biogeme 2.6a [Mon Apr 17 15:32:48 CEST 2017]
Michel Bierlaire, EPFL
This file has automatically been generated.
Tue Apr 18 19:33:02 2017
Tip: click on the columns headers to sort a table [Credits]
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Example of a mixture of logit model with panel data, for a transportation mode choice with 3 alternatives:
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- Train
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- Car
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- Swissmetro, an hypothetical high-speed train
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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).
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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.
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| 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: | -3715.863 |
| Likelihood ratio test: | 6497.599 |
| Rho-square: | 0.466 |
| Adjusted rho-square: | 0.465 |
| Final gradient norm: | +2.010e+11 |
| Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
| Iterations: | 53 |
| Run time: | 18:22 |
| Variance-covariance: | from finite difference hessian |
| Sample file: | ../swissmetro.dat |
Utility parameters
| Name | Value | Std err | t-test | p-value | |
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| ASC_CAR | 0.157 | 0.0143 | 10.93 | 0.00 | | | | | |
| ASC_SM | 0.00 | fixed | | | | | | | |
| ASC_TRAIN | -1.31 | 0.214 | -6.12 | 0.00 | | | | | |
| B_COST | -2.78 | 0.143 | -19.42 | 0.00 | | | | | |
| B_TIME_0 | 0.00 | fixed | | | | | | | |
| B_TIME_OTHER | -4.42 | 0.159 | -27.73 | 0.00 | | | | | |
| SIGMA_CAR | 3.33 | 0.211 | 15.75 | 0.00 | | | | | |
| SIGMA_SM | 1.42 | 0.182 | 7.83 | 0.00 | | | | | |
| SIGMA_TRAIN | -3.43 | 0.230 | -14.95 | 0.00 | | | | | |
| W_0 | 9.95e-12 | 2.72e-10 | 0.04 | 0.97 | * | | | | |
| W_OTHER | 1.00 | 0.0486 | 20.57 | 0.00 | | | | | |
| ZERO | 0.00 | fixed | | | | | | | |
Utility functions
| Id | Name | Availability | Specification |
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| 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 |
Variance of random coefficients
| Name | Value | Std err | t-test | Robust Std err | Robust t-test |
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ZERO_SIGMA_CAR | 11.1 | 1.41 | 7.87 | |
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ZERO_SIGMA_SM | 2.02 | 0.516 | 3.92 | |
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ZERO_SIGMA_TRAIN | 1.64e+177 | 1.58 | 1041049566046618132718899763830902769673906427582254461119785963330686852859266869775041594777911198389303320394027517804685217257791990721444195332318679275862932195563244879872.00 | |
Correlation of coefficients
| Coefficient1 | Coefficient2 | Covariance | Correlation | t-test | p-value | | Rob. cov. | Rob. corr. | Rob. t-test | p-value | |
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ASC_CAR | ASC_TRAIN | -2.92e-05 | -0.00952 | 6.83 | 0.00 | | |
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ASC_CAR | B_COST | -5.47e-05 | -0.0266 | 20.36 | 0.00 | | |
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ASC_CAR | B_TIME_OTHER | 9.05e-05 | 0.0396 | 28.70 | 0.00 | | |
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ASC_CAR | SIGMA_CAR | 7.34e-05 | 0.0242 | -15.00 | 0.00 | | |
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ASC_CAR | SIGMA_SM | -1.51e-05 | -0.00579 | -6.95 | 0.00 | | |
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ASC_CAR | SIGMA_TRAIN | 2.93e-05 | 0.00890 | 15.61 | 0.00 | | |
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ASC_CAR | W_0 | 0.00216 | 5.54e+08 | 0.00 | 1.00 | * | |
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ASC_CAR | W_OTHER | 7.07e-14 | 1.01e-10 | -16.64 | 0.00 | | |
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ASC_TRAIN | B_COST | 0.0113 | 0.366 | 7.02 | 0.00 | | |
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ASC_TRAIN | B_TIME_OTHER | -0.0103 | -0.302 | 10.24 | 0.00 | | |
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ASC_TRAIN | SIGMA_CAR | 0.0168 | 0.372 | -19.45 | 0.00 | | |
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ASC_TRAIN | SIGMA_SM | 0.000242 | 0.00622 | -9.77 | 0.00 | | |
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ASC_TRAIN | SIGMA_TRAIN | 0.0223 | 0.454 | 9.13 | 0.00 | | |
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ASC_TRAIN | W_0 | 2.98e-17 | 5.11e-07 | -6.12 | 0.00 | | |
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ASC_TRAIN | W_OTHER | -0.00120 | -0.116 | -10.27 | 0.00 | | |
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B_COST | B_TIME_OTHER | 0.00771 | 0.338 | 9.35 | 0.00 | | |
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B_COST | SIGMA_CAR | -0.0135 | -0.446 | -20.12 | 0.00 | | |
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B_COST | SIGMA_SM | -0.00855 | -0.329 | -15.83 | 0.00 | | |
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B_COST | SIGMA_TRAIN | 0.0253 | 0.767 | 4.31 | 0.00 | | |
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B_COST | W_0 | 1.01e-17 | 2.60e-07 | -19.42 | 0.00 | | |
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B_COST | W_OTHER | 0.00474 | 0.680 | -32.64 | 0.00 | | |
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B_TIME_OTHER | SIGMA_CAR | -0.0275 | -0.816 | -21.91 | 0.00 | | |
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B_TIME_OTHER | SIGMA_SM | -0.00134 | -0.0463 | -23.64 | 0.00 | | |
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B_TIME_OTHER | SIGMA_TRAIN | 0.0299 | 0.818 | -7.28 | 0.00 | | |
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B_TIME_OTHER | W_0 | 1.48e-17 | 3.40e-07 | -27.73 | 0.00 | | |
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B_TIME_OTHER | W_OTHER | 0.000810 | 0.105 | -33.52 | 0.00 | | |
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SIGMA_CAR | SIGMA_SM | -0.000998 | -0.0260 | 6.76 | 0.00 | | |
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SIGMA_CAR | SIGMA_TRAIN | -0.0398 | -0.819 | 16.08 | 0.00 | | |
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SIGMA_CAR | W_0 | -2.49e-17 | -4.33e-07 | 15.75 | 0.00 | | |
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SIGMA_CAR | W_OTHER | 0.00258 | 0.251 | 11.38 | 0.00 | | |
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SIGMA_SM | SIGMA_TRAIN | -0.00384 | -0.0921 | 15.89 | 0.00 | | |
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SIGMA_SM | W_0 | -3.37e-20 | -6.81e-10 | 7.83 | 0.00 | | |
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SIGMA_SM | W_OTHER | 0.00162 | 0.183 | 2.36 | 0.02 | | |
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SIGMA_TRAIN | W_0 | 3.30e-17 | 5.28e-07 | -14.95 | 0.00 | | |
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SIGMA_TRAIN | W_OTHER | -9.94e-05 | -0.00890 | -18.85 | 0.00 | | |
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W_0 | W_OTHER | -1.15e-18 | -8.68e-08 | -20.57 | 0.00 | | |
User defined linear constraints
1*W_0 + 1*W_OTHER = 1 [1 = 1]
Smallest singular value of the hessian: 4.4737e-06
Unidentifiable model
The log likelihood is (almost) flat along the following combinations of parameters
| Sing. value | = | 4.4737e-06 |
| 0.00168287 | * | Param[26] |
| -0.0752131 | * | Param[34] |
| 0.705103 | * | Param[44] |
| -0.705103 | * | Param[45] |
| Sing. value | = | 5.27237e-06 |
| 0.00397538 | * | ASC_TRAIN |
| 0.00118951 | * | B_COST |
| 0.00248431 | * | B_TIME_OTHER |
| -0.00229561 | * | SIGMA_CAR |
| -0.000711553 | * | SIGMA_SM |
| 0.00418114 | * | SIGMA_TRAIN |
| -0.0381252 | * | Param[9] |
| 0.031762 | * | Param[10] |
| -0.00585088 | * | Param[11] |
| -0.000699227 | * | Param[12] |
| -0.00222232 | * | Param[13] |
| 0.00863205 | * | Param[14] |
| -0.0053476 | * | Param[15] |
| -0.000170112 | * | Param[17] |
| 0.0356615 | * | Param[18] |
| 0.0784948 | * | Param[19] |
| 0.000286429 | * | Param[20] |
| -0.00130339 | * | Param[21] |
| -0.00168432 | * | Param[22] |
| -0.234094 | * | Param[23] |
| -0.00323306 | * | Param[24] |
| 0.951375 | * | Param[26] |
| -0.00395284 | * | Param[27] |
| -0.0292212 | * | Param[28] |
| 0.00164591 | * | Param[29] |
| 0.000437576 | * | Param[30] |
| -0.00147906 | * | Param[31] |
| 0.0553174 | * | Param[32] |
| 0.00255462 | * | Param[33] |
| -0.000120044 | * | Param[34] |
| -0.0365951 | * | Param[36] |
| -0.0669605 | * | Param[37] |
| -0.0004223 | * | Param[38] |
| -0.00032695 | * | Param[39] |
| 0.000875599 | * | Param[40] |
| 0.142185 | * | Param[41] |
| -0.00115635 | * | Param[42] |
| -0.00114208 | * | Param[44] |
| 0.00114137 | * | Param[45] |
| Sing. value | = | 6.29111e-06 |
| -0.000253471 | * | Param[26] |
| -0.997167 | * | Param[34] |
| -0.0531836 | * | Param[44] |
| 0.0531833 | * | Param[45] |
| Sing. value | = | 6.30888e-06 |
| 1 | * | Param[16] |