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Tue Feb 21 07:30:50 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 sigma associated with Swissmetro is normalized to 0, as a previous estimation identified it as the minimum variance (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: | 6 |
Number of observations: | 6768 |
Number of individuals: | 752 |
Null log-likelihood: | -6964.663 |
Init log-likelihood: | -3789.894 |
Final log-likelihood: | -3787.169 |
Likelihood ratio test: | 6354.988 |
Rho-square: | 0.456 |
Adjusted rho-square: | 0.455 |
Final gradient norm: | +8.179e-06 |
Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
Iterations: | 13 |
Run time: | 09h 36:18 |
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 | -0.767 | 0.190 | -4.03 | 0.00 | 0.301 | -2.55 | 0.01 | ||
ASC_SM | 0.00 | fixed | |||||||
ASC_TRAIN | -2.08 | 0.252 | -8.23 | 0.00 | 0.341 | -6.09 | 0.00 | ||
B_COST | -3.13 | 0.178 | -17.54 | 0.00 | 0.304 | -10.29 | 0.00 | ||
B_TIME | -3.31 | 0.156 | -21.16 | 0.00 | 0.472 | -7.01 | 0.00 | ||
SIGMA_CAR | 4.23 | 0.256 | 16.55 | 0.00 | 0.600 | 7.06 | 0.00 | ||
SIGMA_TRAIN | 3.60 | 0.215 | 16.79 | 0.00 | 0.245 | 14.70 | 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 | 17.9 | 2.17 | 8.27 | ||
ZERO_SIGMA_TRAIN | 13.0 | 1.55 | 8.40 |
Coefficient1 | Coefficient2 | Covariance | Correlation | t-test | p-value | Rob. cov. | Rob. corr. | Rob. t-test | p-value | ||
---|---|---|---|---|---|---|---|---|---|---|---|
B_COST | B_TIME | 0.0131 | 0.470 | 1.02 | 0.31 | * | 0.0810 | 0.565 | 0.45 | 0.65 | * |
SIGMA_CAR | SIGMA_TRAIN | 0.00757 | 0.138 | 2.03 | 0.04 | 0.0253 | 0.172 | 1.04 | 0.30 | * | |
ASC_TRAIN | B_COST | 0.000758 | 0.0168 | 3.44 | 0.00 | -0.0251 | -0.242 | 2.07 | 0.04 | ||
ASC_TRAIN | B_TIME | -0.0120 | -0.305 | 3.67 | 0.00 | -0.114 | -0.706 | 1.63 | 0.10 | * | |
ASC_CAR | ASC_TRAIN | 0.00151 | 0.0315 | 4.21 | 0.00 | 0.000728 | 0.00709 | 2.89 | 0.00 | ||
ASC_CAR | B_COST | 0.00677 | 0.199 | 10.11 | 0.00 | 0.0450 | 0.492 | 7.74 | 0.00 | ||
ASC_CAR | B_TIME | 0.000283 | 0.00952 | 10.36 | 0.00 | 0.0137 | 0.0964 | 4.75 | 0.00 | ||
ASC_TRAIN | SIGMA_TRAIN | -0.0325 | -0.600 | -13.59 | 0.00 | -0.0170 | -0.203 | -12.39 | 0.00 | ||
ASC_CAR | SIGMA_CAR | -0.00370 | -0.0760 | -15.14 | 0.00 | -0.135 | -0.749 | -5.89 | 0.00 | ||
ASC_CAR | SIGMA_TRAIN | -0.000155 | -0.00380 | -15.21 | 0.00 | -0.00723 | -0.0979 | -10.75 | 0.00 | ||
B_TIME | SIGMA_CAR | -0.0309 | -0.772 | -19.36 | 0.00 | -0.107 | -0.377 | -8.45 | 0.00 | ||
B_COST | SIGMA_CAR | -0.0213 | -0.466 | -19.69 | 0.00 | -0.0878 | -0.482 | -9.29 | 0.00 | ||
ASC_TRAIN | SIGMA_CAR | 0.0143 | 0.221 | -19.91 | 0.00 | 0.0483 | 0.236 | -10.24 | 0.00 | ||
B_COST | SIGMA_TRAIN | -0.00633 | -0.165 | -22.38 | 0.00 | -0.0239 | -0.321 | -15.05 | 0.00 | ||
B_TIME | SIGMA_TRAIN | -0.00519 | -0.155 | -24.30 | 0.00 | -0.0412 | -0.357 | -11.44 | 0.00 |
Smallest singular value of the hessian: 4.73825