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Choice model with a latent variable: sequential estimation (Monte-Carlo)
Mixture of logit, with Monte-Carlo integration Measurement equation for the indicators. Sequential estimation.
- author:
Michel Bierlaire, EPFL
- date:
Thu Apr 13 18:00:05 2023
import sys
import biogeme.biogeme_logging as blog
import biogeme.biogeme as bio
import biogeme.exceptions as excep
from biogeme import models
from biogeme.results import bioResults
from biogeme.expressions import (
Beta,
bioDraws,
MonteCarlo,
exp,
log,
)
from read_or_estimate import read_or_estimate
from optima import (
database,
age_65_more,
moreThanOneCar,
moreThanOneBike,
individualHouse,
male,
haveChildren,
haveGA,
highEducation,
WaitingTimePT,
Choice,
TimePT_scaled,
TimeCar_scaled,
MarginalCostPT_scaled,
CostCarCHF_scaled,
distance_km_scaled,
PurpHWH,
PurpOther,
ScaledIncome,
)
logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b04latent_choice_seq_mc.py')
Example b04latent_choice_seq_mc.py
Read the estimates from the structural equation estimation.
MODELNAME = 'b02one_latent_ordered'
try:
struct_results = bioResults(pickleFile=f'saved_results/{MODELNAME}.pickle')
except excep.BiogemeError:
print(
f'Run first the script {MODELNAME}.py in order to generate the '
f'file {MODELNAME}.pickle, and move it to the directory saved_results'
)
sys.exit()
struct_betas = struct_results.getBetaValues()
Coefficients.
coef_intercept = struct_betas['coef_intercept']
coef_age_65_more = struct_betas['coef_age_65_more']
coef_haveGA = struct_betas['coef_haveGA']
coef_moreThanOneCar = struct_betas['coef_moreThanOneCar']
coef_moreThanOneBike = struct_betas['coef_moreThanOneBike']
coef_individualHouse = struct_betas['coef_individualHouse']
coef_male = struct_betas['coef_male']
coef_haveChildren = struct_betas['coef_haveChildren']
coef_highEducation = struct_betas['coef_highEducation']
Latent variable: structural equation.
Define a random parameter, normally distributed, designed to be used for numerical integration
sigma_s = Beta('sigma_s', 1, None, None, 0)
error_component = sigma_s * bioDraws('EC', 'NORMAL_MLHS')
Piecewise linear specification for income.
thresholds = [None, 4, 6, 8, 10, None]
formula_income = models.piecewiseFormula(
variable=ScaledIncome,
thresholds=thresholds,
betas=[
struct_betas['beta_ScaledIncome_minus_inf_4'],
struct_betas['beta_ScaledIncome_4_6'],
struct_betas['beta_ScaledIncome_6_8'],
struct_betas['beta_ScaledIncome_8_10'],
struct_betas['beta_ScaledIncome_10_inf'],
],
)
CARLOVERS = (
coef_intercept
+ coef_age_65_more * age_65_more
+ formula_income
+ coef_moreThanOneCar * moreThanOneCar
+ coef_moreThanOneBike * moreThanOneBike
+ coef_individualHouse * individualHouse
+ coef_male * male
+ coef_haveChildren * haveChildren
+ coef_haveGA * haveGA
+ coef_highEducation * highEducation
+ error_component
)
Choice model.
ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
ASC_PT = Beta('ASC_PT', 0, None, None, 1)
ASC_SM = Beta('ASC_SM', 0, None, None, 0)
BETA_COST_HWH = Beta('BETA_COST_HWH', 0, None, None, 0)
BETA_COST_OTHER = Beta('BETA_COST_OTHER', 0, None, None, 0)
BETA_DIST = Beta('BETA_DIST', 0, None, None, 0)
BETA_TIME_CAR_REF = Beta('BETA_TIME_CAR_REF', 0, None, 0, 0)
BETA_TIME_PT_REF = Beta('BETA_TIME_PT_REF', 0, None, 0, 0)
BETA_WAITING_TIME = Beta('BETA_WAITING_TIME', 0, None, None, 0)
The coefficient of the latent variable should be initialized to something different from zero. If not, the algorithm may be trapped in a local optimum, and never change the value.
BETA_TIME_PT_CL = Beta('BETA_TIME_PT_CL', -0.01, None, None, 0)
BETA_TIME_CAR_CL = Beta('BETA_TIME_CAR_CL', -0.01, None, None, 0)
Definition of utility functions:.
BETA_TIME_PT = BETA_TIME_PT_REF * exp(BETA_TIME_PT_CL * CARLOVERS)
V0 = (
ASC_PT
+ BETA_TIME_PT * TimePT_scaled
+ BETA_WAITING_TIME * WaitingTimePT
+ BETA_COST_HWH * MarginalCostPT_scaled * PurpHWH
+ BETA_COST_OTHER * MarginalCostPT_scaled * PurpOther
)
BETA_TIME_CAR = BETA_TIME_CAR_REF * exp(BETA_TIME_CAR_CL * CARLOVERS)
V1 = (
ASC_CAR
+ BETA_TIME_CAR * TimeCar_scaled
+ BETA_COST_HWH * CostCarCHF_scaled * PurpHWH
+ BETA_COST_OTHER * CostCarCHF_scaled * PurpOther
)
V2 = ASC_SM + BETA_DIST * distance_km_scaled
Associate utility functions with the numbering of alternatives.
V = {0: V0, 1: V1, 2: V2}
Conditional on omega, we have a logit model (called the kernel).
condprob = models.logit(V, None, Choice)
We integrate over omega using numerical integration
loglike = log(MonteCarlo(condprob))
#
# Create the Biogeme object. As the objective is to illustrate the
# syntax, we calculate the Monte-Carlo approximation with a small
# number of draws. To achieve that, we provide a parameter file
# different from the default one: `few_draws.toml<few_draws.toml>`_
the_biogeme = bio.BIOGEME(database, loglike, parameter_file='few_draws.toml')
the_biogeme.modelName = 'b04latent_choice_seq_mc'
File few_draws.toml has been parsed.
If estimation results are saved on file, we read them to speed up the process. If not, we estimate the parameters.
results = read_or_estimate(the_biogeme=the_biogeme, directory='saved_results')
print(f'Estimated betas: {len(results.data.betaValues)}')
print(f'Final log likelihood: {results.data.logLike:.3f}')
print(f'Output file: {results.data.htmlFileName}')
results.writeLaTeX()
print(f'LaTeX file: {results.data.latexFileName}')
Estimated betas: 11
Final log likelihood: -1154.746
Output file: b04latent_choice_seq_mc.html
Results saved in file b04latent_choice_seq_mc.tex
LaTeX file: b04latent_choice_seq_mc.tex
results.getEstimatedParameters()
Total running time of the script: (0 minutes 0.541 seconds)