biogeme 2.2 [Sam 17 déc 2011 18:36:48 CET]

Michel Bierlaire, EPFL

This file has automatically been generated.

Sun Dec 18 15:28:23 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.
The analytical derivatives are explicitly provided by the user.
Model: Mixed Multinomial Logit
Number of draws: 5
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: -5322.913
Likelihood ratio test: 3283.500
Rho-square: 0.236
Adjusted rho-square: 0.235
Final gradient norm: +3.450e-04
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 15
Run time: 00:02
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_CAR-0.1300.0442-2.940.000.0541-2.400.02
ASC_SM0.00fixed
ASC_TRAIN-0.6750.0558-12.100.000.0753-8.960.00
B_COST-1.100.0530-20.780.000.0699-15.760.00
B_TIME0.2560.04665.490.000.07793.290.00
B_TIME_S-0.3330.0616-5.410.000.130-2.560.01

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_S0.1110.04102.71

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
ASC_CAR B_TIME_S-0.000181-0.06652.600.01 0.0006080.08641.490.14 *
ASC_TRAIN B_TIME_S-1.65e-05-0.00480-4.100.00 0.002350.240-2.550.01
ASC_TRAIN B_COST-2.24e-05-0.007585.520.00 -0.000465-0.08843.980.00
B_TIME B_TIME_S0.0003670.1288.150.00 0.004270.4214.900.00
ASC_CAR B_TIME0.001200.581-9.260.00 0.003010.714-7.070.00
B_COST B_TIME_S0.0002160.0663-9.780.00 0.0003950.0434-5.300.00
ASC_CAR ASC_TRAIN0.001460.59211.770.00 0.003130.76911.280.00
ASC_CAR B_COST0.0004530.19315.650.00 0.0002280.060211.330.00
B_COST B_TIME-0.000461-0.186-17.670.00 -0.00133-0.244-11.640.00
ASC_TRAIN B_TIME0.001870.720-23.730.00 0.004960.845-21.780.00

Smallest singular value of the hessian: 5.96458