def p(x_new, reg=reg_choice):
y = ohie_0m.ohp_all_ever_admin
x = ohie_0m.hhinc_pctfpl_0m.values.reshape((-1, 1))
if reg == 'linear':
model = LinearRegression().fit(x, y)
return model.predict(x_new)
elif reg == 'probit':
probit_model = Probit(y, x).fit()
return probit_model.predict(x_new)
def eta0(x_new, reg=reg_choice):
y = ohie_0m_d0.health_gen_bin_0m
x = ohie_0m_d0.hhinc_pctfpl_0m.values.reshape((-1, 1))
if reg == 'linear':
model = LinearRegression().fit(x, y)
return model.predict(x_new)
elif reg == 'probit':
probit_model = Probit(y, x).fit()
return probit_model.predict(x_new)
class GenericZeroInflated(CountModel):
__doc__ = """
Generiz Zero Inflated model for count data
%(params)s
%(extra_params)s
Attributes
-----------
endog : array
A reference to the endogenous response variable
exog : array
A reference to the exogenous design.
exog_infl: array
A reference to the zero-inflated exogenous design.
""" % {'params' : base._model_params_doc,
'extra_params' : _doc_zi_params + base._missing_param_doc}
def __init__(self, endog, exog, exog_infl=None, offset=None,
inflation='logit', exposure=None, missing='none', **kwargs):
super(GenericZeroInflated, self).__init__(endog, exog, offset=offset,
exposure=exposure,
missing=missing, **kwargs)
if exog_infl is None:
self.k_inflate = 1
self.exog_infl = np.ones((endog.size, self.k_inflate),
dtype=np.float64)
else:
self.exog_infl = exog_infl
self.k_inflate = exog_infl.shape[1]
if len(exog.shape) == 1:
self.k_exog = 1
else:
self.k_exog = exog.shape[1]
self.infl = inflation
if inflation == 'logit':
self.model_infl = Logit(np.zeros(self.exog_infl.shape[0]),
self.exog_infl)
self._hessian_inflate = self._hessian_logit
elif inflation == 'probit':
self.model_infl = Probit(np.zeros(self.exog_infl.shape[0]),
self.exog_infl)
self._hessian_inflate = self._hessian_probit
else:
raise TypeError("inflation == %s, which is not handled"
% inflation)
self.inflation = inflation
self.k_extra = self.k_inflate
if len(self.exog) != len(self.exog_infl):
raise ValueError('exog and exog_infl have different number of'
'observation. `missing` handling is not supported')
infl_names = ['inflate_%s' % i for i in self.model_infl.data.param_names]
self.exog_names[:] = infl_names + list(self.exog_names)
self.exog_infl = np.asarray(self.exog_infl, dtype=np.float64)
self._init_keys.extend(['exog_infl', 'inflation'])
self._null_drop_keys = ['exog_infl']
def loglike(self, params):
"""
Loglikelihood of Generic Zero Inflated model
Parameters
----------
params : array-like
The parameters of the model.
Returns
-------
loglike : float
The log-likelihood function of the model evaluated at `params`.
See notes.
Notes
--------
.. math:: \\ln L=\\sum_{y_{i}=0}\\ln(w_{i}+(1-w_{i})*P_{main\\_model})+
\\sum_{y_{i}>0}(\\ln(1-w_{i})+L_{main\\_model})
where P - pdf of main model, L - loglike function of main model.
"""
return np.sum(self.loglikeobs(params))
def loglikeobs(self, params):
"""
Loglikelihood for observations of Generic Zero Inflated model
Parameters
----------
params : array-like
The parameters of the model.
Returns
-------
loglike : ndarray
The log likelihood for each observation of the model evaluated
at `params`. See Notes
Notes
--------
.. math:: \\ln L=\\ln(w_{i}+(1-w_{i})*P_{main\\_model})+
\\ln(1-w_{i})+L_{main\\_model}
where P - pdf of main model, L - loglike function of main model.
for observations :math:`i=1,...,n`
"""
params_infl = params[:self.k_inflate]
params_main = params[self.k_inflate:]
y = self.endog
w = self.model_infl.predict(params_infl)
w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps)
llf_main = self.model_main.loglikeobs(params_main)
zero_idx = np.nonzero(y == 0)[0]
nonzero_idx = np.nonzero(y)[0]
llf = np.zeros_like(y, dtype=np.float64)
llf[zero_idx] = (np.log(w[zero_idx] +
(1 - w[zero_idx]) * np.exp(llf_main[zero_idx])))
llf[nonzero_idx] = np.log(1 - w[nonzero_idx]) + llf_main[nonzero_idx]
return llf
def fit(self, start_params=None, method='bfgs', maxiter=35,
full_output=1, disp=1, callback=None,
cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs):
if start_params is None:
offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0)
if np.size(offset) == 1 and offset == 0:
offset = None
start_params = self._get_start_params()
if callback is None:
# work around perfect separation callback #3895
callback = lambda *x: x
mlefit = super(GenericZeroInflated, self).fit(start_params=start_params,
maxiter=maxiter, disp=disp, method=method,
full_output=full_output, callback=callback,
**kwargs)
zipfit = self.result_class(self, mlefit._results)
result = self.result_class_wrapper(zipfit)
if cov_kwds is None:
cov_kwds = {}
result._get_robustcov_results(cov_type=cov_type,
use_self=True, use_t=use_t, **cov_kwds)
return result
fit.__doc__ = DiscreteModel.fit.__doc__
def fit_regularized(self, start_params=None, method='l1',
maxiter='defined_by_method', full_output=1, disp=1, callback=None,
alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4,
qc_tol=0.03, **kwargs):
if np.size(alpha) == 1 and alpha != 0:
k_params = self.k_exog + self.k_inflate
alpha = alpha * np.ones(k_params)
extra = self.k_extra - self.k_inflate
alpha_p = alpha[:-(self.k_extra - extra)] if (self.k_extra
and np.size(alpha) > 1) else alpha
if start_params is None:
offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0)
if np.size(offset) == 1 and offset == 0:
offset = None
start_params = self.model_main.fit_regularized(
start_params=start_params, method=method, maxiter=maxiter,
full_output=full_output, disp=0, callback=callback,
alpha=alpha_p, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol,
size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs).params
start_params = np.append(np.ones(self.k_inflate), start_params)
cntfit = super(CountModel, self).fit_regularized(
start_params=start_params, method=method, maxiter=maxiter,
full_output=full_output, disp=disp, callback=callback,
alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol,
size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs)
if method in ['l1', 'l1_cvxopt_cp']:
discretefit = self.result_class_reg(self, cntfit)
else:
raise TypeError(
"argument method == %s, which is not handled" % method)
return self.result_class_reg_wrapper(discretefit)
fit_regularized.__doc__ = DiscreteModel.fit_regularized.__doc__
def score_obs(self, params):
"""
Generic Zero Inflated model score (gradient) vector of the log-likelihood
Parameters
----------
params : array-like
The parameters of the model
Returns
-------
score : ndarray, 1-D
The score vector of the model, i.e. the first derivative of the
loglikelihood function, evaluated at `params`
"""
params_infl = params[:self.k_inflate]
params_main = params[self.k_inflate:]
y = self.endog
w = self.model_infl.predict(params_infl)
w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps)
score_main = self.model_main.score_obs(params_main)
llf_main = self.model_main.loglikeobs(params_main)
llf = self.loglikeobs(params)
zero_idx = np.nonzero(y == 0)[0]
nonzero_idx = np.nonzero(y)[0]
mu = self.model_main.predict(params_main)
dldp = np.zeros((self.exog.shape[0], self.k_exog), dtype=np.float64)
dldw = np.zeros_like(self.exog_infl, dtype=np.float64)
dldp[zero_idx,:] = (score_main[zero_idx].T *
(1 - (w[zero_idx]) / np.exp(llf[zero_idx]))).T
dldp[nonzero_idx,:] = score_main[nonzero_idx]
if self.inflation == 'logit':
dldw[zero_idx,:] = (self.exog_infl[zero_idx].T * w[zero_idx] *
(1 - w[zero_idx]) *
(1 - np.exp(llf_main[zero_idx])) /
np.exp(llf[zero_idx])).T
dldw[nonzero_idx,:] = -(self.exog_infl[nonzero_idx].T *
w[nonzero_idx]).T
elif self.inflation == 'probit':
return approx_fprime(params, self.loglikeobs)
return np.hstack((dldw, dldp))
def score(self, params):
return self.score_obs(params).sum(0)
def _hessian_main(self, params):
pass
def _hessian_logit(self, params):
params_infl = params[:self.k_inflate]
params_main = params[self.k_inflate:]
y = self.endog
w = self.model_infl.predict(params_infl)
w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps)
score_main = self.model_main.score_obs(params_main)
llf_main = self.model_main.loglikeobs(params_main)
llf = self.loglikeobs(params)
zero_idx = np.nonzero(y == 0)[0]
nonzero_idx = np.nonzero(y)[0]
hess_arr = np.zeros((self.k_inflate, self.k_exog + self.k_inflate))
pmf = np.exp(llf)
#d2l/dw2
for i in range(self.k_inflate):
for j in range(i, -1, -1):
hess_arr[i, j] = ((
self.exog_infl[zero_idx, i] * self.exog_infl[zero_idx, j] *
(w[zero_idx] * (1 - w[zero_idx]) * ((1 -
np.exp(llf_main[zero_idx])) * (1 - 2 * w[zero_idx]) *
np.exp(llf[zero_idx]) - (w[zero_idx] - w[zero_idx]**2) *
(1 - np.exp(llf_main[zero_idx]))**2) /
pmf[zero_idx]**2)).sum() -
(self.exog_infl[nonzero_idx, i] * self.exog_infl[nonzero_idx, j] *
w[nonzero_idx] * (1 - w[nonzero_idx])).sum())
#d2l/dpdw
for i in range(self.k_inflate):
for j in range(self.k_exog):
hess_arr[i, j + self.k_inflate] = -(score_main[zero_idx, j] *
w[zero_idx] * (1 - w[zero_idx]) *
self.exog_infl[zero_idx, i] / pmf[zero_idx]).sum()
return hess_arr
def _hessian_probit(self, params):
pass
def hessian(self, params):
"""
Generic Zero Inflated model Hessian matrix of the loglikelihood
Parameters
----------
params : array-like
The parameters of the model
Returns
-------
hess : ndarray, (k_vars, k_vars)
The Hessian, second derivative of loglikelihood function,
evaluated at `params`
Notes
-----
"""
hess_arr_main = self._hessian_main(params)
hess_arr_infl = self._hessian_inflate(params)
if hess_arr_main is None or hess_arr_infl is None:
return approx_hess(params, self.loglike)
dim = self.k_exog + self.k_inflate
hess_arr = np.zeros((dim, dim))
hess_arr[:self.k_inflate,:] = hess_arr_infl
hess_arr[self.k_inflate:,self.k_inflate:] = hess_arr_main
tri_idx = np.triu_indices(self.k_exog + self.k_inflate, k=1)
hess_arr[tri_idx] = hess_arr.T[tri_idx]
return hess_arr
def predict(self, params, exog=None, exog_infl=None, exposure=None,
offset=None, which='mean'):
"""
Predict response variable of a count model given exogenous variables.
Parameters
----------
params : array-like
The parameters of the model
exog : array, optional
A reference to the exogenous design.
If not assigned, will be used exog from fitting.
exog_infl : array, optional
A reference to the zero-inflated exogenous design.
If not assigned, will be used exog from fitting.
offset : array, optional
Offset is added to the linear prediction with coefficient equal to 1.
exposure : array, optional
Log(exposure) is added to the linear prediction with coefficient
equal to 1. If exposure is specified, then it will be logged by the method.
The user does not need to log it first.
which : string, optional
Define values that will be predicted.
'mean', 'mean-main', 'linear', 'mean-nonzero', 'prob-zero, 'prob', 'prob-main'
Default is 'mean'.
Notes
-----
"""
if exog is None:
exog = self.exog
if exog_infl is None:
exog_infl = self.exog_infl
if exposure is None:
exposure = getattr(self, 'exposure', 0)
else:
exposure = np.log(exposure)
if offset is None:
offset = 0
params_infl = params[:self.k_inflate]
params_main = params[self.k_inflate:]
prob_main = 1 - self.model_infl.predict(params_infl, exog_infl)
lin_pred = np.dot(exog, params_main[:self.exog.shape[1]]) + exposure + offset
# Refactor: This is pretty hacky,
# there should be an appropriate predict method in model_main
# this is just prob(y=0 | model_main)
tmp_exog = self.model_main.exog
tmp_endog = self.model_main.endog
tmp_offset = getattr(self.model_main, 'offset', ['no'])
tmp_exposure = getattr(self.model_main, 'exposure', ['no'])
self.model_main.exog = exog
self.model_main.endog = np.zeros((exog.shape[0]))
self.model_main.offset = offset
self.model_main.exposure = exposure
llf = self.model_main.loglikeobs(params_main)
self.model_main.exog = tmp_exog
self.model_main.endog = tmp_endog
# tmp_offset might be an array with elementwise equality testing
if len(tmp_offset) == 1 and tmp_offset[0] == 'no':
del self.model_main.offset
else:
self.model_main.offset = tmp_offset
if len(tmp_exposure) == 1 and tmp_exposure[0] == 'no':
del self.model_main.exposure
else:
self.model_main.exposure = tmp_exposure
# end hack
prob_zero = (1 - prob_main) + prob_main * np.exp(llf)
if which == 'mean':
return prob_main * np.exp(lin_pred)
elif which == 'mean-main':
return np.exp(lin_pred)
elif which == 'linear':
return lin_pred
elif which == 'mean-nonzero':
return prob_main * np.exp(lin_pred) / (1 - prob_zero)
elif which == 'prob-zero':
return prob_zero
elif which == 'prob-main':
return prob_main
elif which == 'prob':
return self._predict_prob(params, exog, exog_infl, exposure, offset)
else:
raise ValueError('which = %s is not available' % which)
class GenericZeroInflated(CountModel):
__doc__ = """
Generic Zero Inflated Model
%(params)s
%(extra_params)s
Attributes
----------
endog : ndarray
A reference to the endogenous response variable
exog : ndarray
A reference to the exogenous design.
exog_infl : ndarray
A reference to the zero-inflated exogenous design.
""" % {'params' : base._model_params_doc,
'extra_params' : _doc_zi_params + base._missing_param_doc}
def __init__(self, endog, exog, exog_infl=None, offset=None,
inflation='logit', exposure=None, missing='none', **kwargs):
super(GenericZeroInflated, self).__init__(endog, exog, offset=offset,
exposure=exposure,
missing=missing, **kwargs)
if exog_infl is None:
self.k_inflate = 1
self._no_exog_infl = True
self.exog_infl = np.ones((endog.size, self.k_inflate),
dtype=np.float64)
else:
self.exog_infl = exog_infl
self.k_inflate = exog_infl.shape[1]
self._no_exog_infl = False
if len(exog.shape) == 1:
self.k_exog = 1
else:
self.k_exog = exog.shape[1]
self.infl = inflation
if inflation == 'logit':
self.model_infl = Logit(np.zeros(self.exog_infl.shape[0]),
self.exog_infl)
self._hessian_inflate = self._hessian_logit
elif inflation == 'probit':
self.model_infl = Probit(np.zeros(self.exog_infl.shape[0]),
self.exog_infl)
self._hessian_inflate = self._hessian_probit
else:
raise ValueError("inflation == %s, which is not handled"
% inflation)
self.inflation = inflation
self.k_extra = self.k_inflate
if len(self.exog) != len(self.exog_infl):
raise ValueError('exog and exog_infl have different number of'
'observation. `missing` handling is not supported')
infl_names = ['inflate_%s' % i for i in self.model_infl.data.param_names]
self.exog_names[:] = infl_names + list(self.exog_names)
self.exog_infl = np.asarray(self.exog_infl, dtype=np.float64)
self._init_keys.extend(['exog_infl', 'inflation'])
self._null_drop_keys = ['exog_infl']
def _get_exogs(self):
"""list of exogs, for internal use in post-estimation
"""
return (self.exog, self.exog_infl)
def loglike(self, params):
"""
Loglikelihood of Generic Zero Inflated model.
Parameters
----------
params : array_like
The parameters of the model.
Returns
-------
loglike : float
The log-likelihood function of the model evaluated at `params`.
See notes.
Notes
--------
.. math:: \\ln L=\\sum_{y_{i}=0}\\ln(w_{i}+(1-w_{i})*P_{main\\_model})+
\\sum_{y_{i}>0}(\\ln(1-w_{i})+L_{main\\_model})
where P - pdf of main model, L - loglike function of main model.
"""
return np.sum(self.loglikeobs(params))
def loglikeobs(self, params):
"""
Loglikelihood for observations of Generic Zero Inflated model.
Parameters
----------
params : array_like
The parameters of the model.
Returns
-------
loglike : ndarray
The log likelihood for each observation of the model evaluated
at `params`. See Notes for definition.
Notes
--------
.. math:: \\ln L=\\ln(w_{i}+(1-w_{i})*P_{main\\_model})+
\\ln(1-w_{i})+L_{main\\_model}
where P - pdf of main model, L - loglike function of main model.
for observations :math:`i=1,...,n`
"""
params_infl = params[:self.k_inflate]
params_main = params[self.k_inflate:]
y = self.endog
w = self.model_infl.predict(params_infl)
w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps)
llf_main = self.model_main.loglikeobs(params_main)
zero_idx = np.nonzero(y == 0)[0]
nonzero_idx = np.nonzero(y)[0]
llf = np.zeros_like(y, dtype=np.float64)
llf[zero_idx] = (np.log(w[zero_idx] +
(1 - w[zero_idx]) * np.exp(llf_main[zero_idx])))
llf[nonzero_idx] = np.log(1 - w[nonzero_idx]) + llf_main[nonzero_idx]
return llf
@Appender(DiscreteModel.fit.__doc__)
def fit(self, start_params=None, method='bfgs', maxiter=35,
full_output=1, disp=1, callback=None,
cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs):
if start_params is None:
offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0)
if np.size(offset) == 1 and offset == 0:
offset = None
start_params = self._get_start_params()
if callback is None:
# work around perfect separation callback #3895
callback = lambda *x: x
mlefit = super(GenericZeroInflated, self).fit(start_params=start_params,
maxiter=maxiter, disp=disp, method=method,
full_output=full_output, callback=callback,
**kwargs)
zipfit = self.result_class(self, mlefit._results)
result = self.result_class_wrapper(zipfit)
if cov_kwds is None:
cov_kwds = {}
result._get_robustcov_results(cov_type=cov_type,
use_self=True, use_t=use_t, **cov_kwds)
return result
@Appender(DiscreteModel.fit_regularized.__doc__)
def fit_regularized(self, start_params=None, method='l1',
maxiter='defined_by_method', full_output=1, disp=1, callback=None,
alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4,
qc_tol=0.03, **kwargs):
_validate_l1_method(method)
if np.size(alpha) == 1 and alpha != 0:
k_params = self.k_exog + self.k_inflate
alpha = alpha * np.ones(k_params)
extra = self.k_extra - self.k_inflate
alpha_p = alpha[:-(self.k_extra - extra)] if (self.k_extra
and np.size(alpha) > 1) else alpha
if start_params is None:
offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0)
if np.size(offset) == 1 and offset == 0:
offset = None
start_params = self.model_main.fit_regularized(
start_params=start_params, method=method, maxiter=maxiter,
full_output=full_output, disp=0, callback=callback,
alpha=alpha_p, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol,
size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs).params
start_params = np.append(np.ones(self.k_inflate), start_params)
cntfit = super(CountModel, self).fit_regularized(
start_params=start_params, method=method, maxiter=maxiter,
full_output=full_output, disp=disp, callback=callback,
alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol,
size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs)
discretefit = self.result_class_reg(self, cntfit)
return self.result_class_reg_wrapper(discretefit)
def score_obs(self, params):
"""
Generic Zero Inflated model score (gradient) vector of the log-likelihood
Parameters
----------
params : array_like
The parameters of the model
Returns
-------
score : ndarray, 1-D
The score vector of the model, i.e. the first derivative of the
loglikelihood function, evaluated at `params`
"""
params_infl = params[:self.k_inflate]
params_main = params[self.k_inflate:]
y = self.endog
w = self.model_infl.predict(params_infl)
w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps)
score_main = self.model_main.score_obs(params_main)
llf_main = self.model_main.loglikeobs(params_main)
llf = self.loglikeobs(params)
zero_idx = np.nonzero(y == 0)[0]
nonzero_idx = np.nonzero(y)[0]
mu = self.model_main.predict(params_main)
# TODO: need to allow for complex to use CS numerical derivatives
dldp = np.zeros((self.exog.shape[0], self.k_exog), dtype=np.float64)
dldw = np.zeros_like(self.exog_infl, dtype=np.float64)
dldp[zero_idx,:] = (score_main[zero_idx].T *
(1 - (w[zero_idx]) / np.exp(llf[zero_idx]))).T
dldp[nonzero_idx,:] = score_main[nonzero_idx]
if self.inflation == 'logit':
dldw[zero_idx,:] = (self.exog_infl[zero_idx].T * w[zero_idx] *
(1 - w[zero_idx]) *
(1 - np.exp(llf_main[zero_idx])) /
np.exp(llf[zero_idx])).T
dldw[nonzero_idx,:] = -(self.exog_infl[nonzero_idx].T *
w[nonzero_idx]).T
elif self.inflation == 'probit':
return approx_fprime(params, self.loglikeobs)
return np.hstack((dldw, dldp))
def score(self, params):
return self.score_obs(params).sum(0)
def _hessian_main(self, params):
pass
def _hessian_logit(self, params):
params_infl = params[:self.k_inflate]
params_main = params[self.k_inflate:]
y = self.endog
w = self.model_infl.predict(params_infl)
w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps)
score_main = self.model_main.score_obs(params_main)
llf_main = self.model_main.loglikeobs(params_main)
llf = self.loglikeobs(params)
zero_idx = np.nonzero(y == 0)[0]
nonzero_idx = np.nonzero(y)[0]
hess_arr = np.zeros((self.k_inflate, self.k_exog + self.k_inflate))
pmf = np.exp(llf)
#d2l/dw2
for i in range(self.k_inflate):
for j in range(i, -1, -1):
hess_arr[i, j] = ((
self.exog_infl[zero_idx, i] * self.exog_infl[zero_idx, j] *
(w[zero_idx] * (1 - w[zero_idx]) * ((1 -
np.exp(llf_main[zero_idx])) * (1 - 2 * w[zero_idx]) *
np.exp(llf[zero_idx]) - (w[zero_idx] - w[zero_idx]**2) *
(1 - np.exp(llf_main[zero_idx]))**2) /
pmf[zero_idx]**2)).sum() -
(self.exog_infl[nonzero_idx, i] * self.exog_infl[nonzero_idx, j] *
w[nonzero_idx] * (1 - w[nonzero_idx])).sum())
#d2l/dpdw
for i in range(self.k_inflate):
for j in range(self.k_exog):
hess_arr[i, j + self.k_inflate] = -(score_main[zero_idx, j] *
w[zero_idx] * (1 - w[zero_idx]) *
self.exog_infl[zero_idx, i] / pmf[zero_idx]).sum()
return hess_arr
def _hessian_probit(self, params):
pass
def hessian(self, params):
"""
Generic Zero Inflated model Hessian matrix of the loglikelihood
Parameters
----------
params : array_like
The parameters of the model
Returns
-------
hess : ndarray, (k_vars, k_vars)
The Hessian, second derivative of loglikelihood function,
evaluated at `params`
Notes
-----
"""
hess_arr_main = self._hessian_main(params)
hess_arr_infl = self._hessian_inflate(params)
if hess_arr_main is None or hess_arr_infl is None:
return approx_hess(params, self.loglike)
dim = self.k_exog + self.k_inflate
hess_arr = np.zeros((dim, dim))
hess_arr[:self.k_inflate,:] = hess_arr_infl
hess_arr[self.k_inflate:,self.k_inflate:] = hess_arr_main
tri_idx = np.triu_indices(self.k_exog + self.k_inflate, k=1)
hess_arr[tri_idx] = hess_arr.T[tri_idx]
return hess_arr
def predict(self, params, exog=None, exog_infl=None, exposure=None,
offset=None, which='mean', y_values=None):
"""
Predict response variable or other statistic given exogenous variables.
Parameters
----------
params : array_like
The parameters of the model.
exog : ndarray, optional
Explanatory variables for the main count model.
If ``exog`` is None, then the data from the model will be used.
exog_infl : ndarray, optional
Explanatory variables for the zero-inflation model.
``exog_infl`` has to be provided if ``exog`` was provided unless
``exog_infl`` in the model is only a constant.
offset : ndarray, optional
Offset is added to the linear predictor of the mean function with
coefficient equal to 1.
Default is zero if exog is not None, and the model offset if exog
is None.
exposure : ndarray, optional
Log(exposure) is added to the linear predictor with coefficient
equal to 1. If exposure is specified, then it will be logged by
the method. The user does not need to log it first.
Default is one if exog is is not None, and it is the model exposure
if exog is None.
which : str (optional)
Statitistic to predict. Default is 'mean'.
- 'mean' : the conditional expectation of endog E(y | x),
i.e. exp of linear predictor.
- 'linear' : the linear predictor of the mean function.
- 'var' : returns the estimated variance of endog implied by the
model.
- 'mean-main' : mean of the main count model
- 'prob-main' : probability of selecting the main model.
The probability of zero inflation is ``1 - prob-main``.
- 'mean-nonzero' : expected value conditional on having observation
larger than zero, E(y | X, y>0)
- 'prob-zero' : probability of observing a zero count. P(y=0 | x)
- 'prob' : probabilities of each count from 0 to max(endog), or
for y_values if those are provided. This is a multivariate
return (2-dim when predicting for several observations).
y_values : array_like
Values of the random variable endog at which pmf is evaluated.
Only used if ``which="prob"``
"""
no_exog = False
if exog is None:
no_exog = True
exog = self.exog
if exog_infl is None:
if no_exog:
exog_infl = self.exog_infl
else:
if self._no_exog_infl:
exog_infl = np.ones((len(exog), 1))
else:
exog_infl = np.asarray(exog_infl)
if exog_infl.ndim == 1 and self.k_inflate == 1:
exog_infl = exog_infl[:, None]
if exposure is None:
if no_exog:
exposure = getattr(self, 'exposure', 0)
else:
exposure = 0
else:
exposure = np.log(exposure)
if offset is None:
if no_exog:
offset = getattr(self, 'offset', 0)
else:
offset = 0
params_infl = params[:self.k_inflate]
params_main = params[self.k_inflate:]
prob_main = 1 - self.model_infl.predict(params_infl, exog_infl)
lin_pred = np.dot(exog, params_main[:self.exog.shape[1]]) + exposure + offset
# Refactor: This is pretty hacky,
# there should be an appropriate predict method in model_main
# this is just prob(y=0 | model_main)
tmp_exog = self.model_main.exog
tmp_endog = self.model_main.endog
tmp_offset = getattr(self.model_main, 'offset', False)
tmp_exposure = getattr(self.model_main, 'exposure', False)
self.model_main.exog = exog
self.model_main.endog = np.zeros((exog.shape[0]))
self.model_main.offset = offset
self.model_main.exposure = exposure
llf = self.model_main.loglikeobs(params_main)
self.model_main.exog = tmp_exog
self.model_main.endog = tmp_endog
# tmp_offset might be an array with elementwise equality testing
#if np.size(tmp_offset) == 1 and tmp_offset[0] == 'no':
if tmp_offset is False:
del self.model_main.offset
else:
self.model_main.offset = tmp_offset
#if np.size(tmp_exposure) == 1 and tmp_exposure[0] == 'no':
if tmp_exposure is False:
del self.model_main.exposure
else:
self.model_main.exposure = tmp_exposure
# end hack
prob_zero = (1 - prob_main) + prob_main * np.exp(llf)
if which == 'mean':
return prob_main * np.exp(lin_pred)
elif which == 'mean-main':
return np.exp(lin_pred)
elif which == 'linear':
return lin_pred
elif which == 'mean-nonzero':
return prob_main * np.exp(lin_pred) / (1 - prob_zero)
elif which == 'prob-zero':
return prob_zero
elif which == 'prob-main':
return prob_main
elif which == 'var':
mu = np.exp(lin_pred)
return self._predict_var(params, mu, 1 - prob_main)
elif which == 'prob':
return self._predict_prob(params, exog, exog_infl, exposure,
offset, y_values=y_values)
else:
raise ValueError('which = %s is not available' % which)
def _derivative_predict(self, params, exog=None, transform='dydx'):
"""NotImplemented
"""
raise NotImplementedError
def _derivative_exog(self, params, exog=None, transform="dydx",
dummy_idx=None, count_idx=None):
"""NotImplemented
"""
raise NotImplementedError
def _deriv_mean_dparams(self, params):
"""
Derivative of the expected endog with respect to the parameters.
Parameters
----------
params : ndarray
parameter at which score is evaluated
Returns
-------
The value of the derivative of the expected endog with respect
to the parameter vector.
"""
params_infl = params[:self.k_inflate]
params_main = params[self.k_inflate:]
w = self.model_infl.predict(params_infl)
w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps)
mu = self.model_main.predict(params_main)
score_infl = self.model_infl._deriv_mean_dparams(params_infl)
score_main = self.model_main._deriv_mean_dparams(params_main)
dmat_infl = - mu[:, None] * score_infl
dmat_main = (1 - w[:, None]) * score_main
dmat = np.column_stack((dmat_infl, dmat_main))
return dmat
def _deriv_score_obs_dendog(self, params):
"""derivative of score_obs w.r.t. endog
Parameters
----------
params : ndarray
parameter at which score is evaluated
Returns
-------
derivative : ndarray_2d
The derivative of the score_obs with respect to endog.
"""
raise NotImplementedError
# The below currently does not work, discontinuity at zero
# see https://github.com/statsmodels/statsmodels/pull/7951#issuecomment-996355875 # noqa
from statsmodels.tools.numdiff import _approx_fprime_scalar
endog_original = self.endog
def f(y):
if y.ndim == 2 and y.shape[1] == 1:
y = y[:, 0]
self.endog = y
self.model_main.endog = y
sf = self.score_obs(params)
self.endog = endog_original
self.model_main.endog = endog_original
return sf
ds = _approx_fprime_scalar(self.endog[:, None], f, epsilon=1e-2)
return ds
def flip_bits(y, p):
x = np.random.rand(y.shape[0], 1) < p
y[x < p] = 1 - y[x < p]
return y
n, d = 100, 2
data_x = np.random.randn(n, d)
w = np.random.randn(d, 1)
data_y = flip_bits((data_x @ w > 0), 0)
lam = 1e-2
# statsmodel.Probit
sm_probit_reg = Probit(exog=data_x, endog=data_y).fit(disp=0, method='bfgs')
sm_probit_prob = sm_probit_reg.predict(exog=data_x)
# Our Implementation:
probit_reg = ProbitReg()
# EM:
em_w, obj_trace_em = probit_reg.probreg_fit_em(data_x, data_y, lam)
em_ypred, em_prob = probit_reg.predict(data_x, em_w)
# gradient:
gradient_w, obj_trace_gradient = probit_reg.probit_reg_fit_gradient(
data_x, data_y, lam)
gradient_ypred, gradient_prob = probit_reg.predict(data_x, gradient_w)
plt.figure()
plt.plot(sm_probit_prob, em_prob, 'o')
class ProbitRegression(Learner):
"""
The probit regression learning algorithm. Given data, this class
constructs and stores a probability unit regression mdl that can
be used to quantify the probability of testing data-points taking
on certain class values.
"""
def __init__(self, alpha: float, **params: any):
"""
Initialises the Probit regression algorithm.
:param alpha: regularization term alpha.
:param params: Ignored.
"""
super().__init__(**params)
self.name = 'Probit Regression'
self.alpha = alpha
self.gamma = 0.5
self.add_intercept = True
self.binary_points = True
self.beta = list()
self.data: Optional[RecordSet] = None
self.model: Optional[Probit] = None # will be set during fit
def fit(self, rs: RecordSet) -> None:
"""
fit a Probit regression mdl
:param rs: The record set to fit with.
"""
# set params
self.data = cp.deepcopy(rs)
patterns = self.data.entries[:, :-1]
out = self.data.entries[:, -1:]
if self.add_intercept:
intercept = np.ones((patterns.shape[0], 1))
patterns = np.hstack((intercept, patterns))
# avoid error
if self.alpha == 0:
raise Exception("Alpha Probit too low to obtain reliable results")
self.model = Probit(endog=out.ravel(), exog=patterns)
self.model = self.model.fit_regularized(alpha=self.alpha,
maxiter=10e5,
disp=False)
def predict(self, rs: RecordSet) -> np.ndarray:
"""
Assigns a predicted class label to the given record sets.
:param rs: The record set to assign predictions to.
:return: A column vector of predictions corresponding to the record set's rows.
"""
# set params
patterns = rs.entries[:, :-1]
if self.add_intercept:
intercept = np.ones((patterns.shape[0], 1))
patterns = np.hstack((intercept, patterns))
# predict
predictions = self.model.predict(exog=patterns)
if self.binary_points:
predictions = self.discrete_points(predictions=predictions)
# return 2d
predictions = np.reshape(predictions, (-1, 1))
return predictions
def discrete_points(self, predictions):
"""
Turns probabilities into discrete classes
:param predictions: The predicted class probabilities
:return: A vector with discrete classes
"""
n = predictions.shape[0]
for i in range(0, n):
if predictions[i] >= self.gamma:
predictions[i] = 1
else:
predictions[i] = 0
return predictions
