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

Michel Bierlaire, EPFL

This file has automatically been generated.

Sun Dec 18 15:28:12 2011

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
We introduce error components with alternative specific variance. The model is not identified, but its estimation is required to identify which SIGMA should be normalized (see Walker, 2001).
For seminonparametric terms are included to test the distribution of the error component for the Train alternative (see Fosgerau and Bierlaire, 2007)
Model: Mixed Multinomial Logit for panel data
Number of draws: 5
Number of estimated parameters: 11
Number of observations: 6768
Number of individuals: 752
Null log-likelihood: -6964.663
Init log-likelihood: -6155.783
Final log-likelihood: -4714.746
Likelihood ratio test: 4499.835
Rho-square: 0.323
Adjusted rho-square: 0.321
Final gradient norm: +3.805e-04
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 26
Run time: 00:07
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-0.02870.0700-0.410.68*0.273-0.110.92*
ASC_SM0.00fixed
ASC_TRAIN-0.9320.0978-9.530.000.382-2.440.01
B_COST-1.490.0752-19.860.000.260-5.730.00
B_TIME-1.540.0833-18.530.000.454-3.400.00
SIGMA_CAR-0.7790.106-7.340.000.362-2.150.03
SIGMA_SM1.540.080719.080.000.2605.930.00
SIGMA_TRAIN-1.830.109-16.790.000.350-5.210.00
SMP10.6990.022431.170.000.021931.960.00
SMP2-0.6330.0275-23.040.000.0271-23.340.00
SMP30.4310.028615.040.000.028615.060.00
SMP4-0.1050.0245-4.300.000.0231-4.560.00
ZERO0.00fixed

Utility functions

IdNameAvailabilitySpecification
1A1_TRAINTRAIN_AV_SPASC_TRAIN * one + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED + ZERO [ SIGMA_TRAIN ] * one
2A2_SMSM_AVASC_SM * one + B_TIME * SM_TT_SCALED + B_COST * SM_COST_SCALED + ZERO [ SIGMA_SM ] * one
3A3_CarCAR_AV_SPASC_CAR * one + B_TIME * CAR_TT_SCALED + B_COST * CAR_CO_SCALED + ZERO [ SIGMA_CAR ] * one

Seminonparametric transform

Base parameter: ZERO_SIGMA_TRAIN

List of terms:

Term of order Coefficient
1SMP1
2SMP2
3SMP3
4SMP4

Variance of random coefficients

NameValueStd errt-testRobust Std errRobust t-test
ZERO_SIGMA_CAR0.6070.1663.67
ZERO_SIGMA_SM3.370.24913.56
ZERO_SIGMA_TRAIN3.330.3978.39

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
B_COST B_TIME0.001270.2020.500.62 *0.03430.2900.110.91 *
ASC_CAR SMP41.12e-116.51e-091.030.30 *-0.000250-0.03960.280.78 *
ASC_TRAIN SIGMA_CAR-7.99e-05-0.00769-1.050.29 *0.01240.0894-0.300.76 *
SIGMA_CAR SMP2-1.31e-11-4.48e-09-1.330.18 *8.59e-050.00875-0.400.69 *
B_TIME SIGMA_TRAIN-0.000964-0.1061.960.05 -0.0318-0.2000.450.65 *
B_COST SIGMA_TRAIN-0.000565-0.06912.440.01 -0.00615-0.06750.740.46 *
ASC_TRAIN SMP21.76e-116.55e-09-2.940.00 -0.000324-0.0313-0.780.44 *
ASC_TRAIN B_TIME-0.00524-0.6433.720.00 -0.160-0.9210.750.46 *
ASC_TRAIN B_COST1.38e-050.001884.550.00 -0.0141-0.1421.140.25 *
B_COST SIGMA_CAR0.0003140.0394-5.590.00 -0.00502-0.0533-1.560.12 *
B_TIME SIGMA_CAR3.02e-050.00341-5.670.00 -0.0191-0.116-1.250.21 *
ASC_CAR SMP3-8.35e-12-4.16e-09-6.080.00 1.45e-050.00185-1.670.09 *
SIGMA_CAR SMP42.41e-129.28e-10-6.190.00 4.35e-050.00520-1.860.06 *
ASC_CAR SIGMA_CAR0.001690.2276.630.00 0.02790.2821.940.05 *
SIGMA_CAR SIGMA_TRAIN-2.26e-05-0.001966.880.00 0.003100.02442.100.04
ASC_TRAIN SIGMA_TRAIN0.003720.3497.560.00 0.03720.2782.030.04
ASC_CAR SMP23.80e-121.97e-098.040.00 -0.000295-0.03982.190.03
ASC_TRAIN SMP41.82e-117.62e-09-8.200.00 -0.000195-0.0221-2.160.03
SMP1 SMP30.0002220.3469.050.00 0.0001870.2988.830.00
ASC_CAR SMP1-1.07e-11-6.79e-09-9.900.00 4.94e-050.00826-2.660.01
SIGMA_SM SMP1-3.52e-12-1.95e-0910.030.00 -0.000163-0.02873.220.00
B_TIME SMP2-8.28e-12-3.62e-09-10.380.00 0.0005840.0474-2.010.04
SIGMA_TRAIN SMP25.89e-121.97e-09-10.630.00 -0.000374-0.0394-3.390.00
B_COST SMP2-4.63e-12-2.24e-09-10.740.00 4.92e-050.00697-3.290.00
SIGMA_CAR SMP3-6.76e-12-2.22e-09-11.010.00 0.0001240.0120-3.340.00
ASC_CAR B_TIME-0.00346-0.59411.060.00 -0.112-0.9032.130.03
ASC_CAR ASC_TRAIN0.004090.59711.390.00 0.09380.8974.940.00
SIGMA_SM SMP3-2.21e-12-9.55e-1012.950.00 -5.80e-05-0.007804.240.00
ASC_TRAIN SMP3-1.57e-11-5.61e-09-13.370.00 -6.70e-05-0.00612-3.550.00
SMP3 SMP4-7.73e-05-0.11013.510.00 -3.78e-05-0.057214.190.00
SIGMA_CAR SMP1-9.71e-12-4.08e-09-13.630.00 -1.71e-05-0.00216-4.080.00
ASC_CAR SIGMA_TRAIN0.0004140.054414.250.00 0.01540.1604.400.00
ASC_CAR B_COST0.0007210.13715.340.00 -0.00744-0.1043.690.00
SIGMA_TRAIN SMP41.21e-114.53e-09-15.430.00 -0.000354-0.0438-4.890.00
ASC_TRAIN SMP1-1.31e-11-5.99e-09-16.250.00 3.03e-050.00362-4.260.00
B_TIME SMP4-8.40e-12-4.12e-09-16.570.00 0.0004800.0457-3.170.00
ASC_CAR SIGMA_SM0.001430.252-16.950.00 0.03460.488-5.810.00
B_COST SMP4-2.08e-13-1.13e-10-17.560.00 5.13e-050.00853-5.310.00
SMP1 SMP4-0.000407-0.74118.380.00 -0.000340-0.67319.560.00
SMP2 SMP40.0002880.428-18.930.00 0.0002340.373-18.660.00
SIGMA_SM SMP41.94e-129.82e-1019.500.00 0.0001070.01786.320.00
SIGMA_CAR SIGMA_SM0.002000.234-19.760.00 0.05050.537-7.430.00
SIGMA_TRAIN SMP3-1.32e-11-4.24e-09-20.060.00 0.0002890.0288-6.440.00
ASC_TRAIN SIGMA_SM0.001560.198-21.710.00 0.04260.428-6.890.00
B_TIME SMP33.85e-121.62e-09-22.420.00 -0.000167-0.0128-4.330.00
SIGMA_TRAIN SMP1-1.28e-11-5.26e-09-22.740.00 0.0002570.0335-7.210.00
B_TIME SIGMA_SM-0.00224-0.333-23.030.00 -0.0501-0.425-5.040.00
B_COST SMP3-2.34e-12-1.09e-09-23.920.00 0.0002420.0324-7.370.00
B_COST SIGMA_SM-0.00178-0.293-24.190.00 -0.0149-0.220-7.460.00
SMP2 SMP3-0.000175-0.222-24.250.00 -0.000174-0.225-24.390.00
SIGMA_SM SMP2-1.21e-12-5.45e-1025.480.00 -3.54e-05-0.005038.310.00
B_TIME SMP15.22e-122.79e-09-26.000.00 -0.000124-0.0125-4.930.00
B_COST SMP1-2.10e-12-1.24e-09-27.950.00 7.88e-050.0138-8.400.00
SIGMA_SM SIGMA_TRAIN0.002850.32529.940.00 0.05660.62312.140.00
SMP1 SMP23.95e-050.064138.800.00 5.35e-050.090140.030.00

Smallest singular value of the hessian: 5.71165