biogeme 2.6a [Mon Apr 17 15:32:48 CEST 2017]

Michel Bierlaire, EPFL

This file has automatically been generated.

Tue Apr 18 19:08:55 2017

Tip: click on the columns headers to sort a table [Credits]

Example of a mixture of logit model with panel data 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 Logit for panel data
Number of Hess-Train draws: 500
Number of estimated parameters: 5
Number of observations: 6768
Number of individuals: 752
Null log likelihood: -6964.663
Init log likelihood: -6964.663
Final log likelihood: -4360.039
Likelihood ratio test: 5209.247
Rho-square: 0.374
Adjusted rho-square: 0.373
Final gradient norm: +7.111e-05
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 23
Run time: 03:16
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_CAR0.2800.05674.930.000.1072.600.01
ASC_SM0.00fixed
ASC_TRAIN-0.5770.0820-7.040.000.146-3.960.00
B_COST-1.650.0775-21.280.000.292-5.650.00
B_TIME-3.220.188-17.100.000.223-14.460.00
B_TIME_S3.640.17420.950.000.24115.100.00

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_S13.21.2610.47

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
ASC_TRAIN B_COST0.0007640.12010.140.00 0.007230.1703.530.00
B_COST B_TIME0.001750.1208.050.00 0.02190.3365.190.00
ASC_CAR B_COST0.0007390.16821.930.00 0.003820.1226.460.00
ASC_CAR ASC_TRAIN0.002910.62613.360.00 0.009030.5767.060.00
ASC_TRAIN B_TIME-0.00660-0.42811.230.00 -0.0153-0.4708.300.00
ASC_CAR B_TIME-0.00437-0.41016.070.00 -0.0112-0.46612.110.00
B_COST B_TIME_S-0.00229-0.170-26.200.00 -0.0204-0.290-12.310.00
ASC_CAR B_TIME_S0.001200.122-19.080.00 0.003200.123-13.350.00
ASC_TRAIN B_TIME_S-0.000804-0.0565-21.480.00 -0.000107-0.00303-14.940.00
B_TIME B_TIME_S-0.0105-0.323-23.290.00 -0.0243-0.453-17.340.00

Smallest singular value of the hessian: 5.0266