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

Michel Bierlaire, EPFL

This file has automatically been generated.

Wed Jul 6 20:03:14 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
We illustrate a case where persons from GROUP 3 have been undersampled.
In order to apply the WESML estimator, weights must be associated to observation.
A weight of 1.0 is associated with GROUP 2 and a weight of 1.2 with GROUP 3
Note that the valie of the log likelihood cannot be compared with the ESML value.
Model: Logit
Number of estimated parameters: 4
Number of observations: 6768
Number of individuals: 6768
Null log likelihood: -7016.870
Init log likelihood: -7016.870
Final log likelihood: -5273.743
Likelihood ratio test: 3486.253
Rho-square: 0.248
Adjusted rho-square: 0.248
Final gradient norm: +6.154e-04
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 13
Run time: 00:00
Variance-covariance: from analytical hessian
Sample file: ../swissmetro.dat

Utility parameters

Name Value Std err t-testp-valueRobust Std err Robust t-testp-value
ASC_CAR-0.1140.0433-2.640.010.0590-1.940.05*
ASC_SM0.00fixed
ASC_TRAIN-0.7570.0558-13.570.000.0824-9.180.00
B_COST-1.120.0522-21.430.000.0673-16.630.00
B_TIME-1.320.0576-22.940.000.106-12.500.00

Utility functions

IdNameAvailabilitySpecification
1A1_TRAINTRAIN_AV_SPASC_TRAIN * one + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
2A2_SMSM_AVASC_SM * one + B_TIME * SM_TT_SCALED + B_COST * SM_COST_SCALED
3A3_CarCAR_AV_SPASC_CAR * one + B_TIME * CAR_TT_SCALED + B_COST * CAR_CO_SCALED

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
B_COST B_TIME0.0005890.1962.890.00 0.002250.3161.910.06 *
ASC_TRAIN B_TIME-0.00229-0.7135.380.00 -0.00773-0.8873.090.00
ASC_TRAIN B_COST-1.17e-05-0.004024.740.00 -0.000900-0.1623.170.00
ASC_CAR B_TIME-0.00147-0.59013.390.00 -0.00497-0.7967.700.00
ASC_CAR B_COST0.0004660.20616.600.00 -4.15e-05-0.010411.170.00
ASC_CAR ASC_TRAIN0.001390.57613.680.00 0.003940.81013.110.00

Smallest singular value of the hessian: 5.89012