biogeme 2.2 [Fri Dec 23 17:20:55 CET 2011]

Michel Bierlaire, EPFL

This file has automatically been generated.

Sun Dec 25 21:20:30 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 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.
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: -5836.619
Final log-likelihood: -5231.403
Likelihood ratio test: 3466.520
Rho-square: 0.249
Adjusted rho-square: 0.248
Final gradient norm: +1.069e-03
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 16
Run time: 15h 55:19
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_CAR0.1740.05823.000.000.06272.780.01
ASC_SM0.00fixed
ASC_TRAIN-0.3460.0676-5.120.000.0733-4.720.00
B_COST-1.380.0746-18.510.000.0979-14.110.00
B_TIME0.5750.06538.810.000.07138.070.00
B_TIME_S1.240.10312.030.000.1339.320.00

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_S1.540.2556.01

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
B_TIME B_TIME_S0.0006000.0892-5.680.00 0.0003680.0388-4.470.00
ASC_CAR B_TIME0.002610.687-8.150.00 0.003130.699-7.630.00
ASC_TRAIN B_COST-0.000691-0.1379.640.00 -0.00130-0.1817.810.00
ASC_CAR B_TIME_S0.001520.254-10.180.00 0.002380.285-8.200.00
ASC_CAR ASC_TRAIN0.002760.70310.560.00 0.003460.75210.640.00
ASC_TRAIN B_TIME_S0.0004450.0638-13.260.00 0.0001930.0198-10.530.00
ASC_CAR B_COST-0.000372-0.085715.790.00 -0.00107-0.17412.430.00
B_COST B_TIME-0.00156-0.321-17.190.00 -0.00281-0.403-13.740.00
B_COST B_TIME_S-0.00270-0.351-17.840.00 -0.00460-0.353-13.720.00
ASC_TRAIN B_TIME0.003410.773-20.540.00 0.004180.801-20.200.00

Smallest singular value of the hessian: 5.86868