def test_cutoff(self):
cc = np.array([0.8, 0.9, 1, 1.2])
sm = Spatial_Markov(self.rpci, self.w, cutoffs=cc, lag_cutoffs=cc)
P = np.array(
[[[0.96703297, 0.03296703, 0., 0., 0.],
[0.10638298, 0.68085106, 0.21276596, 0., 0.],
[0.,
0.14285714, 0.7755102, 0.08163265, 0.], [0., 0., 0.5, 0.5, 0.],
[0., 0., 0., 0., 0.]],
[[0.88636364, 0.10606061, 0.00757576, 0., 0.],
[0.04402516, 0.89308176, 0.06289308, 0., 0.],
[0., 0.05882353, 0.8627451, 0.07843137, 0.],
[0., 0., 0.13846154, 0.86153846, 0.], [0., 0., 0., 0., 1.]],
[[0.78082192, 0.17808219, 0.02739726, 0.01369863, 0.],
[0.03488372, 0.90406977, 0.05813953, 0.00290698, 0.],
[0., 0.05919003, 0.84735202, 0.09034268, 0.00311526],
[0., 0., 0.05811623, 0.92985972, 0.01202405],
[0., 0., 0., 0.14285714, 0.85714286]],
[[0.82692308, 0.15384615, 0., 0.01923077, 0.],
[0.0703125, 0.7890625, 0.125, 0.015625, 0.],
[0.00295858, 0.06213018, 0.82248521, 0.10946746, 0.00295858],
[0., 0.00185529, 0.07606679, 0.88497217, 0.03710575],
[0., 0., 0., 0.07803468, 0.92196532]],
[[0., 0., 0., 0., 0.], [0., 0., 0., 0., 0.],
[0., 0.06666667, 0.9, 0.03333333, 0.],
[0., 0., 0.05660377, 0.90566038, 0.03773585],
[0., 0., 0., 0.03932584, 0.96067416]]])
np.testing.assert_array_almost_equal(P, sm.P)
def __init__(self,
dataset,
w_type,
w_kwds=None,
permutations=0,
cluster_type=None):
y = dataset.census.copy().reset_index()
y = y[['geoid', 'year', cluster_type]]
y = y.groupby(['geoid', 'year']).first().unstack()
y = y.dropna()
tracts = dataset.tracts.copy().merge(
y.reset_index(), on='geoid', how='right')
w_dict = {'rook': Rook, 'queen': Queen, 'knn': KNN, 'kernel': Kernel}
w = w_dict[w_type].from_dataframe(tracts)
y = y.astype(int)
sm = Spatial_Markov(
y,
w,
permutations=permutations,
discrete=True,
variable_name=cluster_type)
self.p = sm.p
self.transitions = sm.transitions
self.P = sm.P
self.T = sm.T
self.summary = sm.summary
self.cluster_type = cluster_type
# keep the spatial markov instance here in case that users want to
# estimate steady state distribution etc
self.sm = sm
def test___init__(self):
sm = Spatial_Markov(self.rpci, self.w, fixed=True, k=5, m=5)
S = np.array(
[[0.43509425, 0.2635327, 0.20363044, 0.06841983, 0.02932278],
[0.13391287, 0.33993305, 0.25153036, 0.23343016, 0.04119356],
[0.12124869, 0.21137444, 0.2635101, 0.29013417, 0.1137326],
[0.0776413, 0.19748806, 0.25352636, 0.22480415, 0.24654013],
[0.01776781, 0.19964349, 0.19009833, 0.25524697, 0.3372434]])
np.testing.assert_array_almost_equal(S, sm.S)
def test_discretized(self):
w = ps.weights.Contiguity.Queen.from_shapefile(
ps.examples.get_path('us48.shp'))
np.random.seed(24788)
sm = Spatial_Markov(self.discretized, w, discrete=True)
answer = np.array([[[92., 88., 75., 95.], [50., 55., 52., 35.],
[45., 48., 58., 48.], [45., 32., 39., 51.]],
[[54., 43., 40., 51.], [92., 97., 91., 89.],
[44., 49., 56., 55.], [40., 35., 75., 50.]],
[[67., 51., 43., 58.], [41., 58., 56., 35.],
[86., 88., 140., 89.], [42., 56., 61., 73.]],
[[56., 51., 39., 38.], [50., 49., 50., 45.],
[41., 61., 55., 46.], [93., 77., 87., 89.]]])
np.testing.assert_array_equal(sm.T, answer)
def test_chi2(self):
f = ps.open(ps.examples.get_path('usjoin.csv'))
pci = np.array([f.by_col[str(y)] for y in range(1929, 2010)])
pci = pci.transpose()
rpci = pci / (pci.mean(axis=0))
w = ps.open(ps.examples.get_path("states48.gal")).read()
w.transform = 'r'
sm = Spatial_Markov(rpci, w, fixed=True, k=5, m=5)
chi = np.array([[4.05598541e+01, 6.44644317e-04, 1.60000000e+01],
[5.54751974e+01, 2.97033748e-06, 1.60000000e+01],
[1.77528996e+01, 3.38563882e-01, 1.60000000e+01],
[4.00390961e+01, 7.68422046e-04, 1.60000000e+01],
[4.67966803e+01, 7.32512065e-05, 1.60000000e+01]])
obs = np.array(sm.chi2)
np.testing.assert_array_almost_equal(obs, chi)
obs = np.array([[4.61209613e+02, 0.00000000e+00, 4.00000000e+00],
[1.48140694e+02, 0.00000000e+00, 4.00000000e+00],
[6.33129261e+01, 5.83089133e-13, 4.00000000e+00],
[7.22778509e+01, 7.54951657e-15, 4.00000000e+00],
[2.32659201e+02, 0.00000000e+00, 4.00000000e+00]])
np.testing.assert_array_almost_equal(obs, np.array(sm.shtest))
def transition(gdf,
cluster_col,
time_var="year",
id_var="geoid",
w_type=None,
permutations=0):
"""
(Spatial) Markov approach to transitional dynamics of neighborhoods.
Parameters
----------
gdf : (geo)DataFrame
Long-form (geo)DataFrame containing neighborhood
attributes with a column defining neighborhood clusters.
cluster_col : string or int
Column name for the neighborhood segmentation, such as
"ward", "kmeans", etc.
time_var : string, optional
Column defining time and or sequencing of the long-form data.
Default is "year".
id_var : string, optional
Column identifying the unique id of spatial units.
Default is "geoid".
w_type : string, optional
Type of spatial weights type ("rook", "queen", "knn" or
"kernel") to be used for spatial structure. Default is
None, if non-spatial Markov transition rates are desired.
permutations : int, optional
number of permutations for use in randomization based
inference (the default is 0).
Return
------
mar : object
if w_type=None, return a giddy.markov.Markov instance;
if w_type is given, return a
giddy.markov.Spatial_Markov instance.
Examples
--------
>>> from geosnap.data import Community
>>> columbus = Community.from_ltdb(msa_fips=columbusfips)
>>> columbus1 = columbus.cluster(columns=['median_household_income',
... 'p_poverty_rate', 'p_edu_college_greater', 'p_unemployment_rate'],
... method='ward', n_clusters=6)
>>> gdf = columbus1.gdf
>>> a = transition(gdf, "ward", w_type="rook")
>>> a.p
array([[0.79189189, 0.00540541, 0.0027027 , 0.13243243, 0.06216216,
0.00540541],
[0.0203252 , 0.75609756, 0.10569106, 0.11382114, 0. ,
0.00406504],
[0.00917431, 0.20183486, 0.75229358, 0.01834862, 0. ,
0.01834862],
[0.1959799 , 0.18341709, 0.00251256, 0.61809045, 0. ,
0. ],
[0.32307692, 0. , 0. , 0. , 0.66153846,
0.01538462],
[0.09375 , 0.0625 , 0. , 0. , 0. ,
0.84375 ]])
>>> a.P[0]
array([[0.82119205, 0. , 0. , 0.10927152, 0.06622517,
0.00331126],
[0.14285714, 0.57142857, 0.14285714, 0.14285714, 0. ,
0. ],
[0.5 , 0. , 0.5 , 0. , 0. ,
0. ],
[0.21428571, 0.14285714, 0. , 0.64285714, 0. ,
0. ],
[0.18918919, 0. , 0. , 0. , 0.78378378,
0.02702703],
[0.28571429, 0. , 0. , 0. , 0. ,
0.71428571]])
"""
gdf_temp = gdf.copy().reset_index()
df = gdf_temp[[id_var, time_var, cluster_col]]
df_wide = (df.pivot(index=id_var, columns=time_var,
values=cluster_col).dropna().astype("int"))
y = df_wide.values
if w_type is None:
mar = Markov(y) # class markov modeling
else:
gdf_one = gdf_temp.drop_duplicates([id_var])
gdf_wide = df_wide.merge(gdf_one, left_index=True, right_on=id_var)
w_dict = {"rook": Rook, "queen": Queen, "knn": KNN, "kernel": Kernel}
w = w_dict[w_type].from_dataframe(gdf_wide)
w.transform = "r"
mar = Spatial_Markov(y,
w,
permutations=permutations,
discrete=True,
variable_name=cluster_col)
return mar
def transition(
gdf,
cluster_col,
temporal_index="year",
unit_index="geoid",
w_type="rook",
w_options=None,
permutations=0,
):
"""
(Spatial) Markov approach to transitional dynamics of neighborhoods.
Parameters
----------
gdf : geopandas.GeoDataFrame or pandas.DataFrame
Long-form geopandas.GeoDataFrame or pandas.DataFrame containing neighborhood
attributes with a column defining neighborhood clusters.
cluster_col : string or int
Column name for the neighborhood segmentation, such as
"ward", "kmeans", etc.
temporal_index : string, optional
Column defining time and or sequencing of the long-form data.
Default is "year".
unit_index : string, optional
Column identifying the unique id of spatial units.
Default is "geoid".
w_type : string, optional
Type of spatial weights type ("rook", "queen", "knn" or
"kernel") to be used for spatial structure. Default is
None, if non-spatial Markov transition rates are desired.
w_options : dict
additional options passed to a libpysal weights constructor
(e.g. `k` for a KNN weights matrix)
permutations : int, optional
number of permutations for use in randomization based
inference (the default is 0).
Returns
--------
mar : giddy.markov.Markov instance or giddy.markov.Spatial_Markov
if w_type=None, a classic Markov instance is returned.
if w_type is given, a Spatial_Markov instance is returned.
Examples
--------
>>> from geosnap import Community
>>> columbus = Community.from_ltdb(msa_fips="18140")
>>> columbus1 = columbus.cluster(columns=['median_household_income',
... 'p_poverty_rate', 'p_edu_college_greater', 'p_unemployment_rate'],
... method='ward', n_clusters=6)
>>> gdf = columbus1.gdf
>>> a = transition(gdf, "ward", w_type="rook")
>>> a.p
array([[0.79189189, 0.00540541, 0.0027027 , 0.13243243, 0.06216216,
0.00540541],
[0.0203252 , 0.75609756, 0.10569106, 0.11382114, 0. ,
0.00406504],
[0.00917431, 0.20183486, 0.75229358, 0.01834862, 0. ,
0.01834862],
[0.1959799 , 0.18341709, 0.00251256, 0.61809045, 0. ,
0. ],
[0.32307692, 0. , 0. , 0. , 0.66153846,
0.01538462],
[0.09375 , 0.0625 , 0. , 0. , 0. ,
0.84375 ]])
>>> a.P[0]
array([[0.82119205, 0. , 0. , 0.10927152, 0.06622517,
0.00331126],
[0.14285714, 0.57142857, 0.14285714, 0.14285714, 0. ,
0. ],
[0.5 , 0. , 0.5 , 0. , 0. ,
0. ],
[0.21428571, 0.14285714, 0. , 0.64285714, 0. ,
0. ],
[0.18918919, 0. , 0. , 0. , 0.78378378,
0.02702703],
[0.28571429, 0. , 0. , 0. , 0. ,
0.71428571]])
"""
if not w_options:
w_options = {}
assert (
unit_index in gdf.columns
), f"The unit_index ({unit_index}) column is not in the geodataframe"
gdf_temp = gdf.copy().reset_index()
df = gdf_temp[[unit_index, temporal_index, cluster_col]]
df_wide = (df.pivot(index=unit_index,
columns=temporal_index,
values=cluster_col).dropna().astype("int"))
y = df_wide.values
if w_type is None:
mar = Markov(y) # class markov modeling
else:
geoms = gdf_temp.groupby(unit_index).first()[gdf_temp.geometry.name]
gdf_wide = df_wide.merge(geoms, left_index=True, right_index=True)
w = Ws[w_type].from_dataframe(gpd.GeoDataFrame(gdf_wide), **w_options)
w.transform = "r"
mar = Spatial_Markov(y,
w,
permutations=permutations,
discrete=True,
variable_name=cluster_col)
return mar