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"""
Test functions for genmod.families.family
"""
import warnings
import pytest
import numpy as np
from numpy.testing import assert_allclose
from scipy import integrate
from statsmodels.compat.scipy import SP_LT_17
from statsmodels.tools.sm_exceptions import (
ValueWarning,
)
import statsmodels.genmod.families as F
from statsmodels.genmod.families.family import Tweedie
import statsmodels.genmod.families.links as L
all_links = {
L.Logit, L.logit, L.Power, L.inverse_power, L.sqrt, L.inverse_squared,
L.identity, L.Log, L.log, L.CDFLink, L.probit, L.cauchy, L.LogLog,
L.loglog, L.CLogLog, L.cloglog, L.NegativeBinomial, L.nbinom
}
poisson_links = {L.Log, L.log, L.identity, L.sqrt}
gaussian_links = {L.Log, L.log, L.identity, L.inverse_power}
gamma_links = {L.Log, L.log, L.identity, L.inverse_power}
binomial_links = {
L.Logit, L.logit, L.probit, L.cauchy, L.Log, L.log, L.CLogLog,
L.cloglog, L.LogLog, L.loglog, L.identity
}
inverse_gaussian_links = {
L.inverse_squared, L.inverse_power, L.identity, L.Log, L.log
}
negative_bionomial_links = {
L.Log, L.log, L.CLogLog, L.cloglog, L.identity, L.NegativeBinomial,
L.nbinom, L.Power
}
tweedie_links = {L.Log, L.log, L.Power}
link_cases = [
(F.Poisson, poisson_links),
(F.Gaussian, gaussian_links),
(F.Gamma, gamma_links),
(F.Binomial, binomial_links),
(F.InverseGaussian, inverse_gaussian_links),
(F.NegativeBinomial, negative_bionomial_links),
(F.Tweedie, tweedie_links)
]
@pytest.mark.parametrize("family, links", link_cases)
def test_invalid_family_link(family, links):
invalid_links = all_links - links
with pytest.raises(ValueError):
with warnings.catch_warnings():
msg = ("Negative binomial dispersion parameter alpha not set. "
"Using default value alpha=1.0.")
warnings.filterwarnings("ignore", message=msg,
category=UserWarning)
warnings.filterwarnings("ignore",
category=FutureWarning)
for link in invalid_links:
family(link())
@pytest.mark.parametrize("family, links", link_cases)
def test_family_link(family, links):
with warnings.catch_warnings():
msg = ("Negative binomial dispersion parameter alpha not set. "
"Using default value alpha=1.0.")
warnings.filterwarnings("ignore", message=msg,
category=ValueWarning)
warnings.filterwarnings("ignore",
category=FutureWarning)
for link in links:
assert family(link())
@pytest.mark.parametrize("family, links", link_cases)
def test_family_link_check(family, links):
# check that we can turn of all link checks
class Hugo():
pass
with warnings.catch_warnings():
msg = ("Negative binomial dispersion parameter alpha not set. "
"Using default value alpha=1.0.")
warnings.filterwarnings("ignore", message=msg,
category=ValueWarning)
assert family(Hugo(), check_link=False)
@pytest.mark.skipif(SP_LT_17, reason="Scipy too old, function not available")
@pytest.mark.parametrize("power", (1.1, 1.5, 1.9))
def test_tweedie_loglike_obs(power):
"""Test that Tweedie loglike is normalized to 1."""
tweedie = Tweedie(var_power=power, eql=False)
mu = 2.0
scale = 2.9
def pdf(y):
return np.squeeze(
np.exp(
tweedie.loglike_obs(endog=y, mu=mu, scale=scale)
)
)
assert_allclose(pdf(0) + integrate.quad(pdf, 0, 1e2)[0], 1, atol=1e-4)

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"""
Test functions for genmod.families.links
"""
import numpy as np
from numpy.testing import assert_allclose, assert_equal, assert_array_less
from scipy import stats
import pytest
import statsmodels.genmod.families as families
from statsmodels.tools import numdiff as nd
# Family instances
links = families.links
logit = links.Logit()
inverse_power = links.InversePower()
sqrt = links.Sqrt()
inverse_squared = links.InverseSquared()
identity = links.Identity()
log = links.Log()
logc = links.LogC()
probit = links.Probit()
cauchy = links.Cauchy()
cloglog = links.CLogLog()
loglog = links.LogLog()
negbinom = links.NegativeBinomial()
# TODO: parametrize all these tess
Links = [logit, inverse_power, sqrt, inverse_squared, identity,
log, logc, probit, cauchy, cloglog, loglog, negbinom]
# links with defined second derivative of inverse link.
LinksISD = [inverse_power, sqrt, inverse_squared, identity,
logc, cauchy, probit, loglog]
def get_domainvalue(link):
"""
Get a value in the domain for a given family.
"""
z = -np.log(np.random.uniform(0, 1))
if isinstance(link, links.CLogLog): # prone to overflow
z = min(z, 3)
elif isinstance(link, links.LogLog):
z = max(z, -3)
elif isinstance(link, (links.NegativeBinomial, links.LogC)):
# domain is negative numbers
z = -z
return z
def test_inverse():
# Logic check that link.inverse(link) and link(link.inverse)
# are the identity.
np.random.seed(3285)
for link in Links:
for k in range(10):
p = np.random.uniform(0, 1) # In domain for all families
d = link.inverse(link(p))
assert_allclose(d, p, atol=1e-8, err_msg=str(link))
z = get_domainvalue(link)
d = link(link.inverse(z))
assert_allclose(d, z, atol=1e-8, err_msg=str(link))
def test_deriv():
# Check link function derivatives using numeric differentiation.
np.random.seed(24235)
for link in Links:
for k in range(10):
p = np.random.uniform(0, 1)
if isinstance(link, links.Cauchy):
p = np.clip(p, 0.03, 0.97)
d = link.deriv(p)
da = nd.approx_fprime(np.r_[p], link)
assert_allclose(d, da, rtol=1e-6, atol=1e-6,
err_msg=str(link))
if not isinstance(link, (type(inverse_power),
type(inverse_squared),
type(logc))):
# check monotonically increasing
assert_array_less(-d, 0)
def test_deriv2():
# Check link function second derivatives using numeric differentiation.
np.random.seed(24235)
for link in Links:
for k in range(10):
p = np.random.uniform(0, 1)
p = np.clip(p, 0.01, 0.99)
if isinstance(link, links.cauchy):
p = np.clip(p, 0.03, 0.97)
d = link.deriv2(p)
da = nd.approx_fprime(np.r_[p], link.deriv)
assert_allclose(d, da, rtol=5e-6, atol=1e-6,
err_msg=str(link))
def test_inverse_deriv():
# Logic check that inverse_deriv equals 1/link.deriv(link.inverse)
np.random.seed(24235)
for link in Links:
for k in range(10):
z = get_domainvalue(link)
d = link.inverse_deriv(z)
f = 1 / link.deriv(link.inverse(z))
assert_allclose(d, f, rtol=1e-8, atol=1e-10,
err_msg=str(link))
def test_inverse_deriv2():
# Check second derivative of inverse link using numeric differentiation.
np.random.seed(24235)
for link in LinksISD:
for k in range(10):
z = get_domainvalue(link)
d2 = link.inverse_deriv2(z)
d2a = nd.approx_fprime(np.r_[z], link.inverse_deriv)
assert_allclose(d2, d2a, rtol=5e-6, atol=1e-6,
err_msg=str(link))
def test_invlogit_stability():
z = [1123.4910007309222, 1483.952316802719, 1344.86033748641,
706.339159002542, 1167.9986375146532, 663.8345826933115,
1496.3691686913917, 1563.0763842182257, 1587.4309332296314,
697.1173174974248, 1333.7256198289665, 1388.7667560586933,
819.7605431778434, 1479.9204150555015, 1078.5642245164856,
480.10338454985896, 1112.691659145772, 534.1061908007274,
918.2011296406588, 1280.8808515887802, 758.3890788775948,
673.503699841035, 1556.7043357878208, 819.5269028006679,
1262.5711060356423, 1098.7271535253608, 1482.811928490097,
796.198809756532, 893.7946963941745, 470.3304989319786,
1427.77079226037, 1365.2050226373822, 1492.4193201661922,
871.9922191949931, 768.4735925445908, 732.9222777654679,
812.2382651982667, 495.06449978924525]
zinv = logit.inverse(z)
assert_equal(zinv, np.ones_like(z))
class MyCLogLog(links.Link):
def __call__(self, p):
# p = self._clean(p)
return np.log(-np.log(1 - p))
def inverse(self, z):
return 1 - np.exp(-np.exp(z))
def deriv(self, p):
# p = self._clean(p)
return 1. / ((p - 1) * (np.log(1 - p)))
class CasesCDFLink():
# just as namespace to hold cases for test_cdflink
link_pairs = [
(links.CDFLink(dbn=stats.gumbel_l), links.CLogLog()),
(links.CDFLink(dbn=stats.gumbel_r), links.LogLog()),
(links.CDFLink(dbn=stats.norm), links.Probit()),
(links.CDFLink(dbn=stats.logistic), links.Logit()),
(links.CDFLink(dbn=stats.t(1)), links.Cauchy()),
# approximation of t by normal is not good enough for rtol, atol
# (links.CDFLink(dbn=stats.t(1000000)), links.Probit()),
(MyCLogLog(), links.CLogLog()), # not a cdflink, but compares
]
methods = ['__call__', 'deriv', 'inverse', 'inverse_deriv', 'deriv2',
'inverse_deriv2']
p = np.linspace(0, 1, 6)
eps = 1e-3
p = np.clip(p, eps, 1 - eps)
@pytest.mark.parametrize("m", CasesCDFLink.methods)
@pytest.mark.parametrize("link1, link2", CasesCDFLink.link_pairs)
def test_cdflink(m, link1, link2):
p = CasesCDFLink.p
res1 = getattr(link1, m)(p)
res2 = getattr(link2, m)(p)
assert_allclose(res1, res2, atol=1e-8, rtol=1e-8)