This file has automatically been generated.
Sun Dec 18 15:28:12 2011
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). |
For seminonparametric terms are included to test the distribution of the error component for the Train alternative (see Fosgerau and Bierlaire, 2007) |
Model: | Mixed Multinomial Logit for panel data |
Number of draws: | 5 |
Number of estimated parameters: | 11 |
Number of observations: | 6768 |
Number of individuals: | 752 |
Null log-likelihood: | -6964.663 |
Init log-likelihood: | -6155.783 |
Final log-likelihood: | -4714.746 |
Likelihood ratio test: | 4499.835 |
Rho-square: | 0.323 |
Adjusted rho-square: | 0.321 |
Final gradient norm: | +3.805e-04 |
Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
Iterations: | 26 |
Run time: | 00:07 |
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 | -0.0287 | 0.0700 | -0.41 | 0.68 | * | 0.273 | -0.11 | 0.92 | * |
ASC_SM | 0.00 | fixed | |||||||
ASC_TRAIN | -0.932 | 0.0978 | -9.53 | 0.00 | 0.382 | -2.44 | 0.01 | ||
B_COST | -1.49 | 0.0752 | -19.86 | 0.00 | 0.260 | -5.73 | 0.00 | ||
B_TIME | -1.54 | 0.0833 | -18.53 | 0.00 | 0.454 | -3.40 | 0.00 | ||
SIGMA_CAR | -0.779 | 0.106 | -7.34 | 0.00 | 0.362 | -2.15 | 0.03 | ||
SIGMA_SM | 1.54 | 0.0807 | 19.08 | 0.00 | 0.260 | 5.93 | 0.00 | ||
SIGMA_TRAIN | -1.83 | 0.109 | -16.79 | 0.00 | 0.350 | -5.21 | 0.00 | ||
SMP1 | 0.699 | 0.0224 | 31.17 | 0.00 | 0.0219 | 31.96 | 0.00 | ||
SMP2 | -0.633 | 0.0275 | -23.04 | 0.00 | 0.0271 | -23.34 | 0.00 | ||
SMP3 | 0.431 | 0.0286 | 15.04 | 0.00 | 0.0286 | 15.06 | 0.00 | ||
SMP4 | -0.105 | 0.0245 | -4.30 | 0.00 | 0.0231 | -4.56 | 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 |
Base parameter: ZERO_SIGMA_TRAIN
List of terms:
Term of order | Coefficient |
---|---|
1 | SMP1 |
2 | SMP2 |
3 | SMP3 |
4 | SMP4 |
Name | Value | Std err | t-test | Robust Std err | Robust t-test |
---|---|---|---|---|---|
ZERO_SIGMA_CAR | 0.607 | 0.166 | 3.67 | ||
ZERO_SIGMA_SM | 3.37 | 0.249 | 13.56 | ||
ZERO_SIGMA_TRAIN | 3.33 | 0.397 | 8.39 |
Coefficient1 | Coefficient2 | Covariance | Correlation | t-test | p-value | Rob. cov. | Rob. corr. | Rob. t-test | p-value | ||
---|---|---|---|---|---|---|---|---|---|---|---|
B_COST | B_TIME | 0.00127 | 0.202 | 0.50 | 0.62 | * | 0.0343 | 0.290 | 0.11 | 0.91 | * |
ASC_CAR | SMP4 | 1.12e-11 | 6.51e-09 | 1.03 | 0.30 | * | -0.000250 | -0.0396 | 0.28 | 0.78 | * |
ASC_TRAIN | SIGMA_CAR | -7.99e-05 | -0.00769 | -1.05 | 0.29 | * | 0.0124 | 0.0894 | -0.30 | 0.76 | * |
SIGMA_CAR | SMP2 | -1.31e-11 | -4.48e-09 | -1.33 | 0.18 | * | 8.59e-05 | 0.00875 | -0.40 | 0.69 | * |
B_TIME | SIGMA_TRAIN | -0.000964 | -0.106 | 1.96 | 0.05 | -0.0318 | -0.200 | 0.45 | 0.65 | * | |
B_COST | SIGMA_TRAIN | -0.000565 | -0.0691 | 2.44 | 0.01 | -0.00615 | -0.0675 | 0.74 | 0.46 | * | |
ASC_TRAIN | SMP2 | 1.76e-11 | 6.55e-09 | -2.94 | 0.00 | -0.000324 | -0.0313 | -0.78 | 0.44 | * | |
ASC_TRAIN | B_TIME | -0.00524 | -0.643 | 3.72 | 0.00 | -0.160 | -0.921 | 0.75 | 0.46 | * | |
ASC_TRAIN | B_COST | 1.38e-05 | 0.00188 | 4.55 | 0.00 | -0.0141 | -0.142 | 1.14 | 0.25 | * | |
B_COST | SIGMA_CAR | 0.000314 | 0.0394 | -5.59 | 0.00 | -0.00502 | -0.0533 | -1.56 | 0.12 | * | |
B_TIME | SIGMA_CAR | 3.02e-05 | 0.00341 | -5.67 | 0.00 | -0.0191 | -0.116 | -1.25 | 0.21 | * | |
ASC_CAR | SMP3 | -8.35e-12 | -4.16e-09 | -6.08 | 0.00 | 1.45e-05 | 0.00185 | -1.67 | 0.09 | * | |
SIGMA_CAR | SMP4 | 2.41e-12 | 9.28e-10 | -6.19 | 0.00 | 4.35e-05 | 0.00520 | -1.86 | 0.06 | * | |
ASC_CAR | SIGMA_CAR | 0.00169 | 0.227 | 6.63 | 0.00 | 0.0279 | 0.282 | 1.94 | 0.05 | * | |
SIGMA_CAR | SIGMA_TRAIN | -2.26e-05 | -0.00196 | 6.88 | 0.00 | 0.00310 | 0.0244 | 2.10 | 0.04 | ||
ASC_TRAIN | SIGMA_TRAIN | 0.00372 | 0.349 | 7.56 | 0.00 | 0.0372 | 0.278 | 2.03 | 0.04 | ||
ASC_CAR | SMP2 | 3.80e-12 | 1.97e-09 | 8.04 | 0.00 | -0.000295 | -0.0398 | 2.19 | 0.03 | ||
ASC_TRAIN | SMP4 | 1.82e-11 | 7.62e-09 | -8.20 | 0.00 | -0.000195 | -0.0221 | -2.16 | 0.03 | ||
SMP1 | SMP3 | 0.000222 | 0.346 | 9.05 | 0.00 | 0.000187 | 0.298 | 8.83 | 0.00 | ||
ASC_CAR | SMP1 | -1.07e-11 | -6.79e-09 | -9.90 | 0.00 | 4.94e-05 | 0.00826 | -2.66 | 0.01 | ||
SIGMA_SM | SMP1 | -3.52e-12 | -1.95e-09 | 10.03 | 0.00 | -0.000163 | -0.0287 | 3.22 | 0.00 | ||
B_TIME | SMP2 | -8.28e-12 | -3.62e-09 | -10.38 | 0.00 | 0.000584 | 0.0474 | -2.01 | 0.04 | ||
SIGMA_TRAIN | SMP2 | 5.89e-12 | 1.97e-09 | -10.63 | 0.00 | -0.000374 | -0.0394 | -3.39 | 0.00 | ||
B_COST | SMP2 | -4.63e-12 | -2.24e-09 | -10.74 | 0.00 | 4.92e-05 | 0.00697 | -3.29 | 0.00 | ||
SIGMA_CAR | SMP3 | -6.76e-12 | -2.22e-09 | -11.01 | 0.00 | 0.000124 | 0.0120 | -3.34 | 0.00 | ||
ASC_CAR | B_TIME | -0.00346 | -0.594 | 11.06 | 0.00 | -0.112 | -0.903 | 2.13 | 0.03 | ||
ASC_CAR | ASC_TRAIN | 0.00409 | 0.597 | 11.39 | 0.00 | 0.0938 | 0.897 | 4.94 | 0.00 | ||
SIGMA_SM | SMP3 | -2.21e-12 | -9.55e-10 | 12.95 | 0.00 | -5.80e-05 | -0.00780 | 4.24 | 0.00 | ||
ASC_TRAIN | SMP3 | -1.57e-11 | -5.61e-09 | -13.37 | 0.00 | -6.70e-05 | -0.00612 | -3.55 | 0.00 | ||
SMP3 | SMP4 | -7.73e-05 | -0.110 | 13.51 | 0.00 | -3.78e-05 | -0.0572 | 14.19 | 0.00 | ||
SIGMA_CAR | SMP1 | -9.71e-12 | -4.08e-09 | -13.63 | 0.00 | -1.71e-05 | -0.00216 | -4.08 | 0.00 | ||
ASC_CAR | SIGMA_TRAIN | 0.000414 | 0.0544 | 14.25 | 0.00 | 0.0154 | 0.160 | 4.40 | 0.00 | ||
ASC_CAR | B_COST | 0.000721 | 0.137 | 15.34 | 0.00 | -0.00744 | -0.104 | 3.69 | 0.00 | ||
SIGMA_TRAIN | SMP4 | 1.21e-11 | 4.53e-09 | -15.43 | 0.00 | -0.000354 | -0.0438 | -4.89 | 0.00 | ||
ASC_TRAIN | SMP1 | -1.31e-11 | -5.99e-09 | -16.25 | 0.00 | 3.03e-05 | 0.00362 | -4.26 | 0.00 | ||
B_TIME | SMP4 | -8.40e-12 | -4.12e-09 | -16.57 | 0.00 | 0.000480 | 0.0457 | -3.17 | 0.00 | ||
ASC_CAR | SIGMA_SM | 0.00143 | 0.252 | -16.95 | 0.00 | 0.0346 | 0.488 | -5.81 | 0.00 | ||
B_COST | SMP4 | -2.08e-13 | -1.13e-10 | -17.56 | 0.00 | 5.13e-05 | 0.00853 | -5.31 | 0.00 | ||
SMP1 | SMP4 | -0.000407 | -0.741 | 18.38 | 0.00 | -0.000340 | -0.673 | 19.56 | 0.00 | ||
SMP2 | SMP4 | 0.000288 | 0.428 | -18.93 | 0.00 | 0.000234 | 0.373 | -18.66 | 0.00 | ||
SIGMA_SM | SMP4 | 1.94e-12 | 9.82e-10 | 19.50 | 0.00 | 0.000107 | 0.0178 | 6.32 | 0.00 | ||
SIGMA_CAR | SIGMA_SM | 0.00200 | 0.234 | -19.76 | 0.00 | 0.0505 | 0.537 | -7.43 | 0.00 | ||
SIGMA_TRAIN | SMP3 | -1.32e-11 | -4.24e-09 | -20.06 | 0.00 | 0.000289 | 0.0288 | -6.44 | 0.00 | ||
ASC_TRAIN | SIGMA_SM | 0.00156 | 0.198 | -21.71 | 0.00 | 0.0426 | 0.428 | -6.89 | 0.00 | ||
B_TIME | SMP3 | 3.85e-12 | 1.62e-09 | -22.42 | 0.00 | -0.000167 | -0.0128 | -4.33 | 0.00 | ||
SIGMA_TRAIN | SMP1 | -1.28e-11 | -5.26e-09 | -22.74 | 0.00 | 0.000257 | 0.0335 | -7.21 | 0.00 | ||
B_TIME | SIGMA_SM | -0.00224 | -0.333 | -23.03 | 0.00 | -0.0501 | -0.425 | -5.04 | 0.00 | ||
B_COST | SMP3 | -2.34e-12 | -1.09e-09 | -23.92 | 0.00 | 0.000242 | 0.0324 | -7.37 | 0.00 | ||
B_COST | SIGMA_SM | -0.00178 | -0.293 | -24.19 | 0.00 | -0.0149 | -0.220 | -7.46 | 0.00 | ||
SMP2 | SMP3 | -0.000175 | -0.222 | -24.25 | 0.00 | -0.000174 | -0.225 | -24.39 | 0.00 | ||
SIGMA_SM | SMP2 | -1.21e-12 | -5.45e-10 | 25.48 | 0.00 | -3.54e-05 | -0.00503 | 8.31 | 0.00 | ||
B_TIME | SMP1 | 5.22e-12 | 2.79e-09 | -26.00 | 0.00 | -0.000124 | -0.0125 | -4.93 | 0.00 | ||
B_COST | SMP1 | -2.10e-12 | -1.24e-09 | -27.95 | 0.00 | 7.88e-05 | 0.0138 | -8.40 | 0.00 | ||
SIGMA_SM | SIGMA_TRAIN | 0.00285 | 0.325 | 29.94 | 0.00 | 0.0566 | 0.623 | 12.14 | 0.00 | ||
SMP1 | SMP2 | 3.95e-05 | 0.0641 | 38.80 | 0.00 | 5.35e-05 | 0.0901 | 40.03 | 0.00 |
Smallest singular value of the hessian: 5.71165