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

Michel Bierlaire, EPFL

This file has automatically been generated.

Wed Jul 6 20:06:15 2016

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

Example of a nested logit model for a transportation mode choice with 3 alternatives:
- Train
- Car
- Swissmetro, an hypothetical high-speed train
Alternatives Train and Car are grouped in the same nest, as their error terms are expected to share unobserved attributes associated with existing alternatives.
Although this should be discouraged, we illustrate here a normalization of the nested logit model from the bottom.
Model: Nested Logit
Number of estimated parameters: 5
Number of observations: 6768
Number of individuals: 6768
Null log likelihood: -6964.663
Init log likelihood: -6964.663
Final log likelihood: -5236.900
Likelihood ratio test: 3455.526
Rho-square: 0.248
Adjusted rho-square: 0.247
Final gradient norm: +3.112e-04
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 20
Run time: 00:00
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-0.3430.0830-4.140.000.119-2.890.00
ASC_SM0.00fixed
ASC_TRAIN-1.050.103-10.210.000.165-6.370.00
B_COST-1.760.0999-17.610.000.149-11.790.00
B_TIME-1.850.101-18.220.000.226-8.180.00

Homogeneity parameter (mu)

ValueStd errt-test0p-valuet-test1p-valueRobust Std errRobust t-test0p-valueRobust t-test1p-value
0.4868390.027917.450.00-18.390.000.038912.510.00-13.18560.00

Model parameters

NameValueStd errt-test 0p-valuet-test 1p-valueRobust Std errRobust t-test 0p-valueRobust t-test 1p-value
EXISTING1.00fixed
FUTURE1.00fixed

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_TIME0.003430.3390.750.46 *0.01620.4820.430.67 *
ASC_TRAIN B_TIME-0.00435-0.4174.620.00 -0.0262-0.7052.200.03
ASC_TRAIN B_COST0.003310.3215.990.00 0.001690.06843.300.00
ASC_CAR B_TIME-0.00269-0.32010.010.00 -0.0159-0.5944.830.00
ASC_CAR B_COST0.003050.36813.660.00 0.002990.1688.120.00
ASC_CAR ASC_TRAIN0.007060.82612.200.00 0.01810.9219.800.00

Smallest singular value of the hessian: 1.39506