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Wed Jul 6 20:17:01 2016
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. |
| 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: | -3841.012 |
| Final log likelihood: | -3839.008 |
| Likelihood ratio test: | 6251.311 |
| Rho-square: | 0.449 |
| Adjusted rho-square: | 0.448 |
| Final gradient norm: | +3.094e-05 |
| Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
| Iterations: | 12 |
| Run time: | 03:20 |
| 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 | -0.906 | 0.193 | -4.69 | 0.00 | 0.523 | -1.73 | 0.08 | * | |
| ASC_SM | 0.00 | fixed | |||||||
| ASC_TRAIN | -1.93 | 0.223 | -8.67 | 0.00 | 0.356 | -5.43 | 0.00 | ||
| B_COST | -2.77 | 0.168 | -16.51 | 0.00 | 0.330 | -8.38 | 0.00 | ||
| B_TIME | -3.04 | 0.144 | -21.09 | 0.00 | 0.567 | -5.37 | 0.00 | ||
| SIGMA_CAR | 4.14 | 0.266 | 15.56 | 0.00 | 0.636 | 6.51 | 0.00 | ||
| SIGMA_TRAIN | 3.37 | 0.193 | 17.46 | 0.00 | 0.298 | 11.32 | 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 | inf | 2.20 | inf | ||
| ZERO_SIGMA_TRAIN | 11.4 | 1.30 | 8.73 |
| Coefficient1 | Coefficient2 | Covariance | Correlation | t-test | p-value | Rob. cov. | Rob. corr. | Rob. t-test | p-value | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| B_COST | B_TIME | 0.0123 | 0.508 | 1.77 | 0.08 | * | 0.0441 | 0.236 | 0.47 | 0.64 | * |
| SIGMA_CAR | SIGMA_TRAIN | 0.00675 | 0.132 | 2.50 | 0.01 | -0.0480 | -0.254 | 1.00 | 0.32 | * | |
| ASC_TRAIN | B_TIME | -0.0102 | -0.318 | 3.69 | 0.00 | -0.145 | -0.721 | 1.29 | 0.20 | * | |
| ASC_TRAIN | B_COST | -0.00380 | -0.102 | 2.86 | 0.00 | 0.0136 | 0.115 | 1.83 | 0.07 | * | |
| ASC_CAR | ASC_TRAIN | 0.00162 | 0.0377 | 3.54 | 0.00 | 0.0921 | 0.495 | 2.20 | 0.03 | ||
| ASC_CAR | B_TIME | 0.00260 | 0.0935 | 9.29 | 0.00 | -0.117 | -0.393 | 2.35 | 0.02 | ||
| ASC_CAR | B_COST | 0.0118 | 0.364 | 9.10 | 0.00 | 0.0750 | 0.434 | 3.86 | 0.00 | ||
| ASC_CAR | SIGMA_CAR | -0.0176 | -0.343 | -13.33 | 0.00 | -0.278 | -0.835 | -4.54 | 0.00 | ||
| ASC_TRAIN | SIGMA_CAR | 0.00974 | 0.164 | -19.11 | 0.00 | -0.0320 | -0.142 | -7.87 | 0.00 | ||
| B_TIME | SIGMA_TRAIN | -0.00514 | -0.185 | -24.53 | 0.00 | -0.115 | -0.684 | -8.01 | 0.00 | ||
| B_COST | SIGMA_CAR | -0.0279 | -0.626 | -17.56 | 0.00 | -0.0929 | -0.442 | -8.26 | 0.00 | ||
| B_TIME | SIGMA_CAR | -0.0256 | -0.667 | -19.01 | 0.00 | -0.00831 | -0.0230 | -8.33 | 0.00 | ||
| ASC_CAR | SIGMA_TRAIN | 0.00333 | 0.0895 | -16.42 | 0.00 | 0.0841 | 0.540 | -9.71 | 0.00 | ||
| ASC_TRAIN | SIGMA_TRAIN | -0.0245 | -0.569 | -14.39 | 0.00 | 0.0282 | 0.266 | -13.31 | 0.00 | ||
| B_COST | SIGMA_TRAIN | -0.00197 | -0.0608 | -23.32 | 0.00 | -0.00269 | -0.0274 | -13.62 | 0.00 |
Smallest singular value of the hessian: 4.76873