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Tue Apr 18 19:12:10 2017
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| 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. |
| This example shows that constraining one of the sigma to zero does *not* lead to the same model. It is not a proper normalization, as discussed by Walker (2001, Appendix C). |
| The estimates for the logit model are used as starting points for the estimation |
| Model: | Mixed Logit for panel data |
| Number of Hess-Train draws: | 500 |
| Number of estimated parameters: | 6 |
| Number of observations: | 6768 |
| Number of individuals: | 752 |
| Null log likelihood: | -6964.663 |
| Init log likelihood: | -3840.088 |
| Final log likelihood: | -3837.739 |
| Likelihood ratio test: | 6253.847 |
| Rho-square: | 0.449 |
| Adjusted rho-square: | 0.448 |
| Final gradient norm: | +4.594e-05 |
| Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
| Iterations: | 12 |
| Run time: | 02:22 |
| 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 | -1.03 | 0.197 | -5.24 | 0.00 | 0.646 | -1.60 | 0.11 | * | |
| ASC_SM | 0.00 | fixed | |||||||
| ASC_TRAIN | -2.19 | 0.234 | -9.37 | 0.00 | 0.482 | -4.54 | 0.00 | ||
| B_COST | -2.85 | 0.171 | -16.69 | 0.00 | 0.424 | -6.73 | 0.00 | ||
| B_TIME | -2.90 | 0.146 | -19.85 | 0.00 | 0.590 | -4.92 | 0.00 | ||
| SIGMA_CAR | 4.08 | 0.304 | 13.42 | 0.00 | 1.18 | 3.46 | 0.00 | ||
| SIGMA_TRAIN | 3.55 | 0.222 | 15.99 | 0.00 | 0.271 | 13.10 | 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 |
| 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 | 16.7 | 2.49 | 6.71 | ||
| ZERO_SIGMA_TRAIN | 12.6 | 1.58 | 7.99 |
| Coefficient1 | Coefficient2 | Covariance | Correlation | t-test | p-value | Rob. cov. | Rob. corr. | Rob. t-test | p-value | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| B_COST | B_TIME | 0.0118 | 0.474 | 0.32 | 0.75 | * | 0.0296 | 0.118 | 0.08 | 0.94 | * |
| SIGMA_CAR | SIGMA_TRAIN | 0.00638 | 0.0944 | 1.48 | 0.14 | * | 0.0403 | 0.126 | 0.45 | 0.65 | * |
| ASC_TRAIN | B_TIME | -0.0105 | -0.307 | 2.29 | 0.02 | -0.226 | -0.793 | 0.70 | 0.48 | * | |
| ASC_TRAIN | B_COST | 0.000972 | 0.0244 | 2.31 | 0.02 | 0.0649 | 0.318 | 1.25 | 0.21 | * | |
| ASC_CAR | B_TIME | 0.000331 | 0.0115 | 7.65 | 0.00 | -0.146 | -0.382 | 1.82 | 0.07 | * | |
| ASC_CAR | ASC_TRAIN | 0.00504 | 0.109 | 4.00 | 0.00 | 0.206 | 0.661 | 2.37 | 0.02 | ||
| ASC_CAR | SIGMA_CAR | -0.0132 | -0.220 | -12.88 | 0.00 | -0.660 | -0.865 | -2.89 | 0.00 | ||
| ASC_CAR | B_COST | 0.0118 | 0.351 | 8.61 | 0.00 | 0.186 | 0.680 | 3.83 | 0.00 | ||
| ASC_TRAIN | SIGMA_CAR | 0.00793 | 0.112 | -17.31 | 0.00 | -0.205 | -0.361 | -4.39 | 0.00 | ||
| B_COST | SIGMA_CAR | -0.0296 | -0.569 | -16.30 | 0.00 | -0.325 | -0.649 | -4.65 | 0.00 | ||
| B_TIME | SIGMA_CAR | -0.0295 | -0.662 | -16.80 | 0.00 | 0.0227 | 0.0325 | -5.36 | 0.00 | ||
| ASC_CAR | SIGMA_TRAIN | -0.00367 | -0.0838 | -14.83 | 0.00 | -0.0200 | -0.115 | -6.30 | 0.00 | ||
| B_TIME | SIGMA_TRAIN | -0.00365 | -0.112 | -23.11 | 0.00 | -0.0348 | -0.217 | -9.21 | 0.00 | ||
| ASC_TRAIN | SIGMA_TRAIN | -0.0300 | -0.577 | -14.18 | 0.00 | -0.0219 | -0.167 | -9.71 | 0.00 | ||
| B_COST | SIGMA_TRAIN | -0.00411 | -0.108 | -21.74 | 0.00 | -0.0242 | -0.211 | -11.66 | 0.00 |
Smallest singular value of the hessian: 4.75116