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

Michel Bierlaire, EPFL

This file has automatically been generated.

Tue Apr 18 19:03:13 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 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.
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: -6964.663
Final log likelihood: -5214.787
Likelihood ratio test: 3499.751
Rho-square: 0.251
Adjusted rho-square: 0.251
Final gradient norm: +8.813e-04
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 18
Run time: 01:16
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_CAR0.1370.05162.660.010.05172.650.01
ASC_SM0.00fixed
ASC_TRAIN-0.4020.0635-6.330.000.0659-6.100.00
B_COST-1.290.0631-20.380.000.0863-14.890.00
B_TIME-2.260.119-18.980.000.117-19.290.00
B_TIME_S1.660.13911.980.000.13212.570.00

Utility functions

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

Variance of random coefficients

NameValueStd errt-testRobust Std errRobust t-test
B_TIME_B_TIME_S2.750.4605.99

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
ASC_TRAIN B_COST-0.000137-0.03439.710.00 -0.000303-0.05337.940.00
B_COST B_TIME0.002390.3188.430.00 0.003730.3698.330.00
ASC_CAR ASC_TRAIN0.002040.62310.560.00 0.002230.65510.670.00
ASC_TRAIN B_TIME-0.00456-0.60311.240.00 -0.00470-0.60911.210.00
ASC_CAR B_TIME_S0.002980.417-12.070.00 0.002850.417-12.680.00
ASC_CAR B_COST0.0001820.055817.950.00 0.0001280.028614.320.00
ASC_TRAIN B_TIME_S0.001820.207-14.730.00 0.001460.168-15.010.00
ASC_CAR B_TIME-0.00395-0.64215.240.00 -0.00387-0.63815.430.00
B_COST B_TIME_S-0.00259-0.297-17.490.00 -0.00322-0.283-16.640.00
B_TIME B_TIME_S-0.0128-0.774-16.150.00 -0.0115-0.741-16.850.00

Smallest singular value of the hessian: 5.55496