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OP.py
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OP.py
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from __future__ import division
import statsmodels as st
import statsmodels.api as sm
from scipy import stats
import numpy as np
from statsmodels.sandbox.distributions.extras import mvstdnormcdf
from itertools import izip
from scipy.optimize import minimize, fmin_slsqp, approx_fprime
import math
FLOAT_EPS = np.finfo(float).eps
class OrderedProbit(st.discrete.discrete_model.OrderedModel):
"""Ordered Probit
Bla-Bla-Bla
"""
def _ordered_recode(self, endog):
# Recode data to [0,.....,N]
uniques = sorted(set(endog))
return [uniques.index(i) for i in endog]
def __init__(self, endog, exog, offset=None, exposure=None, missing='none',
**kwargs):
self.orig_endog = endog # save original data
endog = self._ordered_recode(endog)
super(OrderedProbit, self).__init__(endog, exog, missing=missing,
offset=offset,
exposure=exposure, **kwargs)
# exposure & offset Yet Not In Use!
if exposure is not None:
self.exposure = np.log(self.exposure)
if offset is None:
delattr(self, 'offset')
if exposure is None:
delattr(self, 'exposure')
def cdf(self, X):
"""
Probit (Normal) cumulative distribution function
Parameters
----------
X : array-like
The linear predictor of the model (XB).
Returns
--------
cdf : ndarray
The cdf evaluated at `X`.
Notes
-----
This function is just an alias for scipy.stats.norm.cdf
"""
return stats.norm._cdf(X)
@staticmethod
def pdf(x):
"""
Probit (Normal) probability density function
Parameters
----------
X : float
"""
pi = math.pi
denom = (2 * pi)**.5
num = math.exp(-(float(x))**2 / 2)
return num / denom
def cons_generator(self, slice, dict_out=True):
"""
Function generates a string of constrants,
required for optimization routine in scipy.optimize.
INPUT: list of slices, e.g. [(2,4),(7,12),(14,19)]
constrants are set in between slices
Great thanks to Ilya Shurov for improving this code
"""
constr = []
for st, fin in slice:
for i in range(st, fin - 1):
if dict_out:
constr.append({"type": "ineq",
"fun": lambda x,
i=i: np.array([float(x[i + 1] - x[i])])})
lambda x, i=i: np.zeros(len(x))
else:
constr.append(lambda x, i=i: np.array([x[i + 1] - x[i]]))
return constr
def cons_fprime(self, x, slice):
lenf = slice[0][1] - 1 - slice[0][0]
fprime = np.zeros(shape=(lenf, len(x)))
for i in range(lenf):
fprime[i, -i - 1], fprime[i, -i - 2] = 1, -1
return fprime[::-1]
def loglike(self, params):
"""
Log-likelihood of ordered probit model
params=(beta, cutoffs)
"""
#X = self.exog
# np.sum(np.log(np.clip(self.cdf(np.dot(X,params[0])),
# FLOAT_EPS, 1)))
#params = [params[:len(self.exog[0])], params[len(self.exog[0]):]]
beta, mu = params[:len(self.exog[0])], params[len(self.exog[0]):]
# print params
# print " ".join([str(len(params[0])),str(len(params[1]))])
# print params[0]
# print params[1]
s = 0
# BASED ON http://web.stanford.edu/class/polisci203/ordered.pdf
for X, Y in izip(self.exog, self.endog):
if Y == 0:
s += np.log(
np.clip(
self.cdf(
mu[Y] -
np.dot(
X,
beta)),
FLOAT_EPS,
1))
elif Y != 0 and Y != max(self.endog):
s += np.log(np.clip(self.cdf(mu[Y] - np.dot(X, beta))
- self.cdf(mu[Y - 1] - np.dot(X, beta)), FLOAT_EPS, 1))
elif Y == max(self.endog):
s += np.log(np.clip(1 -
self.cdf(mu[Y -
1] -
np.dot(X, beta)), FLOAT_EPS, 1))
return s
# return np.sum(np.log(np.clip(self.cdf(params[1][Y] - np.dot(X,params[0])),
# FLOAT_EPS, 1)) for X,Y in izip(self.exog, self.endog) if Y == 0) +\
# np.sum(np.log(np.clip(self.cdf(params[1][Y] - np.dot(X,params[0])) - self.cdf(params[1][Y-1] - np.dot(X,params[0])),
# FLOAT_EPS, 1)) for X,Y in izip(self.exog, self.endog) if Y != 0 and Y != max(self.endog)) +\
# np.sum(np.log(np.clip(1-self.cdf(params[1][Y-1] - np.dot(X,params[0])),
# FLOAT_EPS, 1)) for X,Y in izip(self.exog, self.endog) if Y ==
# max(self.endog))
def fit(self, start_params=None, method='COBYLA', maxiter=500,
full_output=1, disp=1, callback=None, iprint=None, **kwargs):
if start_params is None:
start_params = list(
self.get_start_params()) + range(max(self.endog))
constraints = self.cons_generator(
[(len(self.exog[0]), len(self.exog[0]) + max(self.endog))], dict_out=True)
# http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize
return minimize(fun=lambda x: -self.loglike(x), x0=start_params, method=method, constraints=constraints,
options={'maxiter': maxiter, 'disp': disp}, callback=callback, jac=lambda x: -self.score(x),
**kwargs)
def get_start_params(self):
from statsmodels.api import OLS
return OLS(self.endog, self.exog).fit().params
def score(self, params):
beta, mu = params[:len(self.exog[0])], params[len(self.exog[0]):]
s = np.zeros(len(params))
for X, Y in izip(self.exog, self.endog):
# print s
# print Y
if Y == 0:
# print "Enter zero"
mXb = mu[Y] - np.dot(X, beta)
dif = self.cdf(mXb)
if dif == 0:
dif = FLOAT_EPS
s1 = self.pdf(
mXb) / dif * np.append(np.append(-X, [1]), np.zeros(len(mu) - 1))
s += s1
#s+= np.log(np.clip(self.cdf(mu[Y] - np.dot(X,beta)), FLOAT_EPS, 1))
elif Y != 0 and Y != max(self.endog):
# print "Enter middle"
mXb0 = mu[Y] - np.dot(X, beta)
mXb1 = mu[Y - 1] - np.dot(X, beta)
if mXb1 >= mXb0:
# print "FUCK"
#mXb0 = mXb1 + 10
pass
s1 = (self.pdf(mXb0) - self.pdf(mXb1)) * (-X)
mus = np.zeros(len(mu))
mus[Y], mus[Y - 1] = self.pdf(mXb0), -self.pdf(mXb1)
s1 = np.append(s1, mus)
#print (self.cdf(mXb0) - self.cdf(mXb1))
dif = self.cdf(mXb0) - self.cdf(mXb1)
if dif == 0:
s1 = s1 / FLOAT_EPS
else:
s1 = s1 / dif
s += s1
# s+= np.log(np.clip(self.cdf(mu[Y] - np.dot(X,beta))
# - self.cdf(mu[Y-1] - np.dot(X,beta)), FLOAT_EPS, 1))
elif Y == max(self.endog):
# print "Enter max"
mXb = mu[Y - 1] - np.dot(X, beta)
#print -self.pdf(mXb), (1-self.cdf(mXb))
dif = 1 - self.cdf(mXb)
if dif == 0:
dif = FLOAT_EPS
s1 = - \
self.pdf(
mXb) / dif * np.append(np.append(-X, np.zeros(len(mu) - 1)), [1])
s += s1
#s+= np.log(np.clip(1-self.cdf(mu[Y-1] - np.dot(X,beta)), FLOAT_EPS, 1))
# print s
return s
def se(self, params):
"""
Return standard errors at optimum point
"""
hess = self.hessian(params)
return np.sqrt(np.linalg.inv(-hess).diagonal())
def hessian(self, x0, epsilon=1.e-5, linear_approx=False, *args):
"""
A numerical approximation to the Hessian matrix of loglike function f at
location x0 (hopefully, the minimum)
AUTHOR: jgomezdans , https://gist.github.com/jgomezdans
"""
# ``f`` is the cost function
f = self.loglike
# The next line calculates the first derivative
f1 = self.score(x0)
# This is a linear approximation. Obviously much more efficient
# if cost function is linear
if linear_approx:
f1 = np.matrix(f1)
return f1.transpose() * f1
# Allocate space for the hessian
n = x0.shape[0]
hessian = np.zeros((n, n))
# The next loop fill in the matrix
xx = x0
for j in xrange(n):
xx0 = xx[j] # Store old value
xx[j] = xx0 + epsilon # Perturb with finite difference
# Recalculate the partial derivatives for this new point
f2 = self.score(x0)
hessian[:, j] = (f2 - f1) / epsilon # scale...
xx[j] = xx0 # Restore initial value of x0
return hessian
if __name__ == "__main__":
import numpy as np
import pandas as pd
import matplotlib.pylab as plt
import warnings
from scipy.optimize import minimize, check_grad
from pandas.tools.plotting import scatter_matrix
np.set_printoptions(precision=3, suppress=True)
pd.set_option(
'display.mpl_style',
'default') # Make the graphs a bit prettier
df = pd.read_csv(u"simul_data_CNOP.csv", sep=';').dropna()
dat = df[:2000].copy()
del dat['MONTH'], dat['NO'], dat['Y']
exog = dat
endog = df[:2000].copy()["Y"]
# actuall params from EViews for this model
xstart = [0.014145, 0.058282, 0.327108, -0.257436, 0.025568, -0.056417, 0.339505, 0.027607, -0.108454, -0.009823] +\
[-1.096773, -0.923243, -0.738524, -0.522930, -0.356648, -0.168086, -0.013571, 0.131471, 0.236204, 0.371262,
1.852668, 1.904029, 1.975700, 2.078341, 2.162041, 2.266225, 2.390665, 2.544107, 2.787838, 3.026606]
# IF specify the exact parameters of xstart, then converges in ~37 steps
# NOT to the exact xstart, but close
OP = OrderedProbit(endog, exog)
# print OP.loglike(xstart)
x = OP.fit(
fun='fmin_slsqp',
maxiter=500,
iprint=2,
start_params=list(
np.zeros(10)) +
range(20))
print x
# print OP.score(xstart)