biogeme 2.2 [Mon Dec 5 10:42:04 CET 2011]

Michel Bierlaire, EPFL

This file has automatically been generated.

Fri Dec 23 04:32:34 2011

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 distributed, with a unifrom distribution. 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 curly brackets are associated with a uniform distribution.
Model: Mixed Multinomial Logit
Number of draws: 100000
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: -5215.111
Likelihood ratio test: 3499.105
Rho-square: 0.251
Adjusted rho-square: 0.250
Final gradient norm: +1.692e-02
Diagnostic: Convergence reached...
Iterations: 20
Run time: 15h 44:45
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_CAR0.1450.05272.750.010.05332.720.01
ASC_SM0.00fixed
ASC_TRAIN-0.3850.0638-6.030.000.0660-5.830.00
B_COST-1.280.0627-20.370.000.0866-14.750.00
B_TIME-2.320.129-18.020.000.126-18.410.00
B_TIME_S-2.880.215-13.400.000.200-14.370.00

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_S2.760.4116.70

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
B_TIME B_TIME_S0.02330.8424.380.00 0.02090.8274.660.00
B_COST B_TIME_S0.003670.2737.730.00 0.004440.2568.130.00
B_COST B_TIME0.002340.2908.280.00 0.003530.3238.150.00
ASC_TRAIN B_COST-0.000182-0.04559.750.00 -0.000318-0.05567.990.00
ASC_TRAIN B_TIME_S-0.00475-0.34610.200.00 -0.00454-0.34410.770.00
ASC_CAR ASC_TRAIN0.002180.64910.640.00 0.002410.68510.870.00
ASC_TRAIN B_TIME-0.00530-0.64510.940.00 -0.00549-0.66010.950.00
ASC_CAR B_TIME_S-0.00554-0.49112.340.00 -0.00551-0.51613.010.00
ASC_CAR B_TIME-0.00446-0.65714.660.00 -0.00445-0.66314.830.00
ASC_CAR B_COST0.0001850.055917.870.00 0.0001730.037414.230.00

Smallest singular value of the hessian: 5.30275