biogeme 2.6a [Mon Apr 17 15:32:48 CEST 2017]

Michel Bierlaire, EPFL

This file has automatically been generated.

Tue Apr 18 19:51:22 2017

Tip: click on the columns headers to sort a table [Credits]

Example of a logit model for a transportation mode choice with 3 alternatives:
- Train
- Car
- Swissmetro, an hypothetical high-speed train
The time coefficient is log normally distributed. This is an example of a mixture of logit model.
The syntax for a distributed coefficient is B_TIME [ B_TIME_S ], where
B_TIME is the mean and B_TIME_S squared is the variance.
The square brackets are associated with a normal distribution.
The analytical derivatives are explicitly provided by the user.
Model: Mixed Logit
Number of Hess-Train draws: 500
Number of estimated parameters: 5
Number of observations: 6768
Number of individuals: 6768
Null log likelihood: -6964.663
Init log likelihood: -5836.619
Final log likelihood: -5231.453
Likelihood ratio test: 3466.421
Rho-square: 0.249
Adjusted rho-square: 0.248
Final gradient norm: +5.921e-04
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 17
Run time: 02:44
Variance-covariance: from finite difference hessian
Sample file: ../swissmetro.dat

Utility parameters

Name Value Std err t-testp-valueRobust Std err Robust t-testp-value
ASC_CAR0.1740.05822.990.000.06292.770.01
ASC_SM0.00fixed
ASC_TRAIN-0.3460.0676-5.120.000.0733-4.720.00
B_COST-1.380.0746-18.510.000.0978-14.100.00
B_TIME0.5750.06538.810.000.07138.070.00
B_TIME_S1.240.10411.930.000.1359.180.00

Utility functions

IdNameAvailabilitySpecification
1A1_TRAINTRAIN_AV_SPASC_TRAIN * one + B_COST * TRAIN_COST_SCALED + -(exp(B_TIME [ B_TIME_S ] )) * TRAIN_TT_SCALED
2A2_SMSM_AVASC_SM * one + B_COST * SM_COST_SCALED + -(exp(B_TIME [ B_TIME_S ] )) * SM_TT_SCALED
3A3_CarCAR_AV_SPASC_CAR * one + B_COST * CAR_CO_SCALED + -(exp(B_TIME [ B_TIME_S ] )) * CAR_TT_SCALED

Variance of random coefficients

NameValueStd errt-testRobust Std errRobust t-test
B_TIME_B_TIME_S1.530.2575.96

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
B_TIME B_TIME_S0.0006360.0938-5.650.00 0.0004510.0468-4.430.00
ASC_CAR B_TIME0.002620.688-8.140.00 0.003140.700-7.630.00
ASC_TRAIN B_COST-0.000695-0.1389.630.00 -0.00131-0.1837.800.00
ASC_CAR B_TIME_S0.001570.259-10.130.00 0.002500.294-8.120.00
ASC_TRAIN B_TIME_S0.0004760.0677-13.210.00 0.0002640.0267-10.430.00
ASC_CAR ASC_TRAIN0.002770.70310.560.00 0.003470.75210.630.00
ASC_CAR B_COST-0.000378-0.087215.770.00 -0.00109-0.17712.400.00
B_COST B_TIME_S-0.00273-0.352-17.740.00 -0.00472-0.357-13.570.00
B_COST B_TIME-0.00156-0.321-17.180.00 -0.00282-0.404-13.720.00
ASC_TRAIN B_TIME0.003420.773-20.540.00 0.004190.801-20.200.00

Smallest singular value of the hessian: 5.86902