_moran(moran)
>>> plt.show()
customize plot
>>> plot_moran(moran, zstandard=False,
... fitline_kwds=dict(color='#4393c3'))
>>> plt.show()
"""
figsize = kwargs.pop('figsize', (10, 4))
fig, axs = plt.subplots(1, 2, figsize=figsize,
subplot_kw={'aspect': 'equal'})
plot_moran_simulation(moran, ax=axs[0], fitline_kwds=fitline_kwds, **kwargs)
moran_scatterplot(moran, zstandard=zstandard, ax=axs[1],
scatter_kwds=scatter_kwds, fitline_kwds=fitline_kwds)
axs[0].set(aspect="auto")
if aspect_equal is True:
axs[1].set_aspect("equal", "datalim")
else:
axs[1].set_aspect("auto")
return fig, axs
def _moran_bv_scatterplot(moran_bv, ax=None, aspect_equal=True,
scatter_kwds=None, fitline_kwds=None):
"""
Bivariate Moran Scatterplot.
Parameters
----------
moran_bv : esda.moran.Moran_BV instance
Values of Bivariate Moran's I Autocorrelation Statistics
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
aspect_equal : bool, optional
If True, Axes of Moran Scatterplot will show the same
aspect or visual proportions.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline.
Default =None.
Returns
-------
fig : Matplotlib Figure instance
Bivariate moran scatterplot figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran_BV
>>> from splot.esda import moran_scatterplot
Load data and calculate weights
>>> link_to_data = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link_to_data)
>>> x = gdf['Suicids'].values
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
Calculate Bivariate Moran
>>> moran_bv = Moran_BV(x, y, w)
plot
>>> moran_scatterplot(moran_bv)
>>> plt.show()
customize plot
>>> moran_scatterplot(moran_bv,
... fitline_kwds=dict(color='#4393c3'))
>>> plt.show()
"""
# to set default as an empty dictionary that is later filled with defaults
if scatter_kwds is None:
scatter_kwds = dict()
if fitline_kwds is None:
fitline_kwds = dict()
# define customization
scatter_kwds.setdefault('alpha', 0.6)
scatter_kwds.setdefault('color', splot_colors['moran_base'])
scatter_kwds.setdefault('s', 40)
fitline_kwds.setdefault('alpha', 0.9)
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
# get fig and ax
fig, ax = _create_moran_fig_ax(ax, figsize=(7,7),
aspect_equal=aspect_equal)
# set labels
ax.set_xlabel('Attribute X')
ax.set_ylabel('Spatial Lag of Y')
ax.set_title('Bivariate Moran Scatterplot' +
' (' + str(round(moran_bv.I, 2)) + ')')
# plot and set standards
lag = lag_spatial(moran_bv.w, moran_bv.zy)
fit = OLS(moran_bv.zy[:, None], lag[:, None])
# plot
ax.scatter(moran_bv.zx, lag, **scatter_kwds)
ax.plot(lag, fit.predy, **fitline_kwds)
# v- and hlines
ax.axvline(0, alpha=0.5, color='k', linestyle='--')
ax.axhline(0, alpha=0.5, color='k', linestyle='--')
return fig, ax
[docs]def plot_moran_bv_simulation(moran_bv, ax=None, aspect_equal=True,
fitline_kwds=None, **kwargs):
"""
Bivariate Moran's I simulated reference distribution.
Parameters
----------
moran_bv : esda.moran.Moran_BV instance
Values of Bivariate Moran's I Autocorrelation Statistics
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
aspect_equal : bool, optional
If True, Axes of Moran Scatterplot will show the same
aspect or visual proportions.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the
vertical moran fitline. Default =None.
**kwargs : keyword arguments, optional
Keywords used for creating and designing the figure,
passed to seaborne.kdeplot.
Returns
-------
fig : Matplotlib Figure instance
Bivariate moran reference distribution figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran_BV
>>> from splot.esda import plot_moran_bv_simulation
Load data and calculate weights
>>> link_to_data = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link_to_data)
>>> x = gdf['Suicids'].values
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
Calculate Bivariate Moran
>>> moran_bv = Moran_BV(x, y, w)
plot
>>> plot_moran_bv_simulation(moran_bv)
>>> plt.show()
customize plot
>>> plot_moran_bv_simulation(moran_bv,
... fitline_kwds=dict(color='#4393c3'))
>>> plt.show()
"""
# to set default as an empty dictionary that is later filled with defaults
if fitline_kwds is None:
fitline_kwds = dict()
figsize = kwargs.pop('figsize', (7, 7))
# get fig and ax
fig, ax = _create_moran_fig_ax(ax, figsize,
aspect_equal=aspect_equal)
# plot distribution
shade = kwargs.pop('shade', True)
color = kwargs.pop('color', splot_colors['moran_base'])
sbn.kdeplot(moran_bv.sim, shade=shade, color=color, ax=ax, **kwargs)
# customize plot
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
ax.vlines(moran_bv.I, 0, 1, **fitline_kwds)
ax.vlines(moran_bv.EI_sim, 0, 1)
ax.set_title('Reference Distribution')
ax.set_xlabel('Bivariate Moran I: ' + str(round(moran_bv.I, 2)))
return fig, ax
[docs]def plot_moran_bv(moran_bv, aspect_equal=True,
scatter_kwds=None, fitline_kwds=None, **kwargs):
"""
Bivariate Moran's I simulated reference distribution and scatterplot.
Parameters
----------
moran_bv : esda.moran.Moran_BV instance
Values of Bivariate Moran's I Autocorrelation Statistics
aspect_equal : bool, optional
If True, Axes of Moran Scatterplot will show the same
aspect or visual proportions.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline
and vertical fitline. Default =None.
**kwargs : keyword arguments, optional
Keywords used for creating and designing the figure,
passed to seaborne.kdeplot.
Returns
-------
fig : Matplotlib Figure instance
Bivariate moran scatterplot and reference distribution figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran_BV
>>> from splot.esda import plot_moran_bv
Load data and calculate weights
>>> link_to_data = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link_to_data)
>>> x = gdf['Suicids'].values
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
Calculate Bivariate Moran
>>> moran_bv = Moran_BV(x, y, w)
plot
>>> plot_moran_bv(moran_bv)
>>> plt.show()
customize plot
>>> plot_moran_bv(moran_bv, fitline_kwds=dict(color='#4393c3'))
>>> plt.show()
"""
figsize = kwargs.pop('figsize', (10, 4))
fig, axs = plt.subplots(1, 2, figsize=figsize,
subplot_kw={'aspect': 'equal'})
plot_moran_bv_simulation(moran_bv, ax=axs[0], fitline_kwds=fitline_kwds,
**kwargs)
moran_scatterplot(moran_bv, ax=axs[1], aspect_equal=aspect_equal,
scatter_kwds=scatter_kwds, fitline_kwds=fitline_kwds)
axs[0].set(aspect="auto")
if aspect_equal is True:
axs[1].set_aspect("equal", "datalim")
else:
axs[1].set(aspect="auto")
return fig, axs
def _moran_loc_scatterplot(moran_loc, zstandard=True, p=None, aspect_equal=True,
ax=None, scatter_kwds=None, fitline_kwds=None):
"""
Moran Scatterplot with option of coloring of Local Moran Statistics
Parameters
----------
moran_loc : esda.moran.Moran_Local instance
Values of Moran's I Local Autocorrelation Statistics
p : float, optional
If given, the p-value threshold for significance. Points will
be colored by significance. By default it will not be colored.
Default =None.
aspect_equal : bool, optional
If True, Axes of Moran Scatterplot will show the same
aspect or visual proportions.
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline.
Default =None.
Returns
-------
fig : Matplotlib Figure instance
Moran Local scatterplot figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> import geopandas as gpd
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> from esda.moran import Moran_Local
>>> from splot.esda import moran_scatterplot
Load data and calculate Moran Local statistics
>>> link = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link)
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
>>> m = Moran_Local(y, w)
plot
>>> moran_scatterplot(m)
>>> plt.show()
customize plot
>>> moran_scatterplot(m, p=0.05,
... fitline_kwds=dict(color='#4393c3'))
>>> plt.show()
"""
# to set default as an empty dictionary that is later filled with defaults
if scatter_kwds is None:
scatter_kwds = dict()
if fitline_kwds is None:
fitline_kwds = dict()
if p is not None:
if not isinstance(moran_loc, Moran_Local):
raise ValueError("`moran_loc` is not a\n " +
"esda.moran.Moran_Local instance")
if 'color' in scatter_kwds or 'c' in scatter_kwds or 'cmap' in scatter_kwds:
warnings.warn('To change the color use cmap with a colormap of 5,\n' +
' color defines the LISA category')
# colors
spots = moran_hot_cold_spots(moran_loc, p)
hmap = colors.ListedColormap(['#bababa', '#d7191c', '#abd9e9',
'#2c7bb6', '#fdae61'])
# define customization
scatter_kwds.setdefault('alpha', 0.6)
scatter_kwds.setdefault('s', 40)
fitline_kwds.setdefault('alpha', 0.9)
# get fig and ax
fig, ax = _create_moran_fig_ax(ax, figsize=(7,7),
aspect_equal=aspect_equal)
# set labels
ax.set_xlabel('Attribute')
ax.set_ylabel('Spatial Lag')
ax.set_title('Moran Local Scatterplot')
# plot and set standards
if zstandard is True:
lag = lag_spatial(moran_loc.w, moran_loc.z)
fit = OLS(moran_loc.z[:, None], lag[:, None])
# v- and hlines
ax.axvline(0, alpha=0.5, color='k', linestyle='--')
ax.axhline(0, alpha=0.5, color='k', linestyle='--')
if p is not None:
fitline_kwds.setdefault('color', 'k')
scatter_kwds.setdefault('cmap', hmap)
scatter_kwds.setdefault('c', spots)
ax.plot(lag, fit.predy, **fitline_kwds)
ax.scatter(moran_loc.z, fit.predy,
**scatter_kwds)
else:
scatter_kwds.setdefault('color', splot_colors['moran_base'])
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
ax.plot(lag, fit.predy, **fitline_kwds)
ax.scatter(moran_loc.z, fit.predy, **scatter_kwds)
else:
lag = lag_spatial(moran_loc.w, moran_loc.y)
b, a = np.polyfit(moran_loc.y, lag, 1)
# dashed vert at mean of the attribute
ax.vlines(moran_loc.y.mean(), lag.min(), lag.max(), alpha=0.5,
linestyle='--')
# dashed horizontal at mean of lagged attribute
ax.hlines(lag.mean(), moran_loc.y.min(), moran_loc.y.max(), alpha=0.5,
linestyle='--')
if p is not None:
fitline_kwds.setdefault('color', 'k')
scatter_kwds.setdefault('cmap', hmap)
scatter_kwds.setdefault('c', spots)
ax.plot(moran_loc.y, a + b*moran_loc.y, **fitline_kwds)
ax.scatter(moran_loc.y, lag, **scatter_kwds)
else:
scatter_kwds.setdefault('c', splot_colors['moran_base'])
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
ax.plot(moran_loc.y, a + b*moran_loc.y, **fitline_kwds)
ax.scatter(moran_loc.y, lag, **scatter_kwds)
return fig, ax
[docs]def lisa_cluster(moran_loc, gdf, p=0.05, ax=None,
legend=True, legend_kwds=None, **kwargs):
"""
Create a LISA Cluster map
Parameters
----------
moran_loc : esda.moran.Moran_Local or Moran_Local_BV instance
Values of Moran's Local Autocorrelation Statistic
gdf : geopandas dataframe instance
The Dataframe containing information to plot. Note that `gdf` will be
modified, so calling functions should use a copy of the user
provided `gdf`. (either using gdf.assign() or gdf.copy())
p : float, optional
The p-value threshold for significance. Points will
be colored by significance.
ax : matplotlib Axes instance, optional
Axes in which to plot the figure in multiple Axes layout.
Default = None
legend : boolean, optional
If True, legend for maps will be depicted. Default = True
legend_kwds : dict, optional
Dictionary to control legend formatting options. Example:
``legend_kwds={'loc': 'upper left', 'bbox_to_anchor': (0.92, 1.05)}``
Default = None
**kwargs : keyword arguments, optional
Keywords designing and passed to geopandas.GeoDataFrame.plot().
Returns
-------
fig : matplotlip Figure instance
Figure of LISA cluster map
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran_Local
>>> from splot.esda import lisa_cluster
Data preparation and statistical analysis
>>> link = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link)
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
>>> moran_loc = Moran_Local(y, w)
Plotting
>>> fig = lisa_cluster(moran_loc, gdf)
>>> plt.show()
"""
# retrieve colors5 and labels from mask_local_auto
_, colors5, _, labels = mask_local_auto(moran_loc, p=p)
# define ListedColormap
hmap = colors.ListedColormap(colors5)
if ax is None:
figsize = kwargs.pop('figsize', None)
fig, ax = plt.subplots(1, figsize=figsize)
else:
fig = ax.get_figure()
gdf.assign(cl=labels).plot(column='cl', categorical=True,
k=2, cmap=hmap, linewidth=0.1, ax=ax,
edgecolor='white', legend=legend,
legend_kwds=legend_kwds, **kwargs)
ax.set_axis_off()
ax.set_aspect('equal')
return fig, ax
[docs]def plot_local_autocorrelation(moran_loc, gdf, attribute, p=0.05,
region_column=None, mask=None,
mask_color='#636363', quadrant=None,
aspect_equal=True,
legend=True, scheme='Quantiles',
cmap='YlGnBu', figsize=(15, 4),
scatter_kwds=None, fitline_kwds=None):
'''
Produce three-plot visualisation of Moran Scatteprlot, LISA cluster
and Choropleth maps, with Local Moran region and quadrant masking
Parameters
----------
moran_loc : esda.moran.Moran_Local or Moran_Local_BV instance
Values of Moran's Local Autocorrelation Statistic
gdf : geopandas dataframe
The Dataframe containing information to plot the two maps.
attribute : str
Column name of attribute which should be depicted in Choropleth map.
p : float, optional
The p-value threshold for significance. Points and polygons will
be colored by significance. Default = 0.05.
region_column: string, optional
Column name containing mask region of interest. Default = None
mask: str, optional
Identifier or name of the region to highlight. Default = None
mask_color: str, optional
Color of mask. Default = '#636363'
quadrant : int, optional
Quadrant 1-4 in scatterplot masking values in LISA cluster and
Choropleth maps. Default = None
aspect_equal : bool, optional
If True, Axes of Moran Scatterplot will show the same
aspect or visual proportions.
figsize: tuple, optional
W, h of figure. Default = (15,4)
legend: boolean, optional
If True, legend for maps will be depicted. Default = True
scheme: str, optional
Name of PySAL classifier to be used. Default = 'Quantiles'
cmap: str, optional
Name of matplotlib colormap used for plotting the Choropleth.
Default = 'YlGnBu'
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline
in the scatterplot. Default =None.
Returns
-------
fig : Matplotlib figure instance
Moran Scatterplot, LISA cluster map and Choropleth.
axs : list of Matplotlib axes
Lisat of Matplotlib axes plotted.
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran_Local
>>> from splot.esda import plot_local_autocorrelation
Data preparation and analysis
>>> link = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link)
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
>>> moran_loc = Moran_Local(y, w)
Plotting with quadrant mask and region mask
>>> fig = plot_local_autocorrelation(moran_loc, gdf, 'Donatns', p=0.05,
... region_column='Dprtmnt',
... mask=['Ain'], quadrant=1)
>>> plt.show()
'''
fig, axs = plt.subplots(1, 3, figsize=figsize,
subplot_kw={'aspect': 'equal', 'adjustable':'datalim'})
# Moran Scatterplot
moran_scatterplot(moran_loc, p=p, ax=axs[0],
scatter_kwds=scatter_kwds, fitline_kwds=fitline_kwds)
if aspect_equal is True:
axs[0].set_aspect('equal', 'datalim')
else:
axs[0].set_aspect('auto')
# Lisa cluster map
# TODO: Fix legend_kwds: display boxes instead of points
lisa_cluster(moran_loc, gdf, p=p, ax=axs[1], legend=legend,
legend_kwds={'loc': 'upper left',
'bbox_to_anchor': (0.92, 1.05)})
axs[1].set_aspect('equal')
# Choropleth for attribute
gdf.plot(column=attribute, scheme=scheme, cmap=cmap,
legend=legend, legend_kwds={'loc': 'upper left',
'bbox_to_anchor': (0.92, 1.05)},
ax=axs[2], alpha=1)
axs[2].set_axis_off()
axs[2].set_aspect('equal')
# MASKING QUADRANT VALUES
if quadrant is not None:
# Quadrant masking in Scatterplot
mask_angles = {1: 0, 2: 90, 3: 180, 4: 270} # rectangle angles
# We don't want to change the axis data limits, so use the current ones
xmin, xmax = axs[0].get_xlim()
ymin, ymax = axs[0].get_ylim()
# We are rotating, so we start from 0 degrees and
# figured out the right dimensions for the rectangles for other angles
mask_width = {1: abs(xmax),
2: abs(ymax),
3: abs(xmin),
4: abs(ymin)}
mask_height = {1: abs(ymax),
2: abs(xmin),
3: abs(ymin),
4: abs(xmax)}
axs[0].add_patch(patches.Rectangle((0, 0), width=mask_width[quadrant],
height=mask_height[quadrant],
angle=mask_angles[quadrant],
color='#E5E5E5', zorder=-1, alpha=0.8))
# quadrant selection in maps
non_quadrant = ~(moran_loc.q == quadrant)
mask_quadrant = gdf[non_quadrant]
df_quadrant = gdf.iloc[~non_quadrant]
union2 = df_quadrant.unary_union.boundary
# LISA Cluster mask and cluster boundary
with warnings.catch_warnings(): # temorarily surpress geopandas warning
warnings.filterwarnings('ignore', category=UserWarning)
mask_quadrant.plot(column=attribute, scheme=scheme, color='white',
ax=axs[1], alpha=0.7, zorder=1)
gpd.GeoSeries([union2]).plot(linewidth=1, ax=axs[1], color='#E5E5E5')
# CHOROPLETH MASK
with warnings.catch_warnings(): # temorarily surpress geopandas warning
warnings.filterwarnings('ignore', category=UserWarning)
mask_quadrant.plot(column=attribute, scheme=scheme, color='white',
ax=axs[2], alpha=0.7, zorder=1)
gpd.GeoSeries([union2]).plot(linewidth=1, ax=axs[2], color='#E5E5E5')
# REGION MASKING
if region_column is not None:
# masking inside axs[0] or Moran Scatterplot
ix = gdf[region_column].isin(mask)
df_mask = gdf[ix]
x_mask = moran_loc.z[ix]
y_mask = lag_spatial(moran_loc.w, moran_loc.z)[ix]
axs[0].plot(x_mask, y_mask, color=mask_color, marker='o',
markersize=14, alpha=.8, linestyle="None", zorder=-1)
# masking inside axs[1] or Lisa cluster map
union = df_mask.unary_union.boundary
gpd.GeoSeries([union]).plot(linewidth=2, ax=axs[1], color=mask_color)
# masking inside axs[2] or Chloropleth
gpd.GeoSeries([union]).plot(linewidth=2, ax=axs[2], color=mask_color)
return fig, axs
def _moran_loc_bv_scatterplot(moran_loc_bv, p=None,
aspect_equal=True, ax=None,
scatter_kwds=None,
fitline_kwds=None):
"""
Moran Bivariate Scatterplot with option of coloring of Local Moran Statistics
Parameters
----------
moran_loc : esda.moran.Moran_Local_BV instance
Values of Moran's I Local Autocorrelation Statistics
p : float, optional
If given, the p-value threshold for significance. Points will
be colored by significance. By default it will not be colored.
Default =None.
aspect_equal : bool, optional
If True, Axes of Moran Scatterplot will show the same
aspect or visual proportions.
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline.
Default =None.
Returns
-------
fig : Matplotlib Figure instance
Bivariate Moran Local scatterplot figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> import geopandas as gpd
>>> from libpysal.weights.contiguity import Queen
>>> from libpysal import examples
>>> from esda.moran import Moran_Local_BV
>>> from splot.esda import moran_scatterplot
Load data and calculate Moran Local statistics
>>> link = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link)
>>> x = gdf['Suicids'].values
>>> y = gdf['Donatns'].values
>>> w = Queen.from_dataframe(gdf)
>>> w.transform = 'r'
>>> m = Moran_Local_BV(x, y, w)
Plot
>>> moran_scatterplot(m)
>>> plt.show()
Customize plot
>>> moran_scatterplot(m, p=0.05,
... fitline_kwds=dict(color='#4393c3')))
>>> plt.show()
"""
# to set default as an empty dictionary that is later filled with defaults
if scatter_kwds is None:
scatter_kwds = dict()
if fitline_kwds is None:
fitline_kwds = dict()
if p is not None:
if not isinstance(moran_loc_bv, Moran_Local_BV):
raise ValueError("`moran_loc_bv` is not a\n" +
"esda.moran.Moran_Local_BV instance")
if 'color' in scatter_kwds or 'c' in scatter_kwds or 'cmap' in scatter_kwds:
warnings.warn("To change the color use cmap with a colormap of 5,\n" +
"c defines the LISA category, color will interfere with c")
# colors
spots_bv = moran_hot_cold_spots(moran_loc_bv, p)
hmap = colors.ListedColormap(['#bababa', '#d7191c', '#abd9e9',
'#2c7bb6', '#fdae61'])
# define customization
scatter_kwds.setdefault('alpha', 0.6)
scatter_kwds.setdefault('s', 40)
fitline_kwds.setdefault('alpha', 0.9)
# get fig and ax
fig, ax = _create_moran_fig_ax(ax, figsize=(7,7),
aspect_equal=aspect_equal)
# set labels
ax.set_xlabel('Attribute')
ax.set_ylabel('Spatial Lag')
ax.set_title('Moran BV Local Scatterplot')
# plot and set standards
lag = lag_spatial(moran_loc_bv.w, moran_loc_bv.zy)
fit = OLS(moran_loc_bv.zy[:, None], lag[:, None])
# v- and hlines
ax.axvline(0, alpha=0.5, color='k', linestyle='--')
ax.axhline(0, alpha=0.5, color='k', linestyle='--')
if p is not None:
fitline_kwds.setdefault('color', 'k')
scatter_kwds.setdefault('cmap', hmap)
scatter_kwds.setdefault('c', spots_bv)
ax.plot(lag, fit.predy, **fitline_kwds)
ax.scatter(moran_loc_bv.zx, fit.predy,
**scatter_kwds)
else:
scatter_kwds.setdefault('color', splot_colors['moran_base'])
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
ax.plot(lag, fit.predy, **fitline_kwds)
ax.scatter(moran_loc_bv.zy, fit.predy, **scatter_kwds)
return fig, ax
[docs]def moran_facet(moran_matrix, figsize=(16,12),
scatter_bv_kwds=None, fitline_bv_kwds=None,
scatter_glob_kwds=dict(color='#737373'), fitline_glob_kwds=None):
"""
Moran Facet visualization.
Includes BV Morans and Global Morans on the diagonal.
Parameters
----------
moran_matrix : esda.moran.Moran_BV_matrix instance
Dictionary of Moran_BV objects
figsize : tuple, optional
W, h of figure. Default =(16,12)
scatter_bv_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points of
off-diagonal Moran_BV plots.
Default =None.
fitline_bv_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline of
off-diagonal Moran_BV plots.
Default =None.
scatter_glob_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points of
diagonal Moran plots.
Default =None.
fitline_glob_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline of
diagonal Moran plots.
Default =None.
Returns
-------
fig : Matplotlib Figure instance
Bivariate Moran Local scatterplot figure
axarr : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> import libpysal as lp
>>> import numpy as np
>>> import geopandas as gpd
>>> from esda.moran import Moran_BV_matrix
>>> from splot.esda import moran_facet
Load data and calculate Moran Local statistics
>>> f = gpd.read_file(lp.examples.get_path("sids2.dbf"))
>>> varnames = ['SIDR74', 'SIDR79', 'NWR74', 'NWR79']
>>> vars = [np.array(f[var]) for var in varnames]
>>> w = lp.io.open(lp.examples.get_path("sids2.gal")).read()
>>> moran_matrix = Moran_BV_matrix(vars, w, varnames = varnames)
Plot
>>> fig, axarr = moran_facet(moran_matrix)
>>> plt.show()
Customize plot
>>> fig, axarr = moran_facet(moran_matrix,
... fitline_bv_kwds=dict(color='#4393c3'))
>>> plt.show()
"""
nrows = int(np.sqrt(len(moran_matrix))) + 1
ncols = nrows
fig, axarr = plt.subplots(nrows, ncols, figsize=figsize,
sharey=True, sharex=True)
fig.suptitle('Moran Facet')
for row in range(nrows):
for col in range(ncols):
if row == col:
global_m = Moran(moran_matrix[row, (row+1) % 4].zy,
moran_matrix[row, (row+1) % 4].w)
_moran_global_scatterplot(global_m, ax= axarr[row,col],
scatter_kwds=scatter_glob_kwds,
fitline_kwds=fitline_glob_kwds)
axarr[row, col].set_facecolor('#d9d9d9')
else:
_moran_bv_scatterplot(moran_matrix[row,col],
ax=axarr[row,col],
scatter_kwds=scatter_bv_kwds,
fitline_kwds=fitline_bv_kwds)
axarr[row, col].spines['bottom'].set_visible(False)
axarr[row, col].spines['left'].set_visible(False)
if row == nrows - 1:
axarr[row, col].set_xlabel(str(
moran_matrix[(col+1)%4, col].varnames['x']).format(col))
axarr[row, col].spines['bottom'].set_visible(True)
else:
axarr[row, col].set_xlabel('')
if col == 0:
axarr[row, col].set_ylabel(('Spatial Lag of '+str(
moran_matrix[row, (row+1)%4].varnames['y'])).format(row))
axarr[row, col].spines['left'].set_visible(True)
else:
axarr[row, col].set_ylabel('')
axarr[row, col].set_title('')
plt.tight_layout()
return fig, axarr