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

Michel Bierlaire, EPFL

This file has automatically been generated.

Tue Dec 20 18:48:51 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 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 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: -5214.984
Likelihood ratio test: 3499.359
Rho-square: 0.251
Adjusted rho-square: 0.251
Final gradient norm: +2.019e-02
Diagnostic: Convergence reached...
Iterations: 18
Run time: 09h 13:25
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_CAR0.1370.05162.650.010.05172.650.01
ASC_SM0.00fixed
ASC_TRAIN-0.4020.0635-6.340.000.0659-6.100.00
B_COST-1.290.0631-20.380.000.0863-14.890.00
B_TIME-2.260.119-18.980.000.117-19.300.00
B_TIME_S-1.660.139-11.960.000.132-12.540.00

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_S2.750.4595.98

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
B_COST B_TIME_S0.002580.2962.770.01 0.003210.2822.730.01
B_TIME B_TIME_S0.01280.773-6.790.00 0.01140.740-6.620.00
ASC_TRAIN B_TIME_S-0.00181-0.2067.660.00 -0.00144-0.1657.990.00
B_COST B_TIME0.002380.3178.420.00 0.003720.3688.320.00
ASC_TRAIN B_COST-0.000136-0.03399.710.00 -0.000300-0.05287.930.00
ASC_CAR ASC_TRAIN0.002040.62310.550.00 0.002230.65410.660.00
ASC_CAR B_TIME_S-0.00298-0.41610.750.00 -0.00284-0.41511.170.00
ASC_TRAIN B_TIME-0.00455-0.60311.240.00 -0.00469-0.60911.210.00
ASC_CAR B_TIME-0.00394-0.64215.240.00 -0.00386-0.63715.440.00
ASC_CAR B_COST0.0001840.056617.950.00 0.0001310.029414.320.00

Smallest singular value of the hessian: 5.55565