def test_poisson_formula():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 0.5)
for vb in False, True:
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident)
if vb:
rslt1 = glmm1.fit_vb()
else:
rslt1 = glmm1.fit_map()
# Build categorical variables that match exog_vc
df = pd.DataFrame({"y": y, "x1": exog_fe[:, 0]})
z1 = np.zeros(len(y))
for j, k in enumerate(np.flatnonzero(ident == 0)):
z1[exog_vc[:, k] == 1] = j
df["z1"] = z1
z2 = np.zeros(len(y))
for j, k in enumerate(np.flatnonzero(ident == 1)):
z2[exog_vc[:, k] == 1] = j
df["z2"] = z2
fml = "y ~ 0 + x1"
from collections import OrderedDict
vc_fml = OrderedDict({})
vc_fml["z1"] = "0 + C(z1)"
vc_fml["z2"] = "0 + C(z2)"
glmm2 = PoissonBayesMixedGLM.from_formula(fml, vc_fml, df)
if vb:
rslt2 = glmm2.fit_vb()
else:
rslt2 = glmm2.fit_map()
assert_allclose(rslt1.params, rslt2.params, rtol=1e-5)
def test_doc_examples():
np.random.seed(8767)
n = 200
m = 20
data = pd.DataFrame({"Year": np.random.uniform(0, 1, n),
"Village": np.random.randint(0, m, n)})
data['year_cen'] = data['Year'] - data.Year.mean()
# Binomial outcome
lpr = np.random.normal(size=m)[data.Village]
lpr += np.random.normal(size=m)[data.Village] * data.year_cen
y = (np.random.uniform(size=n) < 1 / (1 + np.exp(-lpr)))
data["y"] = y.astype(np.int)
# These lines should agree with the example in the class docstring.
random = {"a": '0 + C(Village)', "b": '0 + C(Village)*year_cen'}
model = BinomialBayesMixedGLM.from_formula(
'y ~ year_cen', random, data)
result = model.fit_vb()
_ = result
# Poisson outcome
lpr = np.random.normal(size=m)[data.Village]
lpr += np.random.normal(size=m)[data.Village] * data.year_cen
data["y"] = np.random.poisson(np.exp(lpr))
# These lines should agree with the example in the class docstring.
random = {"a": '0 + C(Village)', "b": '0 + C(Village)*year_cen'}
model = PoissonBayesMixedGLM.from_formula(
'y ~ year_cen', random, data)
result = model.fit_vb()
_ = result
def test_poisson_formula():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 0.5)
for vb in False, True:
glmm1 = PoissonBayesMixedGLM(
y, exog_fe, exog_vc, ident)
if vb:
rslt1 = glmm1.fit_vb()
else:
rslt1 = glmm1.fit_map()
# Build categorical variables that match exog_vc
df = pd.DataFrame({"y": y, "x1": exog_fe[:, 0]})
z1 = np.zeros(len(y))
for j,k in enumerate(np.flatnonzero(ident == 0)):
z1[exog_vc[:, k] == 1] = j
df["z1"] = z1
z2 = np.zeros(len(y))
for j,k in enumerate(np.flatnonzero(ident == 1)):
z2[exog_vc[:, k] == 1] = j
df["z2"] = z2
fml = "y ~ 0 + x1"
from collections import OrderedDict
vc_fml = OrderedDict({})
vc_fml["z1"] = "0 + C(z1)"
vc_fml["z2"] = "0 + C(z2)"
glmm2 = PoissonBayesMixedGLM.from_formula(fml, vc_fml, df)
if vb:
rslt2 = glmm2.fit_vb()
else:
rslt2 = glmm2.fit_map()
assert_allclose(rslt1.params, rslt2.params, rtol=1e-5)
for rslt in rslt1, rslt2:
cp = rslt.cov_params()
p = len(rslt.params)
if vb:
assert_equal(cp.shape, np.r_[p,])
assert_equal(cp > 0, True*np.ones(p))
else:
assert_equal(cp.shape, np.r_[p, p])
np.linalg.cholesky(cp)
def test_poisson_formula():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 0.5)
for vb in False, True:
glmm1 = PoissonBayesMixedGLM(
y, exog_fe, exog_vc, ident)
if vb:
rslt1 = glmm1.fit_vb()
else:
rslt1 = glmm1.fit_map()
# Build categorical variables that match exog_vc
df = pd.DataFrame({"y": y, "x1": exog_fe[:, 0]})
z1 = np.zeros(len(y))
for j,k in enumerate(np.flatnonzero(ident == 0)):
z1[exog_vc[:, k] == 1] = j
df["z1"] = z1
z2 = np.zeros(len(y))
for j,k in enumerate(np.flatnonzero(ident == 1)):
z2[exog_vc[:, k] == 1] = j
df["z2"] = z2
fml = "y ~ 0 + x1"
vc_fml = {}
vc_fml["z1"] = "0 + C(z1)"
vc_fml["z2"] = "0 + C(z2)"
glmm2 = PoissonBayesMixedGLM.from_formula(fml, vc_fml, df)
if vb:
rslt2 = glmm2.fit_vb()
else:
rslt2 = glmm2.fit_map()
assert_allclose(rslt1.params, rslt2.params, rtol=1e-5)
for rslt in rslt1, rslt2:
cp = rslt.cov_params()
p = len(rslt.params)
if vb:
assert_equal(cp.shape, np.r_[p,])
assert_equal(cp > 0, True*np.ones(p))
else:
assert_equal(cp.shape, np.r_[p, p])
np.linalg.cholesky(cp)
stats.probplot(gee_model2_results.resid_pearson, plot=plt, fit=True)
axs[1,0].set_xlabel("Theoretical quantiles",fontsize=10)
axs[1,0].set_ylabel("Sample quantiles",fontsize=10)
axs[1,0].set_title("Q-Q plot of normalized residuals",fontsize=10)
plt.subplots_adjust(left=0.12, hspace=0.25)
plt.show()
# model comparison
print(gee_model2_results.qic())
print(gee_model1_results.qic())
# Both models improve, but are not satisfatory, probably because they cannot take account of excessive zeros and they only use cluster-robust standard errors and thus
# cannot model how lower level coefficients vary across groups of the higher level. Python statsmodels has zero-inflated count model methods, but they cannot deal with
# panel/clustered data.
# Approach two to generalized linear models for panel data: Generalized Linear Mixed Effects Model support Poisson models using Bayesian methods
# poisson mixed effects model with one random effect
formula = "cases_count_pos ~ week_of_year + percent_age65over + percent_female + percent_black"
po_bay_panel1 = PoissonBayesMixedGLM.from_formula(formula, {'state': '0 + C(state)'}, US_cases_long_demogr_week)
po_bay_panel1_results = po_bay_panel1.fit_map()
print(po_bay_panel1_results.summary())
# poisson mixed effects model with two independnet random effects
formula = "cases_count_pos ~ week_of_year + percent_age65over + percent_female + percent_black"
po_bay_panel2 = PoissonBayesMixedGLM.from_formula(formula, {'state': '0 + C(state)', "week_of_year": '0 + C(week_of_year)'}, US_cases_long_demogr_week)
po_bay_panel2_results = po_bay_panel2.fit_map()
print(po_bay_panel2_results.summary())
nfl_rush_2019 = nfl_2019[nfl_2019["play_type"] == "rush"]
# first, fit rush outcome models
# 1 - touchdown
rush_penalty_mod = BinomialBayesMixedGLM.from_formula(
'penalty ~ shotgun + no_huddle + qb_dropback + run_location + run_gap',
['0 + rusher_id', '0 + def_id'],
data=nfl_rush_2019)
rush_penalty_result = rush_penalty_mod.fit_vb
# 2 - rushing yards
rush_yard_mod = PoissonBayesMixedGLM.from_formula(
'yards_gained ~ shotgun + no_huddle + qb_dropback + run_location + run_gap',
['0 + rusher_id', '0 + def_id'],
data=nfl_rush_2019)
rush_yard_result = rush_yard_mod.fit_vb()
# 3 - rushing turnovers (fumbles)
rush_turnover_mod = BinomialBayesMixedGLM.from_formula(
'turnover ~ shotgun + no_huddle + qb_dropback + run_location + run_gap',
['0 + rusher_id', '0 + def_id'],
data=nfl_rush_2019)
rush_turnover_result = rush_turnover_mod.fit_vb()
# 4 - penalty (holding)
rush_penalty_mod = BinomialBayesMixedGLM.from_formula(
'penalty ~ shotgun + no_huddle + qb_dropback + run_location + run_gap',