def __init__(self, x, y, regime, permutations=0):
x = np.asarray(x)
y = np.asarray(y)
res = Tau_Local(x, y)
self.n = res.n
self.S = res.S
reg = np.array(regime).flatten()
ur = np.unique(reg).tolist()
k = len(ur)
P = np.zeros((k, self.n))
for i, r in enumerate(reg):
P[ur.index(r), i] = 1 # construct P matrix
w = weights.block_weights(regime)
w.transform = 'b'
W = w.full()[0]
WH = np.ones((self.n, self.n)) - np.eye(self.n) - W
# inter and intraregional decomposition of Tau for the observed value
self.tau_reg = self._calc(W, WH, P, self.S)
if permutations > 0:
tau_reg_sim = np.zeros((permutations, k, k))
larger = np.zeros((k, k))
smaller = np.zeros((k, k))
rids = np.arange(len(x))
for i in range(permutations):
np.random.shuffle(rids)
res = Tau_Local(x[rids], y[rids])
tau_reg_sim[i] = self._calc(W, WH, P, res.S)
larger += np.greater_equal(tau_reg_sim[i], self.tau_reg)
smaller += np.less_equal(tau_reg_sim[i], self.tau_reg)
m = np.less(smaller, larger)
pvalues = (1 + m * smaller +
(1 - m) * larger) / (1. + permutations)
self.tau_reg_sim = tau_reg_sim
self.tau_reg_pvalues = pvalues
def kendallTau(data_df, quantilePolygon):
caseWeekly_unstack = data_df['CasesWeekly'].unstack(level=0)
zip_codes = quantilePolygon
data_df_zipGPD = zip_codes.merge(caseWeekly_unstack,
left_on='zip',
right_on=caseWeekly_unstack.index)
# print(data_df_zipGPD)
W = ps.lib.weights.Queen(data_df_zipGPD.geometry)
W.transform = 'R'
weeks = idx_weekNumber = data_df.index.get_level_values('Week Number')
weeks = np.unique(weeks)
valArray = data_df_zipGPD[weeks].to_numpy()
valArray_fillNan = bfill(valArray).T
valArray_fillNan[np.isnan(valArray_fillNan)] = 0
data_df_zipGPD_bfill = data_df_zipGPD.fillna(method='bfill', axis=1)
data_df_zipGPD_bfill[weeks] = data_df_zipGPD_bfill[weeks].fillna(0)
print(data_df_zipGPD_bfill.isna().sum())
data_df_zipGPD_bfill["idxPlus"] = data_df_zipGPD_bfill["idx"].apply(
lambda x: str(x[0]) + "-" + str(x[1]))
plt.figure()
plt.rcParams.update({'font.size': 30})
ax = data_df_zipGPD_bfill.plot(column="idxPlus", figsize=(20, 20))
plt.title("pop_quantile-5")
# ax=showVector(zs_zip,'quantile')
data_df_zipGPD_bfill.apply(lambda x: ax.annotate(
s=x["idxPlus"], xy=x.geometry.centroid.coords[0], ha='center'),
axis=1)
#Classic Kendall’s tau
tau = giddy.rank.Tau(data_df_zipGPD_bfill[10], data_df_zipGPD_bfill[19])
print("_" * 50, "Classic Kendall’s tau")
#−1≤τ≤1 . Smaller τ indicates higher exchange mobility
print("tau.concordant:", tau.concordant)
print("tau.discordant:", tau.discordant)
print("tau.tau:", tau.tau)
print("tau.tau_p:", tau.tau_p)
#Spatial Kendall’s tau
w_quantile = block_weights(data_df_zipGPD_bfill["idxPlus"])
np.random.seed(12345)
tau_w = giddy.rank.SpatialTau(data_df_zipGPD_bfill[10],
data_df_zipGPD_bfill[19], w_quantile, 999)
print("_" * 50, "Spatial Kendall’s tau")
print("tau_w.concordant:", tau_w.concordant)
print("tau_w.concordant_spatial:", tau_w.concordant_spatial)
print("tau_w.discordant:", tau_w.discordant)
print("tau_w.discordant_spatial:", tau_w.discordant_spatial)
print("tau_w.tau_spatial:", tau_w.tau_spatial)
print("tau_w.tau_spatial_psim:", tau_w.tau_spatial_psim)
#Inter- and Intra-regional decomposition of Kendall’s tau
np.random.seed(12345)
tau_w = giddy.rank.Tau_Regional(data_df_zipGPD_bfill[10],
data_df_zipGPD_bfill[19],
data_df_zipGPD_bfill["idxPlus"], 999)
print("_" * 50, "Inter- and Intra-regional decomposition of Kendall’s tau")
print("tau_w.tau_reg:", tau_w.tau_reg)
print("tau_w.tau_reg_pvalues:", tau_w.tau_reg_pvalues)
print("tau_w.tau_reg * (tau_w.tau_reg_pvalues<0.05):",
tau_w.tau_reg * (tau_w.tau_reg_pvalues < 0.05))
#Local Kendall’s tau
tau_r = giddy.rank.Tau_Local(data_df_zipGPD_bfill[10],
data_df_zipGPD_bfill[19])
LocalKendallTau = pd.DataFrame({
"STATE_NAME":
data_df_zipGPD_bfill['zip'].tolist(),
"$\\tau_r$":
tau_r.tau_local
}).head()
print("Local Kendall’s tau:", LocalKendallTau)
#Local indicator of mobility association-LIMA
#1-Neighbor set LIMA
data_df_zipGPD_bfill_dropZero = data_df_zipGPD_bfill.loc[~(
data_df_zipGPD_bfill[weeks] == 0).all(axis=1)]
# w_quantile_dropZero=block_weights(data_df_zipGPD_bfill_dropZero["idxPlus"]) #prompt mistake divide by zero
W_ = ps.lib.weights.Queen(data_df_zipGPD_bfill_dropZero.geometry)
W_.transform = 'R'
print(data_df_zipGPD_bfill.shape, data_df_zipGPD_bfill_dropZero.shape)
tau_wr = giddy.rank.Tau_Local_Neighbor(data_df_zipGPD_bfill_dropZero[10],
data_df_zipGPD_bfill_dropZero[19],
W_, 999)
# print("tau_wr.tau_ln:",tau_wr.tau_ln)
plt.figure()
data_df_zipGPD_bfill_dropZero["tau_ln"] = tau_wr.tau_ln
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(20, 20))
ln_map = data_df_zipGPD_bfill_dropZero.plot(ax=ax,
column="tau_ln",
cmap='coolwarm',
scheme='equal_interval',
legend=True)
leg = ax.get_legend()
leg.set_bbox_to_anchor((0.8, 0.15, 0.16, 0.2))
ln_map.set_title("Neighbor set LIMA for Covid-19",
fontdict={"fontsize": 20})
ax.set_axis_off()
print("tau_wr.tau_ln_pvalues:", tau_wr.tau_ln_pvalues)
sig_wr = tau_wr.tau_ln * (tau_wr.tau_ln_pvalues < 0.05)
print("sig_wr :", sig_wr)
plt.figure()
data_df_zipGPD_bfill_dropZero["sig_wr"] = sig_wr
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(20, 20))
data_df_zipGPD_bfill_dropZero[data_df_zipGPD_bfill_dropZero["sig_wr"] ==
0].plot(ax=ax,
color='white',
edgecolor='black')
sig_ln_map = data_df_zipGPD_bfill_dropZero[
data_df_zipGPD_bfill_dropZero["sig_wr"] != 0].plot(
ax=ax,
column="sig_wr",
cmap='coolwarm',
scheme='equal_interval',
legend=True)
leg = ax.get_legend()
leg.set_bbox_to_anchor((0.8, 0.15, 0.16, 0.2))
sig_ln_map.set_title("Significant Neighbor set LIMA for Covid=-19",
fontdict={"fontsize": 20})
ax.set_axis_off()
#Neighborhood set LIMA
tau_wwr = giddy.rank.Tau_Local_Neighborhood(
data_df_zipGPD_bfill_dropZero[10], data_df_zipGPD_bfill_dropZero[19],
W_, 999)
print("tau_wwr.tau_lnhood:", tau_wwr.tau_lnhood)
plt.figure()
data_df_zipGPD_bfill_dropZero["tau_lnhood"] = tau_wwr.tau_lnhood
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(20, 20))
ln_map = data_df_zipGPD_bfill_dropZero.plot(ax=ax,
column="tau_lnhood",
cmap='coolwarm',
scheme='equal_interval',
legend=True)
leg = ax.get_legend()
leg.set_bbox_to_anchor((0.8, 0.15, 0.16, 0.2))
ln_map.set_title("Neighborhood set LIMA for Covid-19",
fontdict={"fontsize": 20})
ax.set_axis_off()
print("tau_wwr.tau_lnhood_pvalues:", tau_wwr.tau_lnhood_pvalues)
sig_lnhood = tau_wwr.tau_lnhood * (tau_wwr.tau_lnhood_pvalues < 0.05)
plt.figure()
data_df_zipGPD_bfill_dropZero["sig_lnhood"] = sig_lnhood
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(20, 20))
data_df_zipGPD_bfill_dropZero[data_df_zipGPD_bfill_dropZero["sig_lnhood"]
== 0].plot(ax=ax,
color='white',
edgecolor='black')
sig_ln_map = data_df_zipGPD_bfill_dropZero[
data_df_zipGPD_bfill_dropZero["sig_lnhood"] != 0].plot(
ax=ax, column="sig_lnhood", categorical=True, legend=True)
leg = ax.get_legend()
leg.set_bbox_to_anchor((0.8, 0.15, 0.16, 0.2))
sig_ln_map.set_title(
"Significant Neighborhood set LIMA for U.S. states 1929-2009",
fontdict={"fontsize": 20})
ax.set_axis_off()