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#
# File: 06unifMixtureIntegral.py
# Author: Michel Bierlaire, EPFL
# Date: Wed Dec 21 13:25:26 2011
#
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#
# The mixture logit model is not estimated with simulation. The
# integral is computed numerically using a Gauss-Hermite method. This
# is recommended when there is only one level of integration.
#
from biogeme import *
from headers import *
from loglikelihood import *
from statistics import *
#Parameters to be estimated
# Arguments:
# 1 Name for report. Typically, the same as the variable
# 2 Starting value
# 3 Lower bound
# 4 Upper bound
# 5 0: estimate the parameter, 1: keep it fixed
ASC_CAR = Beta('ASC_CAR',0,-10,10,0)
ASC_TRAIN = Beta('ASC_TRAIN',0,-10,10,0)
ASC_SM = Beta('ASC_SM',0,-10,10,1)
B_TIME = Beta('B_TIME',0,-10,10,0)
B_TIME_S = Beta('B_TIME_S',1,-10,10,0)
B_COST = Beta('B_COST',0,-10,10,0)
# The next statement identifies 'omega' as a random variable. No
# assumption is made about its distribution.
omega = RandomVariable('omega')
# The "Integrate" operator integrates over the whole range of real
# numbers. If an integral on finite bounds must be computed, the
# following change of variables must be performed.
# When omega goes to -infinity, x goes to a.
# When omega goes to +infinity, x goes to b.
a = -1
b = 1
x = a + (b-a) / ( 1 + exp(-omega))
dx = (b-a) * exp(-omega) * (1+exp(-omega))**(-2)
# Define a random parameter, normally distirbuted, designed to be used
# for Monte-Carlo simulation
B_TIME_RND = B_TIME + B_TIME_S * x
# Utility functions
#If the person has a GA (season ticket) her incremental cost is actually 0
#rather than the cost value gathered from the
# network data.
SM_COST = SM_CO * ( GA == 0 )
TRAIN_COST = TRAIN_CO * ( GA == 0 )
# For numerical reasons, it is good practice to scale the data to
# that the values of the parameters are around 1.0.
# A previous estimation with the unscaled data has generated
# parameters around -0.01 for both cost and time. Therefore, time and
# cost are multipled my 0.01.
TRAIN_TT_SCALED = DefineVariable('TRAIN_TT_SCALED', TRAIN_TT / 100.0)
TRAIN_COST_SCALED = DefineVariable('TRAIN_COST_SCALED', TRAIN_COST / 100)
SM_TT_SCALED = DefineVariable('SM_TT_SCALED', SM_TT / 100.0)
SM_COST_SCALED = DefineVariable('SM_COST_SCALED', SM_COST / 100)
CAR_TT_SCALED = DefineVariable('CAR_TT_SCALED', CAR_TT / 100)
CAR_CO_SCALED = DefineVariable('CAR_CO_SCALED', CAR_CO / 100)
V1 = ASC_TRAIN + B_TIME_RND * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
V2 = ASC_SM + B_TIME_RND * SM_TT_SCALED + B_COST * SM_COST_SCALED
V3 = ASC_CAR + B_TIME_RND * CAR_TT_SCALED + B_COST * CAR_CO_SCALED
# Associate utility functions with the numbering of alternatives
V = {1: V1,
2: V2,
3: V3}
# Associate the availability conditions with the alternatives
CAR_AV_SP = DefineVariable('CAR_AV_SP',CAR_AV * ( SP != 0 ))
TRAIN_AV_SP = DefineVariable('TRAIN_AV_SP',TRAIN_AV * ( SP != 0 ))
av = {1: TRAIN_AV_SP,
2: SM_AV,
3: CAR_AV_SP}
# The choice model is a logit, with availability conditions
condprob = bioLogit(V,av,CHOICE)
prob = Integrate(condprob * dx / (b-a),'omega')
# Defines an itertor on the data
rowIterator('obsIter')
# Define the likelihood function for the estimation
BIOGEME_OBJECT.ESTIMATE = Sum(log(prob),'obsIter')
# All observations verifying the following expression will not be
# considered for estimation
# The modeler here has developed the model only for work trips.
# Observations such that the dependent variable CHOICE is 0 are also removed.
exclude = (( PURPOSE != 1 ) * ( PURPOSE != 3 ) + ( CHOICE == 0 )) > 0
BIOGEME_OBJECT.EXCLUDE = exclude
# Statistics
nullLoglikelihood(av,'obsIter')
choiceSet = [1,2,3]
cteLoglikelihood(choiceSet,CHOICE,'obsIter')
availabilityStatistics(av,'obsIter')
BIOGEME_OBJECT.PARAMETERS['optimizationAlgorithm'] = "BIO"
BIOGEME_OBJECT.FORMULAS['Train utility'] = V1
BIOGEME_OBJECT.FORMULAS['Swissmetro utility'] = V2
BIOGEME_OBJECT.FORMULAS['Car utility'] = V3