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 |
Name | Value | Std err | t-test | p-value | Robust Std err | Robust t-test | p-value | ||
---|---|---|---|---|---|---|---|---|---|
ASC_CAR | -0.491 | 0.196 | -2.50 | 0.01 | 0.308 | -1.60 | 0.11 | * | |
ASC_SM | 0.00 | fixed | |||||||
ASC_TRAIN | -1.82 | 0.211 | -8.64 | 0.00 | 0.293 | -6.22 | 0.00 | ||
B_COST | -3.22 | 0.180 | -17.85 | 0.00 | 0.291 | -11.06 | 0.00 | ||
B_TIME | -3.32 | 0.148 | -22.40 | 0.00 | 0.448 | -7.42 | 0.00 | ||
SIGMA_CAR | 3.63 | 0.259 | 14.00 | 0.00 | 0.513 | 7.08 | 0.00 | ||
SIGMA_SM | 2.49 | 0.194 | 12.81 | 0.00 | 0.229 | 10.88 | 0.00 | ||
SIGMA_TRAIN | 2.60 | 0.223 | 11.69 | 0.00 | 0.245 | 10.62 | 0.00 | ||
ZERO | 0.00 | fixed |
Id | Name | Availability | Specification |
---|---|---|---|
1 | A1_TRAIN | TRAIN_AV_SP | ASC_TRAIN * one + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED + ZERO [ SIGMA_TRAIN ] * one |
2 | A2_SM | SM_AV | ASC_SM * one + B_TIME * SM_TT_SCALED + B_COST * SM_COST_SCALED + ZERO [ SIGMA_SM ] * one |
3 | A3_Car | CAR_AV_SP | ASC_CAR * one + B_TIME * CAR_TT_SCALED + B_COST * CAR_CO_SCALED + ZERO [ SIGMA_CAR ] * one |
Name | Value | Std err | t-test | Robust Std err | Robust t-test |
---|---|---|---|---|---|
ZERO_SIGMA_CAR | 13.2 | 1.88 | 7.00 | ||
ZERO_SIGMA_SM | 6.20 | 0.969 | 6.40 | ||
ZERO_SIGMA_TRAIN | 6.78 | 1.16 | 5.85 |
Coefficient1 | Coefficient2 | Covariance | Correlation | t-test | p-value | Rob. cov. | Rob. corr. | Rob. t-test | p-value | ||
---|---|---|---|---|---|---|---|---|---|---|---|
SIGMA_SM | SIGMA_TRAIN | -0.00110 | -0.0255 | -0.38 | 0.71 | * | 0.00983 | 0.175 | -0.37 | 0.71 | * |
B_COST | B_TIME | 0.0129 | 0.483 | 0.60 | 0.55 | * | 0.0602 | 0.462 | 0.25 | 0.80 | * |
SIGMA_CAR | SIGMA_TRAIN | 0.000507 | 0.00878 | 3.02 | 0.00 | -0.00834 | -0.0664 | 1.76 | 0.08 | * | |
SIGMA_CAR | SIGMA_SM | 0.00150 | 0.0297 | 3.57 | 0.00 | 0.0719 | 0.613 | 2.76 | 0.01 | ||
ASC_TRAIN | B_COST | 0.00120 | 0.0316 | 5.11 | 0.00 | 0.00515 | 0.0604 | 3.49 | 0.00 | ||
ASC_CAR | ASC_TRAIN | 0.00830 | 0.200 | 5.16 | 0.00 | 0.0380 | 0.422 | 4.12 | 0.00 | ||
ASC_TRAIN | B_TIME | -0.00637 | -0.204 | 5.32 | 0.00 | -0.0764 | -0.583 | 2.26 | 0.02 | ||
ASC_CAR | SIGMA_TRAIN | -0.00196 | -0.0449 | -10.20 | 0.00 | 0.00506 | 0.0671 | -8.14 | 0.00 | ||
ASC_CAR | B_TIME | -0.00130 | -0.0448 | 11.26 | 0.00 | -0.00149 | -0.0108 | 5.19 | 0.00 | ||
ASC_CAR | B_COST | 0.00635 | 0.179 | 11.29 | 0.00 | 0.0487 | 0.544 | 9.54 | 0.00 | ||
ASC_CAR | SIGMA_SM | 0.00626 | 0.164 | -11.80 | 0.00 | -0.0339 | -0.481 | -6.44 | 0.00 | ||
ASC_TRAIN | SIGMA_TRAIN | -0.0220 | -0.468 | -11.91 | 0.00 | 0.0109 | 0.152 | -12.56 | 0.00 | ||
ASC_CAR | SIGMA_CAR | -0.00595 | -0.117 | -12.02 | 0.00 | -0.119 | -0.757 | -5.34 | 0.00 | ||
ASC_TRAIN | SIGMA_SM | -0.00743 | -0.181 | -13.83 | 0.00 | -0.0433 | -0.645 | -9.10 | 0.00 | ||
ASC_TRAIN | SIGMA_CAR | 0.00921 | 0.168 | -17.85 | 0.00 | -0.0435 | -0.290 | -8.26 | 0.00 | ||
B_COST | SIGMA_CAR | -0.0223 | -0.477 | -18.03 | 0.00 | -0.0751 | -0.503 | -9.71 | 0.00 | ||
B_TIME | SIGMA_CAR | -0.0236 | -0.615 | -18.82 | 0.00 | -0.0349 | -0.152 | -9.52 | 0.00 | ||
B_COST | SIGMA_SM | -0.00779 | -0.222 | -19.48 | 0.00 | -0.0235 | -0.352 | -13.31 | 0.00 | ||
B_COST | SIGMA_TRAIN | -0.00151 | -0.0375 | -19.96 | 0.00 | -0.0193 | -0.271 | -13.59 | 0.00 | ||
B_TIME | SIGMA_SM | -0.0119 | -0.411 | -20.11 | 0.00 | 0.00379 | 0.0370 | -11.74 | 0.00 | ||
B_TIME | SIGMA_TRAIN | -0.00168 | -0.0510 | -21.64 | 0.00 | -0.0630 | -0.574 | -9.53 | 0.00 |
Smallest singular value of the hessian: 4.97977