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Thu Jul 7 08:50:41 2016
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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. The model is not identified, but its estimation is required to identify which SIGMA should be normalized (see Walker, 2001). |
| The time coefficient is assumed to be distributed. It is a discrete distribution with two mass points, one at 0, and one at B_TIME_OTHER. The probabilities assoviated with each mass point are W_0 and W_OTHER, respectively. |
| Model: | Mixed Logit for panel data |
| Number of Hess-Train draws: | 500 |
| Number of estimated parameters: | 9 |
| Number of observations: | 6768 |
| Number of individuals: | 752 |
| Null log likelihood: | -6964.663 |
| Init log likelihood: | -6171.531 |
| Final log likelihood: | -3614.780 |
| Likelihood ratio test: | 6699.766 |
| Rho-square: | 0.481 |
| Adjusted rho-square: | 0.480 |
| Final gradient norm: | +1.063e+03 |
| Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
| Iterations: | 142 |
| Run time: | 12h 28:43 |
| Variance-covariance: | from finite difference hessian |
| Sample file: | ../swissmetro.dat |
| Name | Value | Std err | t-test | p-value | |||||
|---|---|---|---|---|---|---|---|---|---|
| ASC_CAR | 0.110 | 0.203 | 0.54 | 0.59 | * | ||||
| ASC_SM | 0.00 | fixed | |||||||
| ASC_TRAIN | -1.02 | 0.232 | -4.38 | 0.00 | |||||
| B_COST | -3.08 | 0.175 | -17.61 | 0.00 | |||||
| B_TIME_0 | 0.00 | fixed | |||||||
| B_TIME_OTHER | -6.29 | 0.300 | -20.99 | 0.00 | |||||
| SIGMA_CAR | 3.72 | 0.251 | 14.82 | 0.00 | |||||
| SIGMA_SM | 0.860 | 0.311 | 2.77 | 0.01 | |||||
| SIGMA_TRAIN | -3.09 | 0.223 | -13.87 | 0.00 | |||||
| W_0 | 0.202 | 0.0253 | 8.01 | 0.00 | |||||
| W_OTHER | 0.798 | 0.0253 | 31.54 | 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 | 13.8 | 1.87 | 7.41 | ||
| ZERO_SIGMA_SM | 4.76 | 0.535 | 8.88 | ||
| ZERO_SIGMA_TRAIN | 14.7 | 1.38 | 10.68 |
| Coefficient1 | Coefficient2 | Covariance | Correlation | t-test | p-value | Rob. cov. | Rob. corr. | Rob. t-test | p-value | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| ASC_CAR | ASC_TRAIN | 0.0104 | 0.222 | 4.14 | 0.00 | ||||||
| ASC_CAR | B_COST | 0.0102 | 0.288 | 14.09 | 0.00 | ||||||
| ASC_CAR | B_TIME_OTHER | -0.0102 | -0.167 | 16.46 | 0.00 | ||||||
| ASC_CAR | SIGMA_CAR | -0.0138 | -0.272 | -9.94 | 0.00 | ||||||
| ASC_CAR | SIGMA_SM | 0.0174 | 0.276 | -2.34 | 0.02 | ||||||
| ASC_CAR | SIGMA_TRAIN | -8.29e-05 | -0.00184 | 10.62 | 0.00 | ||||||
| ASC_CAR | W_0 | -0.000394 | -0.0769 | -0.45 | 0.66 | * | |||||
| ASC_CAR | W_OTHER | 0.000394 | 0.0769 | -3.40 | 0.00 | ||||||
| ASC_TRAIN | B_COST | 0.00211 | 0.0521 | 7.30 | 0.00 | ||||||
| ASC_TRAIN | B_TIME_OTHER | -0.00731 | -0.105 | 13.27 | 0.00 | ||||||
| ASC_TRAIN | SIGMA_CAR | -0.000733 | -0.0126 | -13.77 | 0.00 | ||||||
| ASC_TRAIN | SIGMA_SM | 0.0110 | 0.153 | -5.24 | 0.00 | ||||||
| ASC_TRAIN | SIGMA_TRAIN | 0.0284 | 0.550 | 9.61 | 0.00 | ||||||
| ASC_TRAIN | W_0 | -0.00125 | -0.214 | -5.11 | 0.00 | ||||||
| ASC_TRAIN | W_OTHER | 0.00125 | 0.214 | -7.96 | 0.00 | ||||||
| B_COST | B_TIME_OTHER | 0.0242 | 0.461 | 11.96 | 0.00 | ||||||
| B_COST | SIGMA_CAR | -0.0239 | -0.544 | -18.09 | 0.00 | ||||||
| B_COST | SIGMA_SM | -0.000805 | -0.0148 | -10.97 | 0.00 | ||||||
| B_COST | SIGMA_TRAIN | 0.00633 | 0.162 | 0.04 | 0.97 | * | |||||
| B_COST | W_0 | -0.000558 | -0.126 | -18.25 | 0.00 | ||||||
| B_COST | W_OTHER | 0.000558 | 0.126 | -22.35 | 0.00 | ||||||
| B_TIME_OTHER | SIGMA_CAR | -0.0378 | -0.502 | -20.94 | 0.00 | ||||||
| B_TIME_OTHER | SIGMA_SM | -0.0117 | -0.125 | -15.61 | 0.00 | ||||||
| B_TIME_OTHER | SIGMA_TRAIN | 0.0192 | 0.287 | -10.07 | 0.00 | ||||||
| B_TIME_OTHER | W_0 | -0.00280 | -0.369 | -20.95 | 0.00 | ||||||
| B_TIME_OTHER | W_OTHER | 0.00280 | 0.369 | -24.33 | 0.00 | ||||||
| SIGMA_CAR | SIGMA_SM | -0.0271 | -0.347 | 6.18 | 0.00 | ||||||
| SIGMA_CAR | SIGMA_TRAIN | -0.00946 | -0.169 | 18.77 | 0.00 | ||||||
| SIGMA_CAR | W_0 | 0.00112 | 0.177 | 14.19 | 0.00 | ||||||
| SIGMA_CAR | W_OTHER | -0.00112 | -0.177 | 11.38 | 0.00 | ||||||
| SIGMA_SM | SIGMA_TRAIN | 0.00875 | 0.126 | 11.00 | 0.00 | ||||||
| SIGMA_SM | W_0 | -0.000321 | -0.0408 | 2.10 | 0.04 | ||||||
| SIGMA_SM | W_OTHER | 0.000321 | 0.0408 | 0.20 | 0.84 | * | |||||
| SIGMA_TRAIN | W_0 | -0.000330 | -0.0586 | -14.59 | 0.00 | ||||||
| SIGMA_TRAIN | W_OTHER | 0.000330 | 0.0586 | -17.45 | 0.00 | ||||||
| W_0 | W_OTHER | -0.000639 | -1.00 | -11.77 | 0.00 |
1*W_0 + 1*W_OTHER = 1 [1 = 1]
Smallest singular value of the hessian: 0.00132978