def test_formulas(self):
np.random.seed(24109403)
exog = np.random.normal(size=(300,4))
exog_re = np.random.normal(size=300)
groups = np.kron(np.arange(100), [1,1,1])
g_errors = exog_re * np.kron(np.random.normal(size=100),
[1,1,1])
endog = exog.sum(1) + g_errors + np.random.normal(size=300)
mdf1 = MixedLM(endog, exog, groups, exog_re).fit()
df = pd.DataFrame({"endog": endog})
for k in range(exog.shape[1]):
df["exog%d" % k] = exog[:,k]
df["exog_re"] = exog_re
md2 = MixedLM.from_formula(
"endog ~ 0 + exog0 + exog1 + exog2 + exog3",
groups=groups, data=df)
md2.set_random("0 + exog_re", data=df)
mdf2 = md2.fit()
assert_almost_equal(mdf1.params, mdf2.params)
# Check that it runs when the dimension of the random effects
# changes following set_random.
md2 = MixedLM.from_formula(
"endog ~ 0 + exog0 + exog1 + exog2 + exog3",
groups=groups, data=df)
md2.set_random("exog_re", data=df)
mdf2 = md2.fit()
def test_formulas(self):
np.random.seed(24109403)
exog = np.random.normal(size=(300, 4))
exog_re = np.random.normal(size=300)
groups = np.kron(np.arange(100), [1, 1, 1])
g_errors = exog_re * np.kron(np.random.normal(size=100), [1, 1, 1])
endog = exog.sum(1) + g_errors + np.random.normal(size=300)
mdf1 = MixedLM(endog, exog, groups, exog_re).fit()
df = pd.DataFrame({"endog": endog})
for k in range(exog.shape[1]):
df["exog%d" % k] = exog[:, k]
df["exog_re"] = exog_re
md2 = MixedLM.from_formula("endog ~ 0 + exog0 + exog1 + exog2 + exog3",
groups=groups,
data=df)
md2.set_random("0 + exog_re", data=df)
mdf2 = md2.fit()
assert_almost_equal(mdf1.params, mdf2.params)
# Check that it runs when the dimension of the random effects
# changes following set_random.
md2 = MixedLM.from_formula("endog ~ 0 + exog0 + exog1 + exog2 + exog3",
groups=groups,
data=df)
md2.set_random("exog_re", data=df)
mdf2 = md2.fit()
def test_default_re(self):
np.random.seed(323590805)
exog = np.random.normal(size=(300, 4))
groups = np.kron(np.arange(100), [1, 1, 1])
g_errors = np.kron(np.random.normal(size=100), [1, 1, 1])
endog = exog.sum(1) + g_errors + np.random.normal(size=300)
mdf1 = MixedLM(endog, exog, groups).fit()
mdf2 = MixedLM(endog, exog, groups, np.ones(300)).fit()
assert_almost_equal(mdf1.params, mdf2.params, decimal=8)
def test_regularized(self):
np.random.seed(3453908)
exog = np.random.normal(size=(400, 5))
groups = np.kron(np.arange(100), np.ones(4))
expected_endog = exog[:, 0] - exog[:, 2]
endog = expected_endog +\
np.kron(np.random.normal(size=100), np.ones(4)) +\
np.random.normal(size=400)
# L1 regularization
md = MixedLM(endog, exog, groups)
mdf1 = md.fit_regularized(alpha=1.)
mdf1.summary()
# L1 regularization
md = MixedLM(endog, exog, groups)
mdf2 = md.fit_regularized(alpha=10 * np.ones(5))
mdf2.summary()
# L2 regularization
pen = penalties.L2()
mdf3 = md.fit_regularized(method=pen, alpha=0.)
mdf3.summary()
# L2 regularization
pen = penalties.L2()
mdf4 = md.fit_regularized(method=pen, alpha=100.)
mdf4.summary()
# Pseudo-Huber regularization
pen = penalties.PseudoHuber(0.3)
mdf4 = md.fit_regularized(method=pen, alpha=1.)
mdf4.summary()
def do1(self, reml, irf, ds_ix):
# No need to check independent random effects when there is
# only one of them.
if irf and ds_ix < 6:
return
irfs = "irf" if irf else "drf"
meth = "reml" if reml else "ml"
rslt = R_Results(meth, irfs, ds_ix)
# Variance component MLE ~ 0 may require manual tweaking of
# algorithm parameters, so exclude from tests for now.
if np.min(np.diag(rslt.cov_re_r)) < 0.01:
print("Skipping %d since solution is on boundary." % ds_ix)
return
# Fit the model
md = MixedLM(rslt.endog, rslt.exog_fe, rslt.groups, rslt.exog_re)
if not irf: # Free random effects covariance
mdf = md.fit(gtol=1e-7, reml=reml)
else: # Independent random effects
k_fe = rslt.exog_fe.shape[1]
k_re = rslt.exog_re.shape[1]
mdf = md.fit(reml=reml,
gtol=1e-7,
free=(np.ones(k_fe), np.eye(k_re)))
assert_almost_equal(mdf.fe_params, rslt.coef, decimal=4)
assert_almost_equal(mdf.cov_re, rslt.cov_re_r, decimal=4)
assert_almost_equal(mdf.sig2, rslt.sig2_r, decimal=4)
pf = rslt.exog_fe.shape[1]
assert_almost_equal(rslt.vcov_r,
mdf.cov_params()[0:pf, 0:pf],
decimal=3)
assert_almost_equal(mdf.likeval, rslt.loglike[0], decimal=2)
# Not supported in R
if not irf:
assert_almost_equal(mdf.ranef()[0], rslt.ranef_postmean, decimal=3)
assert_almost_equal(mdf.ranef_cov()[0],
rslt.ranef_condvar,
decimal=3)
def test_EM(self):
np.random.seed(323590805)
exog = np.random.normal(size=(300, 4))
groups = np.kron(np.arange(100), [1, 1, 1])
g_errors = np.kron(np.random.normal(size=100), [1, 1, 1])
endog = exog.sum(1) + g_errors + np.random.normal(size=300)
mdf1 = MixedLM(endog, exog, groups).fit()
def do1(self, reml, irf, ds_ix):
# No need to check independent random effects when there is
# only one of them.
if irf and ds_ix < 6:
return
irfs = "irf" if irf else "drf"
meth = "reml" if reml else "ml"
rslt = R_Results(meth, irfs, ds_ix)
# Variance component MLE ~ 0 may require manual tweaking of
# algorithm parameters, so exclude from tests for now.
if np.min(np.diag(rslt.cov_re_r)) < 0.01:
print("Skipping %d since solution is on boundary." % ds_ix)
return
# Fit the model
md = MixedLM(rslt.endog, rslt.exog_fe, rslt.groups,
rslt.exog_re)
if not irf: # Free random effects covariance
mdf = md.fit(gtol=1e-7, reml=reml)
else: # Independent random effects
k_fe = rslt.exog_fe.shape[1]
k_re = rslt.exog_re.shape[1]
mdf = md.fit(reml=reml, gtol=1e-7,
free=(np.ones(k_fe), np.eye(k_re)))
assert_almost_equal(mdf.fe_params, rslt.coef, decimal=4)
assert_almost_equal(mdf.cov_re, rslt.cov_re_r, decimal=4)
assert_almost_equal(mdf.sig2, rslt.sig2_r, decimal=4)
pf = rslt.exog_fe.shape[1]
assert_almost_equal(rslt.vcov_r, mdf.cov_params()[0:pf,0:pf],
decimal=3)
assert_almost_equal(mdf.likeval, rslt.loglike[0], decimal=2)
# Not supported in R
if not irf:
assert_almost_equal(mdf.ranef()[0], rslt.ranef_postmean,
decimal=3)
assert_almost_equal(mdf.ranef_cov()[0],
rslt.ranef_condvar,
decimal=3)
def test_regularized(self):
np.random.seed(3453908)
exog = np.random.normal(size=(400,5))
groups = np.kron(np.arange(100), np.ones(4))
expected_endog = exog[:,0] - exog[:,2]
endog = expected_endog +\
np.kron(np.random.normal(size=100), np.ones(4)) +\
np.random.normal(size=400)
# L1 regularization
md = MixedLM(endog, exog, groups)
mdf1 = md.fit_regularized(alpha=1.)
mdf1.summary()
# L1 regularization
md = MixedLM(endog, exog, groups)
mdf2 = md.fit_regularized(alpha=10*np.ones(5))
mdf2.summary()
# L2 regularization
pen = penalties.L2()
mdf3 = md.fit_regularized(method=pen, alpha=0.)
mdf3.summary()
# L2 regularization
pen = penalties.L2()
mdf4 = md.fit_regularized(method=pen, alpha=100.)
mdf4.summary()
# Pseudo-Huber regularization
pen = penalties.PseudoHuber(0.3)
mdf4 = md.fit_regularized(method=pen, alpha=1.)
mdf4.summary()
def test_score(self):
n = 200
m = 5
p = 3
pr = 2
for jl in 0, 1:
for reml in False, True:
for cov_pen_wt in 0, 10:
cov_pen = penalties.PSD(cov_pen_wt)
np.random.seed(355890504)
exog_fe = np.random.normal(size=(n * m, p))
exog_re = np.random.normal(size=(n * m, pr))
endog = exog_fe.sum(1) + np.random.normal(size=n * m)
groups = np.kron(range(n), np.ones(m))
md = MixedLM(endog, exog_fe, groups, exog_re)
md.reml = reml
md.cov_pen = cov_pen
if jl == 0:
like = lambda x: -md.loglike_sqrt(x)
score = lambda x: -md.score_sqrt(x)
else:
like = lambda x: -md.loglike(x)
score = lambda x: -md.score(x)
for kr in range(5):
fe_params = np.random.normal(size=p)
cov_re = np.random.normal(size=(pr, pr))
cov_re = np.dot(cov_re.T, cov_re)
params_prof = md._pack(fe_params, cov_re)
gr = score(params_prof)
ngr = np.zeros_like(gr)
for k in range(len(ngr)):
def f(x):
pp = params_prof.copy()
pp[k] = x
return like(pp)
ngr[k] = derivative(f, params_prof[k], dx=1e-6)
assert_almost_equal(gr / ngr,
np.ones(len(gr)),
decimal=3)
def test_score(self):
n = 200
m = 5
p = 3
pr = 2
for jl in 0,1:
for reml in False,True:
for cov_pen_wt in 0,10:
cov_pen = penalties.PSD(cov_pen_wt)
np.random.seed(355890504)
exog_fe = np.random.normal(size=(n*m, p))
exog_re = np.random.normal(size=(n*m, pr))
endog = exog_fe.sum(1) + np.random.normal(size=n*m)
groups = np.kron(range(n), np.ones(m))
md = MixedLM(endog, exog_fe, groups, exog_re)
md.reml = reml
md.cov_pen = cov_pen
if jl == 0:
like = lambda x: -md.loglike_sqrt(x)
score = lambda x: -md.score_sqrt(x)
else:
like = lambda x: -md.loglike(x)
score = lambda x: -md.score(x)
for kr in range(5):
fe_params = np.random.normal(size=p)
cov_re = np.random.normal(size=(pr,pr))
cov_re = np.dot(cov_re.T, cov_re)
params_prof = md._pack(fe_params, cov_re)
gr = score(params_prof)
ngr = np.zeros_like(gr)
for k in range(len(ngr)):
def f(x):
pp = params_prof.copy()
pp[k] = x
return like(pp)
ngr[k] = derivative(f, params_prof[k],
dx=1e-6)
assert_almost_equal(gr / ngr, np.ones(len(gr)),
decimal=3)