biogeme 2.2 [Fri Dec 23 17:20:55 CET 2011]

Michel Bierlaire, EPFL

This file has automatically been generated.

Thu Feb 16 21:39:27 2012

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).
The estimates for the logit model are used as starting points for the estimation
Model: Mixed Multinomial Logit for panel data
Number of draws: 100000
Number of estimated parameters: 7
Number of observations: 6768
Number of individuals: 752
Null log-likelihood: -6964.663
Init log-likelihood: -3795.353
Final log-likelihood: -3792.883
Likelihood ratio test: 6343.561
Rho-square: 0.455
Adjusted rho-square: 0.454
Final gradient norm: +5.045e-05
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 14
Run time: 10h 42:27
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-0.4910.196-2.500.010.308-1.600.11*
ASC_SM0.00fixed
ASC_TRAIN-1.820.211-8.640.000.293-6.220.00
B_COST-3.220.180-17.850.000.291-11.060.00
B_TIME-3.320.148-22.400.000.448-7.420.00
SIGMA_CAR3.630.25914.000.000.5137.080.00
SIGMA_SM2.490.19412.810.000.22910.880.00
SIGMA_TRAIN2.600.22311.690.000.24510.620.00
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

Variance of random coefficients

NameValueStd errt-testRobust Std errRobust t-test
ZERO_SIGMA_CAR13.21.887.00
ZERO_SIGMA_SM6.200.9696.40
ZERO_SIGMA_TRAIN6.781.165.85

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
SIGMA_SM SIGMA_TRAIN-0.00110-0.0255-0.380.71 *0.009830.175-0.370.71 *
B_COST B_TIME0.01290.4830.600.55 *0.06020.4620.250.80 *
SIGMA_CAR SIGMA_TRAIN0.0005070.008783.020.00 -0.00834-0.06641.760.08 *
SIGMA_CAR SIGMA_SM0.001500.02973.570.00 0.07190.6132.760.01
ASC_TRAIN B_COST0.001200.03165.110.00 0.005150.06043.490.00
ASC_CAR ASC_TRAIN0.008300.2005.160.00 0.03800.4224.120.00
ASC_TRAIN B_TIME-0.00637-0.2045.320.00 -0.0764-0.5832.260.02
ASC_CAR SIGMA_TRAIN-0.00196-0.0449-10.200.00 0.005060.0671-8.140.00
ASC_CAR B_TIME-0.00130-0.044811.260.00 -0.00149-0.01085.190.00
ASC_CAR B_COST0.006350.17911.290.00 0.04870.5449.540.00
ASC_CAR SIGMA_SM0.006260.164-11.800.00 -0.0339-0.481-6.440.00
ASC_TRAIN SIGMA_TRAIN-0.0220-0.468-11.910.00 0.01090.152-12.560.00
ASC_CAR SIGMA_CAR-0.00595-0.117-12.020.00 -0.119-0.757-5.340.00
ASC_TRAIN SIGMA_SM-0.00743-0.181-13.830.00 -0.0433-0.645-9.100.00
ASC_TRAIN SIGMA_CAR0.009210.168-17.850.00 -0.0435-0.290-8.260.00
B_COST SIGMA_CAR-0.0223-0.477-18.030.00 -0.0751-0.503-9.710.00
B_TIME SIGMA_CAR-0.0236-0.615-18.820.00 -0.0349-0.152-9.520.00
B_COST SIGMA_SM-0.00779-0.222-19.480.00 -0.0235-0.352-13.310.00
B_COST SIGMA_TRAIN-0.00151-0.0375-19.960.00 -0.0193-0.271-13.590.00
B_TIME SIGMA_SM-0.0119-0.411-20.110.00 0.003790.0370-11.740.00
B_TIME SIGMA_TRAIN-0.00168-0.0510-21.640.00 -0.0630-0.574-9.530.00

Smallest singular value of the hessian: 4.97977