Source code for statsmodels.miscmodels.count

# -*- coding: utf-8 -*-
"""
Created on Mon Jul 26 08:34:59 2010

Author: josef-pktd

changes:
added offset and zero-inflated version of Poisson
 - kind of ok, need better test cases,
 - a nan in ZIP bse, need to check hessian calculations
 - found error in ZIP loglike
 - all tests pass with

Issues
------
* If true model is not zero-inflated then numerical Hessian for ZIP has zeros
  for the inflation probability and is not invertible.
  -> hessian inverts and bse look ok if row and column are dropped, pinv also works
* GenericMLE: still get somewhere (where?)
   "CacheWriteWarning: The attribute 'bse' cannot be overwritten"
* bfgs is too fragile, doesn't come back
* `nm` is slow but seems to work
* need good start_params and their use in genericmle needs to be checked for
  consistency, set as attribute or method (called as attribute)
* numerical hessian needs better scaling

* check taking parts out of the loop, e.g. factorial(endog) could be precalculated


"""
from __future__ import print_function
import numpy as np
from scipy import stats
from statsmodels.compat.scipy import factorial
import statsmodels.api as sm
from statsmodels.base.model import GenericLikelihoodModel

def maxabs(arr1, arr2):
    return np.max(np.abs(arr1 - arr2))

def maxabsrel(arr1, arr2):
    return np.max(np.abs(arr2 / arr1 - 1))

class NonlinearDeltaCov(object):
    '''Asymptotic covariance by Deltamethod

    the function is designed for 2d array, with rows equal to
    the number of equations and columns equal to the number
    of parameters. 1d params work by chance ?

    fun: R^{m*k) -> R^{m}  where m is number of equations and k is
    the number of parameters.

    equations follow Greene

    '''
    def __init__(self, fun, params, cov_params):
        self.fun = fun
        self.params = params
        self.cov_params = cov_params

    def grad(self, params=None, **kwds):
        if params is None:
            params = self.params
        kwds.setdefault('epsilon', 1e-4)
        from statsmodels.tools.numdiff import approx_fprime
        return approx_fprime(params, self.fun, **kwds)

    def cov(self):
        g = self.grad()
        covar = np.dot(np.dot(g, self.cov_params), g.T)
        return covar

    def expected(self):
        # rename: misnomer, this is the MLE of the fun
        return self.fun(self.params)

    def wald(self, value):
        m = self.expected()
        v = self.cov()
        df = np.size(m)
        diff = m - value
        lmstat = np.dot(np.dot(diff.T, np.linalg.inv(v)), diff)
        return lmstat, stats.chi2.sf(lmstat, df)




[docs]class PoissonGMLE(GenericLikelihoodModel): '''Maximum Likelihood Estimation of Poisson Model This is an example for generic MLE which has the same statistical model as discretemod.Poisson. Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. ''' # copied from discretemod.Poisson
[docs] def nloglikeobs(self, params): """ Loglikelihood of Poisson model Parameters ---------- params : array-like The parameters of the model. Returns ------- The log likelihood of the model evaluated at `params` Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] """ XB = np.dot(self.exog, params) endog = self.endog return np.exp(XB) - endog*XB + np.log(factorial(endog))
[docs] def predict_distribution(self, exog): '''return frozen scipy.stats distribution with mu at estimated prediction ''' if not hasattr(self, result): raise ValueError else: mu = np.exp(np.dot(exog, params)) return stats.poisson(mu, loc=0)
[docs]class PoissonOffsetGMLE(GenericLikelihoodModel): '''Maximum Likelihood Estimation of Poisson Model This is an example for generic MLE which has the same statistical model as discretemod.Poisson but adds offset Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. ''' def __init__(self, endog, exog=None, offset=None, missing='none', **kwds): # let them be none in case user wants to use inheritance if not offset is None: if offset.ndim == 1: offset = offset[:,None] #need column self.offset = offset.ravel() else: self.offset = 0. super(PoissonOffsetGMLE, self).__init__(endog, exog, missing=missing, **kwds) #this was added temporarily for bug-hunting, but shouldn't be needed # def loglike(self, params): # return -self.nloglikeobs(params).sum(0) # original copied from discretemod.Poisson
[docs] def nloglikeobs(self, params): """ Loglikelihood of Poisson model Parameters ---------- params : array-like The parameters of the model. Returns ------- The log likelihood of the model evaluated at `params` Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] """ XB = self.offset + np.dot(self.exog, params) endog = self.endog nloglik = np.exp(XB) - endog*XB + np.log(factorial(endog)) return nloglik
[docs]class PoissonZiGMLE(GenericLikelihoodModel): '''Maximum Likelihood Estimation of Poisson Model This is an example for generic MLE which has the same statistical model as discretemod.Poisson but adds offset and zero-inflation. Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. There are numerical problems if there is no zero-inflation. ''' def __init__(self, endog, exog=None, offset=None, missing='none', **kwds): # let them be none in case user wants to use inheritance super(PoissonZiGMLE, self).__init__(endog, exog, missing=missing, **kwds) if not offset is None: if offset.ndim == 1: offset = offset[:,None] #need column self.offset = offset.ravel() #which way? else: self.offset = 0. #TODO: it's not standard pattern to use default exog if exog is None: self.exog = np.ones((self.nobs,1)) self.nparams = self.exog.shape[1] #what's the shape in regression for exog if only constant self.start_params = np.hstack((np.ones(self.nparams), 0)) self.cloneattr = ['start_params'] #needed for t_test and summary self.exog_names.append('zi') # original copied from discretemod.Poisson
[docs] def nloglikeobs(self, params): """ Loglikelihood of Poisson model Parameters ---------- params : array-like The parameters of the model. Returns ------- The log likelihood of the model evaluated at `params` Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] """ beta = params[:-1] gamm = 1 / (1 + np.exp(params[-1])) #check this # replace with np.dot(self.exogZ, gamma) #print(np.shape(self.offset), self.exog.shape, beta.shape XB = self.offset + np.dot(self.exog, beta) endog = self.endog nloglik = -np.log(1-gamm) + np.exp(XB) - endog*XB + np.log(factorial(endog)) nloglik[endog==0] = - np.log(gamm + np.exp(-nloglik[endog==0])) return nloglik