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_simple_poisson_vb():
y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 1)
exog_vc = sparse.csr_matrix(exog_vc)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt1 = glmm1.fit_map()
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt2 = glmm2.fit_vb(rslt1.params)
rslt1.summary()
rslt2.summary()
assert_allclose(rslt1.params[0:5], np.r_[
-0.07233493, -0.06706505, -0.47159649, 1.12575122, -1.02442201],
rtol=1e-4, atol=1e-4)
assert_allclose(rslt1.cov_params.flat[0:5], np.r_[
0.00790914, 0.00080666, -0.00050719, 0.00022648, 0.00046235],
rtol=1e-4, atol=1e-4)
assert_allclose(rslt2.params[0:5], np.r_[
-0.07088814, -0.06373107, -0.22770786, 1.12923746, -1.26161339],
rtol=1e-4, atol=1e-4)
assert_allclose(rslt2.cov_params[0:5], np.r_[
0.00747782, 0.0092554, 0.04508904, 0.02934488, 0.20312746],
rtol=1e-4, atol=1e-4)
def test_simple_poisson_map():
y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 0.2)
exog_vc = sparse.csr_matrix(exog_vc)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt1 = glmm1.fit_map()
assert_allclose(glmm1.logposterior_grad(rslt1.params),
np.zeros_like(rslt1.params),
atol=1e-3)
# This should give the same answer as above
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt2 = glmm2.fit_map()
assert_allclose(rslt1.params, rslt2.params, atol=1e-4)
# Test the predict method
for linear in False, True:
for exog in None, exog_fe:
pr1 = rslt1.predict(linear=linear, exog=exog)
pr2 = rslt2.predict(linear=linear, exog=exog)
pr3 = glmm1.predict(rslt1.params, linear=linear, exog=exog)
pr4 = glmm2.predict(rslt2.params, linear=linear, exog=exog)
assert_allclose(pr1, pr2, rtol=1e-5)
assert_allclose(pr2, pr3, rtol=1e-5)
assert_allclose(pr3, pr4, rtol=1e-5)
if not linear:
assert_equal(pr1.min() >= 0, True)
assert_equal(pr2.min() >= 0, True)
assert_equal(pr3.min() >= 0, True)
def test_crossed_poisson_map():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 1)
exog_vc = sparse.csr_matrix(exog_vc)
glmm = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident,
vcp_p=0.5)
rslt = glmm.fit_map()
assert_allclose(glmm.logposterior_grad(rslt.params),
np.zeros_like(rslt.params), atol=1e-4)
def test_crossed_poisson_map():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 1)
exog_vc = sparse.csr_matrix(exog_vc)
glmm = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt = glmm.fit_map()
assert_allclose(glmm.logposterior_grad(rslt.params),
np.zeros_like(rslt.params),
atol=1e-4)
def test_simple_poisson_map():
y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 0.2)
exog_vc = sparse.csr_matrix(exog_vc)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident,
vcp_p=0.5)
rslt1 = glmm1.fit_map()
assert_allclose(glmm1.logposterior_grad(rslt1.params),
np.zeros_like(rslt1.params), atol=1e-3)
# This should give the same answer as above
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident,
vcp_p=0.5)
rslt2 = glmm2.fit_map()
assert_allclose(rslt1.params, rslt2.params, atol=1e-4)
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_simple_poisson_vb():
y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 1)
exog_vc = sparse.csr_matrix(exog_vc)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt1 = glmm1.fit_map()
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt2 = glmm2.fit_vb(rslt1.params)
rslt1.summary()
rslt2.summary()
assert_allclose(
rslt1.params[0:5],
np.r_[-0.07233493, -0.06706505, -0.47159649, 1.12575122, -1.02442201],
rtol=1e-4,
atol=1e-4)
assert_allclose(
rslt1.cov_params().flat[0:5],
np.r_[0.00790914, 0.00080666, -0.00050719, 0.00022648, 0.00046235],
rtol=1e-4,
atol=1e-4)
assert_allclose(
rslt2.params[0:5],
np.r_[-0.07088814, -0.06373107, -0.22770786, 1.12923746, -1.26161339],
rtol=1e-4,
atol=1e-4)
assert_allclose(
rslt2.cov_params()[0:5],
np.r_[0.00747782, 0.0092554, 0.04508904, 0.02934488, 0.20312746],
rtol=1e-4,
atol=1e-4)
for rslt in rslt1, rslt2:
cp = rslt.cov_params()
p = len(rslt.params)
if rslt is rslt1:
assert_equal(cp.shape, np.r_[p, p])
np.linalg.cholesky(cp)
else:
assert_equal(cp.shape, np.r_[p,])
assert_equal(cp > 0, True*np.ones(p))
def test_elbo_grad():
for f in range(2):
for j in range(2):
if f == 0:
if j == 0:
y, exog_fe, exog_vc, ident = gen_simple_logit(10, 10, 2)
else:
y, exog_fe, exog_vc, ident = gen_crossed_logit(
10, 10, 1, 2)
elif f == 1:
if j == 0:
y, exog_fe, exog_vc, ident = gen_simple_poisson(
10, 10, 0.5)
else:
y, exog_fe, exog_vc, ident = gen_crossed_poisson(
10, 10, 1, 0.5)
exog_vc = sparse.csr_matrix(exog_vc)
if f == 0:
glmm1 = BinomialBayesMixedGLM(y, exog_fe, exog_vc, ident,
vcp_p=0.5)
else:
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident,
vcp_p=0.5)
rslt1 = glmm1.fit_map()
for k in range(3):
if k == 0:
vb_mean = rslt1.params
vb_sd = np.ones_like(vb_mean)
elif k == 1:
vb_mean = np.zeros(len(vb_mean))
vb_sd = np.ones_like(vb_mean)
else:
vb_mean = np.random.normal(size=len(vb_mean))
vb_sd = np.random.uniform(1, 2, size=len(vb_mean))
mean_grad, sd_grad = glmm1.vb_elbo_grad(vb_mean, vb_sd)
def elbo(vec):
n = len(vec) // 2
return glmm1.vb_elbo(vec[:n], vec[n:])
x = np.concatenate((vb_mean, vb_sd))
g1 = approx_fprime(x, elbo, 1e-5)
n = len(x) // 2
mean_grad_n = g1[:n]
sd_grad_n = g1[n:]
assert_allclose(mean_grad, mean_grad_n, atol=1e-2,
rtol=1e-2)
assert_allclose(sd_grad, sd_grad_n, atol=1e-2,
rtol=1e-2)
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_crossed_poisson_map():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 1)
exog_vc = sparse.csr_matrix(exog_vc)
glmm = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt = glmm.fit_map()
assert_allclose(glmm.logposterior_grad(rslt.params),
np.zeros_like(rslt.params),
atol=1e-4)
# Check dimensions and PSD status of cov_params
cp = rslt.cov_params()
p = len(rslt.params)
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)
def test_crossed_poisson_map():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 1)
exog_vc = sparse.csr_matrix(exog_vc)
glmm = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt = glmm.fit_map()
assert_allclose(
glmm.logposterior_grad(rslt.params),
np.zeros_like(rslt.params),
atol=1e-4)
# Check dimensions and PSD status of cov_params
cp = rslt.cov_params()
p = len(rslt.params)
assert_equal(cp.shape, np.r_[p, p])
np.linalg.cholesky(cp)
def test_crossed_poisson_vb():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 0.5)
glmm1 = PoissonBayesMixedGLM(y,
exog_fe,
exog_vc,
ident,
vcp_p=0.5,
fe_p=0.5)
rslt1 = glmm1.fit_map()
glmm2 = PoissonBayesMixedGLM(y,
exog_fe,
exog_vc,
ident,
vcp_p=0.5,
fe_p=0.5)
rslt2 = glmm2.fit_vb(mean=rslt1.params)
rslt1.summary()
rslt2.summary()
assert_allclose(rslt1.params[0:5],
np.r_[-0.54855281, 0.10458834, -0.68777741, -0.01699925,
0.77200546],
rtol=1e-4,
atol=1e-4)
assert_allclose(rslt2.params[0:5],
np.r_[-0.54691502, 0.22297158, -0.52673802, -0.06218684,
0.74385237],
rtol=1e-4,
atol=1e-4)
def test_simple_poisson_vb():
y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 1)
exog_vc = sparse.csr_matrix(exog_vc)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt1 = glmm1.fit_map()
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt2 = glmm2.fit_vb(rslt1.params)
rslt1.summary()
rslt2.summary()
assert_allclose(rslt1.params[0:5], np.r_[
-0.07233493, -0.06706505, -0.47159649, 1.12575122, -1.02442201],
rtol=1e-4, atol=1e-4)
assert_allclose(rslt1.cov_params.flat[0:5], np.r_[
0.00790914, 0.00080666, -0.00050719, 0.00022648, 0.00046235],
rtol=1e-4, atol=1e-4)
assert_allclose(rslt2.params[0:5], np.r_[
-0.07088814, -0.06373107, -0.22770786, 1.12923746, -1.26161339],
rtol=1e-4, atol=1e-4)
assert_allclose(rslt2.cov_params[0:5], np.r_[
0.00747782, 0.0092554, 0.04508904, 0.02934488, 0.20312746],
rtol=1e-4, atol=1e-4)
def test_crossed_poisson_vb():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 0.5)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5,
fe_p=0.5)
rslt1 = glmm1.fit_map()
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5,
fe_p=0.5)
rslt2 = glmm2.fit_vb(mean=rslt1.params)
rslt1.summary()
rslt2.summary()
assert_allclose(rslt1.params[0:5], np.r_[
-0.54855281, 0.10458834, -0.68777741, -0.01699925, 0.77200546],
rtol=1e-4, atol=1e-4)
assert_allclose(rslt2.params[0:5], np.r_[
-0.54691502, 0.22297158, -0.52673802, -0.06218684, 0.74385237],
rtol=1e-4, atol=1e-4)
def test_crossed_poisson_vb():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 0.5)
glmm1 = PoissonBayesMixedGLM(
y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5)
rslt1 = glmm1.fit_map()
glmm2 = PoissonBayesMixedGLM(
y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5)
rslt2 = glmm2.fit_vb(mean=rslt1.params)
rslt1.summary()
rslt2.summary()
assert_allclose(
rslt1.params[0:5],
np.r_[-0.54855281, 0.10458834, -0.68777741, -0.01699925, 0.77200546],
rtol=1e-4,
atol=1e-4)
assert_allclose(
rslt2.params[0:5],
np.r_[-0.54691502, 0.22297158, -0.52673802, -0.06218684, 0.74385237],
rtol=1e-4,
atol=1e-4)
for rslt in rslt1, rslt2:
cp = rslt.cov_params()
p = len(rslt.params)
if rslt is rslt1:
assert_equal(cp.shape, np.r_[p, p])
np.linalg.cholesky(cp)
else:
assert_equal(cp.shape, np.r_[p,])
assert_equal(cp > 0, True*np.ones(p))
def test_simple_poisson_map():
y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 0.2)
exog_vc = sparse.csr_matrix(exog_vc)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt1 = glmm1.fit_map()
assert_allclose(glmm1.logposterior_grad(rslt1.params),
np.zeros_like(rslt1.params),
atol=1e-3)
# This should give the same answer as above
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt2 = glmm2.fit_map()
assert_allclose(rslt1.params, rslt2.params, atol=1e-4)
def test_simple_poisson_map():
y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 0.2)
exog_vc = sparse.csr_matrix(exog_vc)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt1 = glmm1.fit_map()
assert_allclose(
glmm1.logposterior_grad(rslt1.params),
np.zeros_like(rslt1.params),
atol=1e-3)
# This should give the same answer as above
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt2 = glmm2.fit_map()
assert_allclose(rslt1.params, rslt2.params, atol=1e-4)
# Test the predict method
for linear in False, True:
for exog in None, exog_fe:
pr1 = rslt1.predict(linear=linear, exog=exog)
pr2 = rslt2.predict(linear=linear, exog=exog)
pr3 = glmm1.predict(rslt1.params, linear=linear, exog=exog)
pr4 = glmm2.predict(rslt2.params, linear=linear, exog=exog)
assert_allclose(pr1, pr2, rtol=1e-5)
assert_allclose(pr2, pr3, rtol=1e-5)
assert_allclose(pr3, pr4, rtol=1e-5)
if not linear:
assert_equal(pr1.min() >= 0, True)
assert_equal(pr2.min() >= 0, True)
assert_equal(pr3.min() >= 0, True)
# Check dimensions and PSD status of cov_params
for rslt in rslt1, rslt2:
cp = rslt.cov_params()
p = len(rslt.params)
assert_equal(cp.shape, np.r_[p, p])
np.linalg.cholesky(cp)
def test_simple_poisson_vb():
y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 1)
exog_vc = sparse.csr_matrix(exog_vc)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt1 = glmm1.fit_map()
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt2 = glmm2.fit_vb(rslt1.params)
rslt1.summary()
rslt2.summary()
assert_allclose(rslt1.params[0:5],
np.r_[-0.07233493, -0.06706505, -0.47159649, 1.12575122,
-1.02442201],
rtol=1e-4,
atol=1e-4)
assert_allclose(rslt1.cov_params().flat[0:5],
np.r_[0.00790914, 0.00080666, -0.00050719, 0.00022648,
0.00046235],
rtol=1e-4,
atol=1e-4)
assert_allclose(rslt2.params[0:5],
np.r_[-0.07088814, -0.06373107, -0.22770786, 1.12923746,
-1.26161339],
rtol=1e-4,
atol=1e-4)
assert_allclose(rslt2.cov_params()[0:5],
np.r_[0.00747782, 0.0092554, 0.04508904, 0.02934488,
0.20312746],
rtol=1e-4,
atol=1e-4)
for rslt in rslt1, rslt2:
cp = rslt.cov_params()
p = len(rslt.params)
if rslt is rslt1:
assert_equal(cp.shape, np.r_[p, p])
np.linalg.cholesky(cp)
else:
assert_equal(cp.shape, np.r_[p, ])
assert_equal(cp > 0, True * np.ones(p))
def test_crossed_poisson_vb():
y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 0.5)
glmm1 = PoissonBayesMixedGLM(y,
exog_fe,
exog_vc,
ident,
vcp_p=0.5,
fe_p=0.5)
rslt1 = glmm1.fit_map()
glmm2 = PoissonBayesMixedGLM(y,
exog_fe,
exog_vc,
ident,
vcp_p=0.5,
fe_p=0.5)
rslt2 = glmm2.fit_vb(mean=rslt1.params)
rslt1.summary()
rslt2.summary()
assert_allclose(rslt1.params[0:5],
np.r_[-0.54855281, 0.10458834, -0.68777741, -0.01699925,
0.77200546],
rtol=1e-4,
atol=1e-4)
assert_allclose(rslt2.params[0:5],
np.r_[-0.54691502, 0.22297158, -0.52673802, -0.06218684,
0.74385237],
rtol=1e-4,
atol=1e-4)
for rslt in rslt1, rslt2:
cp = rslt.cov_params()
p = len(rslt.params)
if rslt is rslt1:
assert_equal(cp.shape, np.r_[p, p])
np.linalg.cholesky(cp)
else:
assert_equal(cp.shape, np.r_[p, ])
assert_equal(cp > 0, True * np.ones(p))
def test_simple_poisson_map():
y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 0.2)
exog_vc = sparse.csr_matrix(exog_vc)
glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt1 = glmm1.fit_map()
assert_allclose(
glmm1.logposterior_grad(rslt1.params),
np.zeros_like(rslt1.params),
atol=1e-3)
# This should give the same answer as above
glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5)
rslt2 = glmm2.fit_map()
assert_allclose(rslt1.params, rslt2.params, atol=1e-4)
# Test the predict method
for linear in False, True:
for exog in None, exog_fe:
pr1 = rslt1.predict(linear=linear, exog=exog)
pr2 = rslt2.predict(linear=linear, exog=exog)
pr3 = glmm1.predict(rslt1.params, linear=linear, exog=exog)
pr4 = glmm2.predict(rslt2.params, linear=linear, exog=exog)
assert_allclose(pr1, pr2, rtol=1e-5)
assert_allclose(pr2, pr3, rtol=1e-5)
assert_allclose(pr3, pr4, rtol=1e-5)
if not linear:
assert_equal(pr1.min() >= 0, True)
assert_equal(pr2.min() >= 0, True)
assert_equal(pr3.min() >= 0, True)
# Check dimensions and PSD status of cov_params
for rslt in rslt1, rslt2:
cp = rslt.cov_params()
p = len(rslt.params)
assert_equal(cp.shape, np.r_[p, p])
np.linalg.cholesky(cp)
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',
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())