"""
Conditional logistic, Poisson, and multinomial logit regression
"""
import collections
import itertools
import warnings
import numpy as np
from scipy.special import logsumexp
import statsmodels.base.model as base
import statsmodels.base.wrapper as wrap
from statsmodels.discrete.discrete_model import (
MultinomialResults,
MultinomialResultsWrapper,
)
from statsmodels.formula.formulatools import advance_eval_env
import statsmodels.regression.linear_model as lm
from statsmodels.tools.sm_exceptions import ModelWarning
class _ConditionalModel(base.LikelihoodModel):
def __init__(self, endog, exog, missing="none", **kwargs):
if "groups" not in kwargs:
raise ValueError("'groups' is a required argument")
groups = kwargs["groups"]
if groups.size != endog.size:
msg = "'endog' and 'groups' should have the same dimensions"
raise ValueError(msg)
if exog.shape[0] != endog.size:
msg = "The leading dimension of 'exog' should equal the length of 'endog'"
raise ValueError(msg)
super().__init__(endog, exog, missing=missing, **kwargs)
if self.data.const_idx is not None:
msg = "Conditional models should not have an intercept in the design matrix"
raise ValueError(msg)
exog = self.exog
self.k_params = exog.shape[1]
# Get the row indices for each group
row_ix = {}
for i, g in enumerate(groups):
if g not in row_ix:
row_ix[g] = []
row_ix[g].append(i)
# Split the data into groups and remove groups with no variation
endog, exog = np.asarray(endog), np.asarray(exog)
offset = kwargs.get("offset")
self._endog_grp = []
self._exog_grp = []
self._groupsize = []
if offset is not None:
offset = np.asarray(offset)
self._offset_grp = []
self._offset = []
self._sumy = []
self.nobs = 0
drops = [0, 0]
for _, ix in row_ix.items():
y = endog[ix].flat
if np.std(y) == 0:
drops[0] += 1
drops[1] += len(y)
continue
self.nobs += len(y)
self._endog_grp.append(y)
if offset is not None:
self._offset_grp.append(offset[ix])
self._groupsize.append(len(y))
self._exog_grp.append(exog[ix, :])
self._sumy.append(np.sum(y))
if drops[0] > 0:
msg = (
f"Dropped {drops[0]} groups and {drops[1]} observations for "
f"having no within-group variance"
)
warnings.warn(msg, ModelWarning, stacklevel=2)
# This can be pre-computed
if offset is not None:
self._endofs = []
for k, ofs in enumerate(self._offset_grp):
self._endofs.append(np.dot(self._endog_grp[k], ofs))
# Number of groups
self._n_groups = len(self._endog_grp)
# These are the sufficient statistics
self._xy = []
self._n1 = []
for g in range(self._n_groups):
self._xy.append(np.dot(self._endog_grp[g], self._exog_grp[g]))
self._n1.append(np.sum(self._endog_grp[g]))
def hessian(self, params):
from statsmodels.tools.numdiff import approx_fprime
hess = approx_fprime(params, self.score)
hess = np.atleast_2d(hess)
return hess
def fit(
self,
start_params=None,
method="BFGS",
maxiter=100,
full_output=True,
disp=False,
fargs=(),
callback=None,
retall=False,
skip_hessian=False,
**kwargs,
):
rslt = super().fit(
start_params=start_params,
method=method,
maxiter=maxiter,
full_output=full_output,
disp=disp,
skip_hessian=skip_hessian,
)
if skip_hessian:
cov_params = None
else:
cov_params = rslt.cov_params()
crslt = ConditionalResults(self, rslt.params, cov_params, 1)
crslt.method = method
crslt.nobs = self.nobs
crslt.n_groups = self._n_groups
crslt._group_stats = [
f"{min(self._groupsize):d}",
f"{max(self._groupsize):d}",
f"{np.mean(self._groupsize):.1f}",
]
rslt = ConditionalResultsWrapper(crslt)
return rslt
def fit_regularized(
self, method="elastic_net", alpha=0.0, start_params=None, refit=False, **kwargs
):
"""
Return a regularized fit to a linear regression model.
Parameters
----------
method : {'elastic_net'}
Only the `elastic_net` approach is currently implemented.
alpha : scalar or array_like
The penalty weight. If a scalar, the same penalty weight
applies to all variables in the model. If a vector, it
must have the same length as `params`, and contains a
penalty weight for each coefficient.
start_params : array_like
Starting values for `params`.
refit : bool
If True, the model is refit using only the variables that
have non-zero coefficients in the regularized fit. The
refitted model is not regularized.
**kwargs
Additional keyword argument that are used when fitting the model.
Returns
-------
Results
A results instance.
"""
from statsmodels.base.elastic_net import fit_elasticnet
if method != "elastic_net":
raise ValueError("method for fit_regularized must be elastic_net")
defaults = {"maxiter": 50, "L1_wt": 1, "cnvrg_tol": 1e-10, "zero_tol": 1e-10}
defaults.update(kwargs)
return fit_elasticnet(
self,
method=method,
alpha=alpha,
start_params=start_params,
refit=refit,
**defaults,
)
# Override to allow groups to be passed as a variable name.
@classmethod
def from_formula(cls, formula, data, subset=None, drop_cols=None, *args, **kwargs):
try:
groups = kwargs["groups"]
del kwargs["groups"]
except KeyError as err:
raise ValueError("'groups' is a required argument") from err
if isinstance(groups, str):
groups = data[groups]
if "0+" not in formula.replace(" ", ""):
warnings.warn(
"Conditional models should not include an intercept",
ModelWarning,
stacklevel=2,
)
advance_eval_env(kwargs)
model = super().from_formula(formula, data, *args, groups=groups, **kwargs)
return model
[docs]
class ConditionalLogit(_ConditionalModel):
"""
Fit a conditional logistic regression model to grouped data.
Every group is implicitly given an intercept, but the model is fit using
a conditional likelihood in which the intercepts are not present. Thus,
intercept estimates are not given, but the other parameter estimates can
be interpreted as being adjusted for any group-level confounders.
Parameters
----------
endog : array_like
The response variable, must contain only 0 and 1.
exog : array_like
The array of covariates. Do not include an intercept
in this array.
groups : array_like
Codes defining the groups. This is a required keyword parameter.
missing : str
Available options are 'none', 'drop', and 'raise'. If 'none', no nan
checking is done. If 'drop', any observations with nans are dropped.
If 'raise', an error is raised.
"""
def __init__(self, endog, exog, missing="none", **kwargs):
super().__init__(endog, exog, missing=missing, **kwargs)
if np.any(np.unique(self.endog) != np.r_[0, 1]):
msg = "endog must be coded as 0, 1"
raise ValueError(msg)
self.K = self.exog.shape[1]
# i.e. self.k_params, for compatibility with MNLogit
[docs]
def loglike(self, params):
ll = 0
for g in range(len(self._endog_grp)):
ll += self.loglike_grp(g, params)
return ll
[docs]
def score(self, params):
score = 0
for g in range(self._n_groups):
score += self.score_grp(g, params)
return score
def _denom(self, grp, params, ofs=None):
if ofs is None:
ofs = 0
exb = np.exp(np.dot(self._exog_grp[grp], params) + ofs)
# In the recursions, f may be called multiple times with the
# same arguments, so we memoize the results.
memo = {}
def f(t, k):
if t < k:
return 0
if k == 0:
return 1
try:
return memo[(t, k)]
except KeyError:
pass
v = f(t - 1, k) + f(t - 1, k - 1) * exb[t - 1]
memo[(t, k)] = v
return v
return f(self._groupsize[grp], self._n1[grp])
def _denom_grad(self, grp, params, ofs=None):
if ofs is None:
ofs = 0
ex = self._exog_grp[grp]
exb = np.exp(np.dot(ex, params) + ofs)
# s may be called multiple times in the recursions with the
# same arguments, so memoize the results.
memo = {}
def s(t, k):
if t < k:
return 0, np.zeros(self.k_params)
if k == 0:
return 1, 0
try:
return memo[(t, k)]
except KeyError:
pass
h = exb[t - 1]
a, b = s(t - 1, k)
c, e = s(t - 1, k - 1)
d = c * h * ex[t - 1, :]
u, v = a + c * h, b + d + e * h
memo[(t, k)] = (u, v)
return u, v
return s(self._groupsize[grp], self._n1[grp])
[docs]
def loglike_grp(self, grp, params):
ofs = None
if hasattr(self, "offset"):
ofs = self._offset_grp[grp]
llg = np.dot(self._xy[grp], params)
if ofs is not None:
llg += self._endofs[grp]
llg -= np.log(self._denom(grp, params, ofs))
return llg
[docs]
def score_grp(self, grp, params):
ofs = 0
if hasattr(self, "offset"):
ofs = self._offset_grp[grp]
d, h = self._denom_grad(grp, params, ofs)
return self._xy[grp] - h / d
[docs]
class ConditionalPoisson(_ConditionalModel):
"""
Fit a conditional Poisson regression model to grouped data.
Every group is implicitly given an intercept, but the model is fit using
a conditional likelihood in which the intercepts are not present. Thus,
intercept estimates are not given, but the other parameter estimates can
be interpreted as being adjusted for any group-level confounders.
Parameters
----------
endog : array_like
The response variable
exog : array_like
The covariates
groups : array_like
Codes defining the groups. This is a required keyword parameter.
missing : str
Available options are 'none', 'drop', and 'raise'. If 'none', no nan
checking is done. If 'drop', any observations with nans are dropped.
If 'raise', an error is raised.
"""
[docs]
def loglike(self, params):
ofs = None
if hasattr(self, "offset"):
ofs = self._offset_grp
ll = 0.0
for i in range(len(self._endog_grp)):
xb = np.dot(self._exog_grp[i], params)
if ofs is not None:
xb += ofs[i]
exb = np.exp(xb)
y = self._endog_grp[i]
ll += np.dot(y, xb)
s = exb.sum()
ll -= self._sumy[i] * np.log(s)
return ll
[docs]
def score(self, params):
ofs = None
if hasattr(self, "offset"):
ofs = self._offset_grp
score = 0.0
for i in range(len(self._endog_grp)):
x = self._exog_grp[i]
xb = np.dot(x, params)
if ofs is not None:
xb += ofs[i]
exb = np.exp(xb)
s = exb.sum()
y = self._endog_grp[i]
score += np.dot(y, x)
score -= self._sumy[i] * np.dot(exb, x) / s
return score
[docs]
class ConditionalResults(base.LikelihoodModelResults):
def __init__(self, model, params, normalized_cov_params, scale):
super().__init__(
model, params, normalized_cov_params=normalized_cov_params, scale=scale
)
[docs]
def summary(self, yname=None, xname=None, title=None, alpha=0.05):
"""
Summarize the fitted model.
Parameters
----------
yname : str, optional
Default is `y`
xname : list[str], optional
Names for the exogenous variables, default is "var_xx".
Must match the number of parameters in the model
title : str, optional
Title for the top table. If not None, then this replaces the
default title
alpha : float
Significance level for the confidence intervals
Returns
-------
smry : Summary instance
This holds the summary tables and text, which can be printed or
converted to various output formats.
See Also
--------
statsmodels.iolib.summary.Summary : class to hold summary
results
"""
top_left = [
("Dep. Variable:", None),
("Model:", None),
("Log-Likelihood:", None),
("Method:", [self.method]),
("Date:", None),
("Time:", None),
]
top_right = [
("No. Observations:", None),
("No. groups:", [self.n_groups]),
("Min group size:", [self._group_stats[0]]),
("Max group size:", [self._group_stats[1]]),
("Mean group size:", [self._group_stats[2]]),
]
if title is None:
title = "Conditional Logit Model Regression Results"
# create summary tables
from statsmodels.iolib.summary import Summary
smry = Summary()
smry.add_table_2cols(
self,
gleft=top_left,
gright=top_right, # [],
yname=yname,
xname=xname,
title=title,
)
smry.add_table_params(
self, yname=yname, xname=xname, alpha=alpha, use_t=self.use_t
)
return smry
[docs]
class ConditionalMNLogit(_ConditionalModel):
"""
Fit a conditional multinomial logit model to grouped data.
Parameters
----------
endog : array_like
The dependent variable, must be integer-valued, coded
0, 1, ..., c-1, where c is the number of response
categories.
exog : array_like
The independent variables.
groups : array_like
Codes defining the groups. This is a required keyword parameter.
missing : str
Available options are 'none', 'drop', and 'raise'. If 'none', no nan
checking is done. If 'drop', any observations with nans are dropped.
If 'raise', an error is raised.
Notes
-----
Equivalent to femlogit in Stata.
References
----------
Gary Chamberlain (1980). Analysis of covariance with qualitative
data. The Review of Economic Studies. Vol. 47, No. 1, pp. 225-238.
"""
def __init__(self, endog, exog, missing="none", **kwargs):
super().__init__(endog, exog, missing=missing, **kwargs)
# endog must be integers
self.endog = self.endog.astype(int)
self.k_cat = self.endog.max() + 1
self.df_model = (self.k_cat - 1) * self.exog.shape[1]
self.df_resid = self.nobs - self.df_model
self._ynames_map = {j: str(j) for j in range(self.k_cat)}
self.J = self.k_cat # Unfortunate name, needed for results
self.K = self.exog.shape[1] # for compatibility with MNLogit
if self.endog.min() < 0:
msg = "endog may not contain negative values"
raise ValueError(msg)
grx = collections.defaultdict(list)
for k, v in enumerate(self.groups):
grx[v].append(k)
self._group_labels = list(grx.keys())
self._group_labels.sort()
self._grp_ix = [grx[k] for k in self._group_labels]
[docs]
def fit(
self,
start_params=None,
method="BFGS",
maxiter=100,
full_output=True,
disp=False,
fargs=(),
callback=None,
retall=False,
skip_hessian=False,
generator=None,
**kwargs,
):
if start_params is None:
q = self.exog.shape[1]
c = self.k_cat - 1
if isinstance(generator, (np.random.RandomState, np.random.Generator)):
start_params = generator.normal(size=q * c)
else:
start_params = np.random.normal(size=q * c)
# Do not call super(...).fit because it cannot handle the 2d-params.
rslt = base.LikelihoodModel.fit(
self,
start_params=start_params,
method=method,
maxiter=maxiter,
full_output=full_output,
disp=disp,
skip_hessian=skip_hessian,
)
rslt.params = rslt.params.reshape((self.exog.shape[1], -1))
rslt = MultinomialResults(self, rslt)
# Not clear what the null likelihood should be, there is no intercept
# so the null model is not clearly defined. This is needed for summary
# to work.
rslt.set_null_options(llnull=np.nan)
return MultinomialResultsWrapper(rslt)
[docs]
def loglike(self, params):
q = self.exog.shape[1]
c = self.k_cat - 1
pmat = params.reshape((q, c))
pmat = np.concatenate((np.zeros((q, 1)), pmat), axis=1)
lpr = np.dot(self.exog, pmat)
ll = 0.0
# denom - immediately calculate the sums for the selected elements
for ii in self._grp_ix:
x = lpr[ii, :]
jj = np.arange(x.shape[0], dtype=int)
y = self.endog[ii]
denom = np.sum(x[jj, list(itertools.permutations(y))], axis=1)
ll += x[(jj, y)].sum() - logsumexp(denom)
return ll
[docs]
def score(self, params):
q = self.exog.shape[1]
c = self.k_cat - 1
pmat = params.reshape((q, c))
pmat = np.concatenate((np.zeros((q, 1)), pmat), axis=1)
lpr = np.dot(self.exog, pmat)
grad = np.zeros((q, c))
for ii in self._grp_ix:
x = lpr[ii, :]
jj = np.arange(x.shape[0], dtype=int)
y = self.endog[ii]
denomg = np.zeros((q, c)).T
# Extract itertools.permutations(y) to the list
iter_ = np.array(list(itertools.permutations(y)))
# Instead of iterative exponential value of sums of
# selected elements and their product by selected
# elements from self.exog, we calculate them at
# once (exp_sum, exog_exp_multy).
exp_sum = np.exp(np.sum(x[jj, iter_], axis=1))
denom = np.sum(exp_sum)
ind_exog = np.arange(iter_.shape[1], dtype=np.int32)
hist = len(iter_)
mask = iter_ != 0
iexog = np.take(ind_exog, mask.nonzero()[1])
iexog = iexog.reshape((hist, int(len(iexog) / hist)))
ii_ = np.take(ii, iexog)
exog_exp_multy = self.exog[ii_, :] * exp_sum[:, np.newaxis, np.newaxis]
ind_iter = iter_[mask].reshape((hist, int(len(iter_[mask]) / hist))) - 1
np.add.at(denomg, ind_iter, exog_exp_multy)
denomg = denomg.T
for i, r in enumerate(y):
if r != 0:
grad[:, r - 1] += self.exog[ii[i], :]
grad -= denomg / denom
return grad.flatten()
class ConditionalResultsWrapper(lm.RegressionResultsWrapper):
pass
wrap.populate_wrapper(ConditionalResultsWrapper, ConditionalResults)
