biogeme 2.5 [Dim 19 jui 2016 17:58:58 CEST]

Michel Bierlaire, EPFL

This file has automatically been generated.

Thu Jul 7 17:54:18 2016

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: -5231.175
Likelihood ratio test: 3466.976
Rho-square: 0.249
Adjusted rho-square: 0.248
Final gradient norm: +6.639e-04
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 18
Run time: 02:46
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_CAR0.1750.05803.020.000.06232.810.00
ASC_SM0.00fixed
ASC_TRAIN-0.3450.0676-5.100.000.0733-4.710.00
B_COST-1.380.0747-18.510.000.0978-14.130.00
B_TIME0.5770.06528.840.000.07128.100.00
B_TIME_S1.240.10012.340.000.1269.810.00

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_S1.540.2496.17

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
B_TIME B_TIME_S0.0005290.0807-5.750.00 0.0002190.0244-4.620.00
ASC_CAR B_TIME0.002600.687-8.160.00 0.003100.699-7.660.00
ASC_TRAIN B_COST-0.000685-0.1369.660.00 -0.00128-0.1797.840.00
ASC_CAR B_TIME_S0.001420.243-10.320.00 0.002080.264-8.490.00
ASC_CAR ASC_TRAIN0.002760.70310.560.00 0.003440.75310.670.00
ASC_TRAIN B_TIME_S0.0003810.0560-13.440.00 6.06e-050.00654-10.880.00
ASC_CAR B_COST-0.000357-0.082515.840.00 -0.00102-0.16712.520.00
B_COST B_TIME-0.00156-0.320-17.210.00 -0.00280-0.402-13.770.00
B_COST B_TIME_S-0.00261-0.347-18.140.00 -0.00427-0.346-14.200.00
ASC_TRAIN B_TIME0.003410.772-20.550.00 0.004180.801-20.200.00

Smallest singular value of the hessian: 5.86836