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

Michel Bierlaire, EPFL

This file has automatically been generated.

Tue Feb 21 07:30:50 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 sigma associated with Swissmetro is normalized to 0, as a previous estimation identified it as the minimum variance (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: 6
Number of observations: 6768
Number of individuals: 752
Null log-likelihood: -6964.663
Init log-likelihood: -3789.894
Final log-likelihood: -3787.169
Likelihood ratio test: 6354.988
Rho-square: 0.456
Adjusted rho-square: 0.455
Final gradient norm: +8.179e-06
Diagnostic: Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations: 13
Run time: 09h 36:18
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-0.7670.190-4.030.000.301-2.550.01
ASC_SM0.00fixed
ASC_TRAIN-2.080.252-8.230.000.341-6.090.00
B_COST-3.130.178-17.540.000.304-10.290.00
B_TIME-3.310.156-21.160.000.472-7.010.00
SIGMA_CAR4.230.25616.550.000.6007.060.00
SIGMA_TRAIN3.600.21516.790.000.24514.700.00
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
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_CAR17.92.178.27
ZERO_SIGMA_TRAIN13.01.558.40

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testp-valueRob. cov.Rob. corr.Rob. t-testp-value
B_COST B_TIME0.01310.4701.020.31 *0.08100.5650.450.65 *
SIGMA_CAR SIGMA_TRAIN0.007570.1382.030.04 0.02530.1721.040.30 *
ASC_TRAIN B_COST0.0007580.01683.440.00 -0.0251-0.2422.070.04
ASC_TRAIN B_TIME-0.0120-0.3053.670.00 -0.114-0.7061.630.10 *
ASC_CAR ASC_TRAIN0.001510.03154.210.00 0.0007280.007092.890.00
ASC_CAR B_COST0.006770.19910.110.00 0.04500.4927.740.00
ASC_CAR B_TIME0.0002830.0095210.360.00 0.01370.09644.750.00
ASC_TRAIN SIGMA_TRAIN-0.0325-0.600-13.590.00 -0.0170-0.203-12.390.00
ASC_CAR SIGMA_CAR-0.00370-0.0760-15.140.00 -0.135-0.749-5.890.00
ASC_CAR SIGMA_TRAIN-0.000155-0.00380-15.210.00 -0.00723-0.0979-10.750.00
B_TIME SIGMA_CAR-0.0309-0.772-19.360.00 -0.107-0.377-8.450.00
B_COST SIGMA_CAR-0.0213-0.466-19.690.00 -0.0878-0.482-9.290.00
ASC_TRAIN SIGMA_CAR0.01430.221-19.910.00 0.04830.236-10.240.00
B_COST SIGMA_TRAIN-0.00633-0.165-22.380.00 -0.0239-0.321-15.050.00
B_TIME SIGMA_TRAIN-0.00519-0.155-24.300.00 -0.0412-0.357-11.440.00

Smallest singular value of the hessian: 4.73825