## File 05nestedElasticities.py
## Simple nested logit model for the Optima case study
## Calculation of direct arc elasticities
## Thu May 11 16:38:05 2017
from biogeme import *
from headers import *
from statistics import *
from nested import *
### Three alternatives:
# CAR: automobile
# PT: public transportation
# SM: slow mode (walking, biking)
### List of parameters and their estimated value.
ASC_CAR = Beta('ASC_CAR',0.261291,-10000,10000,0,'ASC_CAR' )
ASC_SM = Beta('ASC_SM',0.0590204,-10000,10000,0,'ASC_SM' )
BETA_TIME_FULLTIME = \
Beta('BETA_TIME_FULLTIME',-1.59709,-10000,10000,0,'BETA_TIME_FULLTIME' )
BETA_TIME_OTHER = \
Beta('BETA_TIME_OTHER',-0.577362,-10000,10000,0,'BETA_TIME_OTHER' )
BETA_DIST_MALE = \
Beta('BETA_DIST_MALE',-0.686327,-10000,10000,0,'BETA_DIST_MALE' )
BETA_DIST_FEMALE = \
Beta('BETA_DIST_FEMALE',-0.83121,-10000,10000,0,'BETA_DIST_FEMALE' )
BETA_DIST_UNREPORTED = \
Beta('BETA_DIST_UNREPORTED',-0.702974,-10000,10000,0,'BETA_DIST_UNREPORTED' )
BETA_COST = \
Beta('BETA_COST',-0.716192,-10000,10000,0,'BETA_COST' )
###Definition of variables:
# For numerical reasons, it is good practice to scale the data to
# that the values of the parameters are around 1.0.
### Warning: when calculation derivatives, the total formula must be
### known to Biogeme. In this case, the use of
### "DefineVariable" must be omitted, if the derivatives must be
### calculated with respect to the original variables (as is often the
### case)
delta_dist = 1
# TimePT_scaled = DefineVariable('TimePT_scaled', TimePT / 200 )
TimePT_scaled = TimePT / 200
#TimeCar_scaled = DefineVariable('TimeCar_scaled', TimeCar / 200 )
TimeCar_scaled = TimeCar / 200
#MarginalCostPT_scaled = DefineVariable('MarginalCostPT_scaled', MarginalCostPT / 10 )
MarginalCostPT_scaled = MarginalCostPT / 10
#CostCarCHF_scaled = DefineVariable('CostCarCHF_scaled', CostCarCHF / 10 )
CostCarCHF_scaled = CostCarCHF / 10
#distance_km_scaled = DefineVariable('distance_km_scaled', distance_km / 5 )
distance_km_scaled = distance_km / 5
distance_km_scaled_after = (distance_km + delta_dist) / 5
male = DefineVariable('male',Gender == 1)
female = DefineVariable('female',Gender == 2)
unreportedGender = DefineVariable('unreportedGender',Gender == -1)
fulltime = DefineVariable('fulltime',OccupStat == 1)
notfulltime = DefineVariable('notfulltime',OccupStat != 1)
### Definition of utility functions:
V_PT = BETA_TIME_FULLTIME * TimePT_scaled * fulltime + \
BETA_TIME_OTHER * TimePT_scaled * notfulltime + \
BETA_COST * MarginalCostPT_scaled
V_CAR = ASC_CAR + \
BETA_TIME_FULLTIME * TimeCar_scaled * fulltime + \
BETA_TIME_OTHER * TimeCar_scaled * notfulltime + \
BETA_COST * CostCarCHF_scaled
V_SM = ASC_SM + \
BETA_DIST_MALE * distance_km_scaled * male + \
BETA_DIST_FEMALE * distance_km_scaled * female + \
BETA_DIST_UNREPORTED * distance_km_scaled * unreportedGender
V_SM_after = ASC_SM + \
BETA_DIST_MALE * distance_km_scaled_after * male + \
BETA_DIST_FEMALE * distance_km_scaled_after * female + \
BETA_DIST_UNREPORTED * distance_km_scaled_after * unreportedGender
# Associate utility functions with the numbering of alternatives
V = {0: V_PT,
1: V_CAR,
2: V_SM}
V_after = {0: V_PT,
1: V_CAR,
2: V_SM_after}
# Associate the availability conditions with the alternatives.
# In this example all alternatives are available for each individual.
av = {0: one,
1: one,
2: one}
### DEFINITION OF THE NESTS:
# 1: nests parameter
# 2: list of alternatives
NEST_NOCAR = Beta('NEST_NOCAR',1.52853,1,10,0,'NEST_NOCAR' )
CAR = 1.0 , [ 1]
NO_CAR = NEST_NOCAR , [ 0, 2]
nests = CAR, NO_CAR
# All observations verifying the following expression will not be
# considered for estimation
exclude = (Choice == -1)
BIOGEME_OBJECT.EXCLUDE = exclude
##
## This has been copied-pasted from the file 01nestedEstimation_param.py
##
## Code for the sensitivity analysis generated after the estimation of the model
names = ['ASC_CAR','ASC_SM','BETA_COST','BETA_DIST_FEMALE','BETA_DIST_MALE','BETA_DIST_UNREPORTED','BETA_TIME_FULLTIME','BETA_TIME_OTHER','NEST_NOCAR']
values = [[0.0100225,-0.0023271,0.00151986,0.00285251,0.00621963,0.00247439,0.0235929,0.0224142,-0.00807837],[-0.0023271,0.0469143,0.00431142,-0.0204402,-0.0223745,-0.00774278,-0.00847539,-0.00394251,0.0389318],[0.00151986,0.00431142,0.0191465,0.00673909,0.00559057,0.00676991,-0.000434418,-0.00579638,0.0155749],[0.00285251,-0.0204402,0.00673909,0.0371974,0.0156282,0.0146385,0.010273,0.00438825,0.0106748],[0.00621963,-0.0223745,0.00559057,0.0156282,0.0258642,0.0112879,0.0218765,0.0109824,-0.0062276],[0.00247439,-0.00774278,0.00676991,0.0146385,0.0112879,0.0385363,0.00725802,0.00507749,0.0131128],[0.0235929,-0.00847539,-0.000434418,0.010273,0.0218765,0.00725802,0.110753,0.0555677,-0.0178209],[0.0224142,-0.00394251,-0.00579638,0.00438825,0.0109824,0.00507749,0.0555677,0.0878987,-0.0248326],[-0.00807837,0.0389318,0.0155749,0.0106748,-0.0062276,0.0131128,-0.0178209,-0.0248326,0.0934272]]
vc = bioMatrix(9,names,values)
BIOGEME_OBJECT.VARCOVAR = vc
# The choice model is a nested logit
prob_pt = nested(V,av,nests,0)
prob_car = nested(V,av,nests,1)
prob_sm = nested(V,av,nests,2)
prob_pt_after = nested(V_after,av,nests,0)
prob_car_after = nested(V_after,av,nests,1)
prob_sm_after = nested(V_after,av,nests,2)
elas_sm_dist = (prob_sm_after - prob_sm) * distance_km / (prob_sm * delta_dist)
# Defines an iterator on the data
rowIterator('obsIter')
#Statistics
nullLoglikelihood(av,'obsIter')
choiceSet = [0,1,2]
cteLoglikelihood(choiceSet,Choice,'obsIter')
availabilityStatistics(av,'obsIter')
theWeight = Weight * 1906 / 0.814484
normalization_pt = 535.086
normalization_car = 1244.77
normalization_sm = 126.147
BIOGEME_OBJECT.STATISTICS['Gender: males'] = \
Sum(male,'obsIter')
BIOGEME_OBJECT.STATISTICS['Gender: females'] = \
Sum(female,'obsIter')
BIOGEME_OBJECT.STATISTICS['Gender: unreported'] = \
Sum(unreportedGender,'obsIter')
BIOGEME_OBJECT.STATISTICS['Occupation: full time'] = \
Sum(fulltime,'obsIter')
BIOGEME_OBJECT.STATISTICS['Sum of weights'] = \
Sum(Weight,'obsIter')
BIOGEME_OBJECT.STATISTICS['Number of entries'] = \
Sum(1-exclude,'obsIter')
BIOGEME_OBJECT.STATISTICS['Normalization for elasticities PT'] = \
Sum(theWeight * prob_pt ,'obsIter')
BIOGEME_OBJECT.STATISTICS['Normalization for elasticities CAR'] = \
Sum(theWeight * prob_car ,'obsIter')
BIOGEME_OBJECT.STATISTICS['Normalization for elasticities SM'] = \
Sum(theWeight * prob_sm ,'obsIter')
BIOGEME_OBJECT.STATISTICS['Occupation: full time'] = Sum(fulltime,'obsIter')
# Define the dictionary for the simulation.
simulate = {'Disag. Elast. SM - Distance': elas_sm_dist,
'Agg. Elast. SM - Distance': elas_sm_dist * prob_sm / normalization_sm}
# Each weight is normalized so that the sum of weights is equal to the numer of entries (1906)
BIOGEME_OBJECT.WEIGHT = theWeight
BIOGEME_OBJECT.SIMULATE = Enumerate(simulate,'obsIter')