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GenLogitclass.py
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GenLogitclass.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun Nov 4 22:17:43 2018
These classes are added to statsmodels package
@author: sedna
"""
import numpy as np
from statsmodels import base
from statsmodels.discrete.discrete_model import BinaryModel
class GenLogit(BinaryModel):
__doc__ = """
Binary choice genlogit model
%(params)s
%(extra_params)s
Attributes
-----------
endog : array
A reference to the endogenous response variable
exog : array
A reference to the exogenous design.
""" % {'params' : base._model_params_doc,
'extra_params' : base._missing_param_doc}
def get_c_value(self):
#self.c= float(input("Shape genlogistic: "))
#self.c=0.35
self.c=0.2
return self.c
def cdf(self, X):
"""
The genlogistic cumulative distribution function
Parameters
----------
X : array-like
`X` is the linear predictor of the logit model. See notes.
c : 'c' is as a shape parameter c>0 [c=1 becomes to logistic case]
Returns
-------
1/(1 + exp(-x))^c
Notes
------
In the genlogit model,
.. math:: \\Lambda\\left(x^{\\prime}\\beta,c\\right)=\\text{Prob}\\left(Y=1|x\\right)=\\frac{1}{\\left(1+e^{-x^{\\prime}\\beta\\right)^{c}}
"""
c = self.get_c_value()
X = np.asarray(X)
return 1/(1+np.exp(-X))**c
def pdf(self, X):
"""
The logistic probability density function
Parameters
-----------
X : array-like
`X` is the linear predictor of the logit model. See notes.
c : 'c' as a shape parameter
Returns
-------
pdf : ndarray
The value of the Logit probability mass function, PMF, for each
point of X. ``np.exp(-x)/(1+np.exp(-X))**2``
Notes
-----
In the genlogit model,
.. math:: \\lambda\\left(x^{\\prime}\\beta,c\\right)=\\frac{c e^{-x^{\\prime}\\beta}}{\\left(1+e^{-x^{\\prime}\\beta}\\right)^{c+1}}
"""
c = self.get_c_value()
X = np.asarray(X)
return c*np.exp(-X)/(1+np.exp(-X))**(c+1)
def loglike(self, params):
"""
Log-likelihood of genlogit model.
Parameters
-----------
params : array-like
The parameters of the logit model.
c : 'c' as a shape parameter
Returns
-------
loglike : float
The log-likelihood function of the model evaluated at `params`.
See notes.
Notes
------
.. math:: \\ln L=\\sum_{i}\\ln\\Lambda\\left({\\prime}\\beta,c\\right)
Where :math:`q=2y-1`. This simplification comes from the fact that the
logistic distribution is symmetric.
"""
X = self.exog
y = self.endog
Lcdf=self.cdf(np.dot(X,params))
Lpdf=self.pdf(np.dot(X,params))
return np.sum( (2*y-1)*np.log(Lcdf) +(1-y)*np.log(Lpdf))
def loglikeobs(self, params):
"""
Log-likelihood of logit model for each observation.
c : 'c' as a shape parameter
Parameters
-----------
params : array-like
The parameters of the logit model.
Returns
-------
loglike : ndarray (nobs,)
The log likelihood for each observation of the model evaluated
at `params`. See Notes
Notes
------
.. math:: \\ln L=\\sum_{i}\\ln\\Lambda\\left(q_{i}x_{i}^{\\prime}\\beta,c\\right)
for observations :math:`i=1,...,n`
where :math:`q=2y-1`. This simplification comes from the fact that the
logistic distribution is symmetric.
"""
X = self.exog
y = self.endog
Lcdf=self.cdf(np.dot(X,params))
Lpdf=self.pdf(np.dot(X,params))
return (2*y-1)*np.log(Lcdf) +(1-y)*np.log(Lpdf)
def score(self, params):
"""
Logit model score (gradient) vector of the log-likelihood
Parameters
----------
params: array-like
The parameters of the model
c : 'c' as a shape parameter
Returns
-------
score : ndarray, 1-D
The score vector of the model, i.e. the first derivative of the
loglikelihood function, evaluated at `params`
Notes
-----
.. math:: \\frac{\\partial\\ln L}{\\partial\\beta}=\\sum_{i=1}^{n}\\left(y_{i}-\\Lambda_{i}\\right)x_{i}
"""
X = self.exog
y = self.endog
Lcdf=self.cdf(np.dot(X,params))
Lpdf=self.pdf(np.dot(X,params))
Lgrad= (1-y)*(1-2.0*Lcdf) + (2.0*y-1.0)*(Lpdf/Lcdf)
return np.dot(Lgrad,X)
def jac(self, params):
"""
Logit model Jacobian of the log-likelihood for each observation
Parameters
----------
params: array-like
The parameters of the model
Returns
-------
jac : ndarray, (nobs, k_vars)
The derivative of the loglikelihood for each observation evaluated
at `params`.
Notes
-----
.. math:: \\frac{\\partial\\ln L_{i}}{\\partial\\beta}=\\left(y_{i}-\\Lambda_{i}\\right)x_{i}
for observations :math:`i=1,...,n`
"""
X = self.exog
y = self.endog
Lcdf=self.cdf(np.dot(X,params))
Lpdf=self.pdf(np.dot(X,params))
Lgrad= (1-y)*(1-2.0*Lcdf) + (2.0*y-1.0)*(Lpdf/Lcdf)
return Lgrad[:,None] * X
def hessian(self, params):
"""
Logit model Hessian matrix of the log-likelihood
Parameters
----------
params : array-like
The parameters of the model
c: 'c' as shape parameter
Returns
-------
hess : ndarray, (k_vars, k_vars)
The Hessian, second derivative of loglikelihood function,
evaluated at `params`
Notes
-----
.. math:: \\frac{\\partial^{2}\\ln L}{\\partial\\beta\\partial\\beta^{\\prime}}=-\\sum_{i}\\Lambda_{i}\\left(1-\\Lambda_{i}\\right)x_{i}x_{i}^{\\prime}
"""
X = self.exog
y = self.endog
Lcdf=self.cdf(np.dot(X,params))
Lpdf=self.pdf(np.dot(X,params))
Lop=Lpdf/Lcdf
Lgrad_grad=2.0*(1-y)*Lpdf
Lgrad_grad+=(1-2.0*y)*(1-2.0*Lcdf)*Lop
Lgrad_grad+=(2.0*y-1.0)*(Lop**2)
return -np.dot(Lgrad_grad*X.T,X)
def fit(self, start_params=None, method='newton', maxiter=35,
full_output=1, disp=1, callback=None, **kwargs):
bnryfit = super(GenLogit, self).fit(start_params=start_params,
method=method, maxiter=maxiter, full_output=full_output,
disp=disp, callback=callback, **kwargs)
discretefit = GenLogitResults(self, bnryfit)
return BinaryResultsWrapper(discretefit)
fit.__doc__ = DiscreteModel.fit.__doc__
class GenLogitResults(BinaryResults):
__doc__ = _discrete_results_docs % {
"one_line_description" : "A results class for Logit Model",
"extra_attr" : ""}
@cache_readonly
def resid_generalized(self):
"""
Generalized residuals
Notes
-----
The generalized residuals for the Logit model are defined
.. math:: y - p
where :math:`p=cdf(X\\beta)`. This is the same as the `resid_response`
for the Logit model.
"""
# Generalized residuals
return self.model.endog - self.predict()