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

Michel Bierlaire, EPFL

This file has automatically been generated.

Sun Dec 18 15:27:10 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 assumed to be distributed. It is a discrete distribution with two mass points, one at 0, and one at B_TIME_OTHER. The probabilities assoviated with each mass point are W_0 and W_OTHER, respectively.
Model: Multinomial Logit
Number of estimated parameters: 6
Number of observations: 6768
Number of individuals: 6768
Null log-likelihood: -6964.663
Init log-likelihood: -6964.663
Final log-likelihood: -5208.498
Likelihood ratio test: 3512.330
Rho-square: 0.252
Adjusted rho-square: 0.251
Final gradient norm: +9.571e+03
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 20
Run time: 00:01
Variance-covariance: from analytical hessian
Sample file: ../swissmetro.dat

Utility parameters

Name Value Std err t-testp-value
ASC_CAR0.1250.02524.950.00
ASC_SM0.00fixed
ASC_TRAIN-0.3980.0259-15.380.00
B_COST-1.260.0387-32.650.00
B_TIME_00.00fixed
B_TIME_OTHER-2.801.80e+308-0.001.00*
W_00.2512.79e+070.001.00*
W_OTHER0.7492.79e+070.001.00*

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
ASC_CAR B_TIME_OTHER2.92e-120.000.001.00 *
ASC_TRAIN B_TIME_OTHER-2.29e-060.000.001.00 *
B_COST B_TIME_OTHER3.47e-050.000.001.00 *
ASC_CAR W_01.74e-132.48e-19-0.001.00 *
W_0 W_OTHER-7.79e+14-1.00-0.001.00 *
ASC_CAR W_OTHER-1.29e-13-1.84e-19-0.001.00 *
ASC_TRAIN W_01.00e-051.39e-11-0.001.00 *
ASC_TRAIN W_OTHER-1.00e-05-1.39e-11-0.001.00 *
B_COST W_0-0.000152-1.40e-10-0.001.00 *
B_COST W_OTHER0.0001521.40e-10-0.001.00 *
B_TIME_OTHER W_01.70e+130.00-0.001.00 *
B_TIME_OTHER W_OTHER-1.70e+130.00-0.001.00 *
ASC_CAR ASC_TRAIN0.0002570.39518.610.00
ASC_TRAIN B_COST0.0002190.21920.840.00
ASC_CAR B_COST0.0003280.33736.150.00

User defined linear constraints

1*W_0 + 1*W_OTHER = 1 [1 = 1]

Smallest singular value of the hessian: 2.73863e-16

Unidentifiable model

The log-likelihood is (almost) flat along the following combinations of parameters

Sing. value=2.73863e-16
-0.0101352*B_TIME_OTHER
-0.463163*W_0
0.463163*W_OTHER
-0.00188832*Param[9]
-0.462432*Param[10]
0.267549*Param[11]
0.00141656*Param[15]
0.267549*Param[16]
-0.462432*Param[17]
Sing. value=5.79646e-08
-0.97388*B_TIME_OTHER
0.00482018*W_0
-0.00482018*W_OTHER
-0.181446*Param[9]
0.00481256*Param[10]
-0.0027844*Param[11]
0.136115*Param[15]
-0.0027844*Param[16]
0.00481256*Param[17]