def set_endog(y, x, w, yend, q, w_lags, lag_q):
# Create spatial lag of y
yl = lag_spatial(w, y)
# spatial and non-spatial instruments
if issubclass(type(yend), np.ndarray):
if lag_q:
lag_vars = sphstack(x, q)
else:
lag_vars = x
spatial_inst = get_lags(w, lag_vars, w_lags)
q = sphstack(q, spatial_inst)
yend = sphstack(yend, yl)
elif yend == None: # spatial instruments only
q = get_lags(w, x, w_lags)
yend = yl
else:
raise Exception("invalid value passed to yend")
return yend, q
lag = lag_spatial(w, x)
spat_lags = lag
for i in range(w_lags - 1):
lag = lag_spatial(w, lag)
spat_lags = sphstack(spat_lags, lag)
return spat_lags
def get_lags(w, x, w_lags):
'''
Calculates a given order of spatial lags and all the smaller orders
Parameters
----------
w : weight
PySAL weights instance
x : array
nxk arrays with the variables to be lagged
w_lags : integer
Maximum order of spatial lag
Returns
--------
rs : array
nxk*(w_lags+1) array with original and spatially lagged variables
'''
lag = lag_spatial(w, x)
spat_lags = lag
for i in range(w_lags - 1):
lag = lag_spatial(w, lag)
spat_lags = sphstack(spat_lags, lag)
return spat_lags
def __calc(self, z):
zl = lag_spatial(self.w, z)
bb = sum(z * zl) / 2.0
zw = 1 - z
zl = lag_spatial(self.w, zw)
ww = sum(zw * zl) / 2.0
bw = self.J - (bb + ww)
return (bb, ww, bw)
def __calc(self, z):
zl = lag_spatial(self.w, z)
bb = sum(z * zl) / 2.0
zw = 1 - z
zl = lag_spatial(self.w, zw)
ww = sum(zw * zl) / 2.0
bw = self.J - (bb + ww)
return (bb, ww, bw)
def __calc(self, z, op):
if op == 'c': # cross-product
zl = lag_spatial(self.w, z)
g = (z * zl).sum()
elif op == 's': # squared difference
zs = np.zeros(z.shape)
z2 = z ** 2
for i, i0 in enumerate(self.w.id_order):
neighbors = self.w.neighbor_offsets[i0]
wijs = self.w.weights[i0]
zw = list(zip(neighbors, wijs))
zs[i] = sum([wij * (z2[i] - 2.0 * z[i] * z[
j] + z2[j]) for j, wij in zw])
g = zs.sum()
elif op == 'a': # absolute difference
zs = np.zeros(z.shape)
for i, i0 in enumerate(self.w.id_order):
neighbors = self.w.neighbor_offsets[i0]
wijs = self.w.weights[i0]
zw = list(zip(neighbors, wijs))
zs[i] = sum([wij * abs(z[i] - z[j]) for j, wij in zw])
g = zs.sum()
else: # any previously defined function op
zs = np.zeros(z.shape)
for i, i0 in enumerate(self.w.id_order):
neighbors = self.w.neighbor_offsets[i0]
wijs = self.w.weights[i0]
zw = list(zip(neighbors, wijs))
zs[i] = sum([wij * op(z, i, j) for j, wij in zw])
g = zs.sum()
return g
def __calc(self, z, op):
if op == 'c': # cross-product
zl = lag_spatial(self.w, z)
g = (z * zl).sum()
elif op == 's': # squared difference
zs = np.zeros(z.shape)
z2 = z**2
for i, i0 in enumerate(self.w.id_order):
neighbors = self.w.neighbor_offsets[i0]
wijs = self.w.weights[i0]
zw = list(zip(neighbors, wijs))
zs[i] = sum([
wij * (z2[i] - 2.0 * z[i] * z[j] + z2[j]) for j, wij in zw
])
g = zs.sum()
elif op == 'a': # absolute difference
zs = np.zeros(z.shape)
for i, i0 in enumerate(self.w.id_order):
neighbors = self.w.neighbor_offsets[i0]
wijs = self.w.weights[i0]
zw = list(zip(neighbors, wijs))
zs[i] = sum([wij * abs(z[i] - z[j]) for j, wij in zw])
g = zs.sum()
else: # any previously defined function op
zs = np.zeros(z.shape)
for i, i0 in enumerate(self.w.id_order):
neighbors = self.w.neighbor_offsets[i0]
wijs = self.w.weights[i0]
zw = list(zip(neighbors, wijs))
zs[i] = sum([wij * op(z, i, j) for j, wij in zw])
g = zs.sum()
return g
def hac_multi(reg, gwk, constant=False):
"""
HAC robust estimation of the variance-covariance matrix for multi-regression object
Parameters
----------
reg : Regression object (OLS or TSLS)
output instance from a regression model
gwk : PySAL weights object
Spatial weights based on kernel functions
Returns
--------
psi : kxk array
Robust estimation of the variance-covariance
"""
if not constant:
reg.hac_var = check_constant(reg.hac_var)
xu = spbroadcast(reg.hac_var, reg.u)
gwkxu = lag_spatial(gwk, xu)
psi0 = spdot(xu.T, gwkxu)
counter = 0
for m in reg.multi:
reg.multi[m].robust = 'hac'
reg.multi[m].name_gwk = reg.name_gwk
try:
psi1 = spdot(reg.multi[m].varb, reg.multi[m].zthhthi)
reg.multi[m].vm = spdot(psi1, np.dot(psi0, psi1.T))
except:
reg.multi[m].vm = spdot(
reg.multi[m].xtxi, np.dot(psi0, reg.multi[m].xtxi))
reg.vm[(counter * reg.kr):((counter + 1) * reg.kr),
(counter * reg.kr):((counter + 1) * reg.kr)] = reg.multi[m].vm
counter += 1
def plot_local_autocorrelation(moran_loc,
gdf,
attribute,
p=0.05,
region_column=None,
mask=None,
mask_color='#636363',
quadrant=None,
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
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 pysal.lib.weights.contiguity import Queen
>>> from pysal.lib import examples
>>> import geopandas as gpd
>>> from pysal.explore.esda.moran import Moran_Local
>>> from pysal.viz.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'})
# Moran Scatterplot
moran_scatterplot(moran_loc,
p=p,
ax=axs[0],
scatter_kwds=scatter_kwds,
fitline_kwds=fitline_kwds)
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_scatterplot(moran_loc,
zstandard=True,
p=None,
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.
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 pysal.lib.weights.contiguity import Queen
>>> from pysal.lib import examples
>>> from pysal.explore.esda.moran import Moran_Local
>>> from pysal.viz.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))
# 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
def _moran_bv_scatterplot(moran_bv,
ax=None,
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.
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 pysal.lib.weights.contiguity import Queen
>>> from pysal.lib import examples
>>> import geopandas as gpd
>>> from pysal.explore.esda.moran import Moran_BV
>>> from pysal.viz.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))
# 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
def _moran_global_scatterplot(moran,
zstandard=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.
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 pysal.lib.weights.contiguity import Queen
>>> from pysal.lib import examples
>>> import geopandas as gpd
>>> from pysal.explore.esda.moran import Moran
>>> from pysal.viz.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))
# 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
def robust_vm(reg, gwk=None, sig2n_k=False):
"""
Robust estimation of the variance-covariance matrix. Estimated by White (default) or HAC (if wk is provided).
Parameters
----------
reg : Regression object (OLS or TSLS)
output instance from a regression model
gwk : PySAL weights object
Optional. Spatial weights based on kernel functions
If provided, returns the HAC variance estimation
sig2n_k : boolean
If True, then use n-k to rescale the vc matrix.
If False, use n. (White only)
Returns
--------
psi : kxk array
Robust estimation of the variance-covariance
Examples
--------
>>> import numpy as np
>>> import pysal.lib
>>> from ols import OLS
>>> from twosls import TSLS
>>> db=pysal.lib.io.open(pysal.lib.examples.get_path("NAT.dbf"),"r")
>>> y = np.array(db.by_col("HR90"))
>>> y = np.reshape(y, (y.shape[0],1))
>>> X = []
>>> X.append(db.by_col("RD90"))
>>> X.append(db.by_col("DV90"))
>>> X = np.array(X).T
Example with OLS with unadjusted standard errors
>>> ols = OLS(y,X)
>>> ols.vm
array([[ 0.17004545, 0.00226532, -0.02243898],
[ 0.00226532, 0.00941319, -0.00031638],
[-0.02243898, -0.00031638, 0.00313386]])
Example with OLS and White
>>> ols = OLS(y,X, robust='white')
>>> ols.vm
array([[ 0.24515481, 0.01093322, -0.03441966],
[ 0.01093322, 0.01798616, -0.00071414],
[-0.03441966, -0.00071414, 0.0050153 ]])
Example with OLS and HAC
>>> wk = pysal.lib.weights.Kernel.from_shapefile(pysal.lib.examples.get_path('NAT.shp'),k=15,function='triangular', fixed=False)
>>> wk.transform = 'o'
>>> ols = OLS(y,X, robust='hac', gwk=wk)
>>> ols.vm
array([[ 0.29213532, 0.01670361, -0.03948199],
[ 0.01655557, 0.02295829, -0.00116874],
[-0.03941483, -0.00119077, 0.00568314]])
Example with 2SLS and White
>>> yd = []
>>> yd.append(db.by_col("UE90"))
>>> yd = np.array(yd).T
>>> q = []
>>> q.append(db.by_col("UE80"))
>>> q = np.array(q).T
>>> tsls = TSLS(y, X, yd, q=q, robust='white')
>>> tsls.vm
array([[ 0.29569954, 0.04119843, -0.02496858, -0.01640185],
[ 0.04119843, 0.03647762, 0.004702 , -0.00987345],
[-0.02496858, 0.004702 , 0.00648262, -0.00292891],
[-0.01640185, -0.00987345, -0.00292891, 0.0053322 ]])
Example with 2SLS and HAC
>>> tsls = TSLS(y, X, yd, q=q, robust='hac', gwk=wk)
>>> tsls.vm
array([[ 0.41985329, 0.06823119, -0.02883889, -0.02788116],
[ 0.06867042, 0.04887508, 0.00497443, -0.01367746],
[-0.02856454, 0.00501402, 0.0072195 , -0.00321604],
[-0.02810131, -0.01364908, -0.00318197, 0.00713251]])
"""
if hasattr(reg, 'h'): # If reg has H, do 2SLS estimator. OLS otherwise.
tsls = True
xu = spbroadcast(reg.h, reg.u)
else:
tsls = False
xu = spbroadcast(reg.x, reg.u)
if gwk: # If gwk do HAC. White otherwise.
gwkxu = lag_spatial(gwk, xu)
psi0 = spdot(xu.T, gwkxu)
else:
psi0 = spdot(xu.T, xu)
if sig2n_k:
psi0 = psi0 * (1. * reg.n / (reg.n - reg.k))
if tsls:
psi1 = spdot(reg.varb, reg.zthhthi)
psi = spdot(psi1, np.dot(psi0, psi1.T))
else:
psi = spdot(reg.xtxi, np.dot(psi0, reg.xtxi))
return psi
def plot_local_autocorrelation(moran_loc, gdf, attribute, p=0.05,
region_column=None, mask=None,
mask_color='#636363', quadrant=None,
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
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 pysal.lib.weights.contiguity import Queen
>>> from pysal.lib import examples
>>> import geopandas as gpd
>>> from pysal.explore.esda.moran import Moran_Local
>>> from pysal.viz.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'})
# Moran Scatterplot
moran_scatterplot(moran_loc, p=p, ax=axs[0],
scatter_kwds=scatter_kwds, fitline_kwds=fitline_kwds)
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_scatterplot(moran_loc, zstandard=True, p=None,
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.
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 pysal.lib.weights.contiguity import Queen
>>> from pysal.lib import examples
>>> from pysal.explore.esda.moran import Moran_Local
>>> from pysal.viz.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))
# 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
def _moran_bv_scatterplot(moran_bv, ax=None, 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.
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 pysal.lib.weights.contiguity import Queen
>>> from pysal.lib import examples
>>> import geopandas as gpd
>>> from pysal.explore.esda.moran import Moran_BV
>>> from pysal.viz.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))
# 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
def _moran_global_scatterplot(moran, zstandard=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.
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 pysal.lib.weights.contiguity import Queen
>>> from pysal.lib import examples
>>> import geopandas as gpd
>>> from pysal.explore.esda.moran import Moran
>>> from pysal.viz.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))
# 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