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Tue Apr 18 19:04:48 2017
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| Example of a logit model for a transportation mode choice with 3 alternatives: |
| - Train |
| - Car |
| - Swissmetro, an hypothetical high-speed train |
| 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 associated with each mass point are W_0 and W_OTHER, respectively. |
| Note that the model is unidentifiable. The objective of this example is to illustrate the Biogeme syntax only. |
| Model: | Logit |
| Number of estimated parameters: | 6 |
| Number of observations: | 6768 |
| Number of individuals: | 6768 |
| Null log likelihood: | -6964.663 |
| Init log likelihood: | -6964.663 |
| Final log likelihood: | -5208.498 |
| Likelihood ratio test: | 3512.330 |
| Rho-square: | 0.252 |
| Adjusted rho-square: | 0.251 |
| Final gradient norm: | +9.571e+03 |
| Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
| Iterations: | 20 |
| Run time: | 00:00 |
| Variance-covariance: | from analytical hessian |
| Sample file: | ../swissmetro.dat |
| Name | Value | Std err | t-test | p-value | |||||
|---|---|---|---|---|---|---|---|---|---|
| ASC_CAR | 0.125 | 0.0252 | 4.95 | 0.00 | |||||
| ASC_SM | 0.00 | fixed | |||||||
| ASC_TRAIN | -0.398 | 0.0259 | -15.38 | 0.00 | |||||
| B_COST | -1.26 | 0.0387 | -32.65 | 0.00 | |||||
| B_TIME_0 | 0.00 | fixed | |||||||
| B_TIME_OTHER | -2.80 | 1.27e+07 | -0.00 | 1.00 | * | ||||
| W_0 | 0.251 | 1.07e+08 | 0.00 | 1.00 | * | ||||
| W_OTHER | 0.749 | 1.07e+08 | 0.00 | 1.00 | * |
| Id | Name | Availability | Specification |
|---|---|---|---|
| 1 | A1_TRAIN | TRAIN_AV_SP | ASC_TRAIN * one + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED |
| 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 |
| Coefficient1 | Coefficient2 | Covariance | Correlation | t-test | p-value | Rob. cov. | Rob. corr. | Rob. t-test | p-value | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| ASC_CAR | ASC_TRAIN | 0.000257 | 0.395 | 18.61 | 0.00 | ||||||
| ASC_CAR | B_COST | 0.000328 | 0.337 | 36.15 | 0.00 | ||||||
| ASC_CAR | B_TIME_OTHER | 3.13e-20 | 9.79e-26 | 0.00 | 1.00 | * | |||||
| ASC_CAR | W_0 | -8.17e-22 | -3.05e-28 | -0.00 | 1.00 | * | |||||
| ASC_CAR | W_OTHER | -8.48e-22 | -3.16e-28 | -0.00 | 1.00 | * | |||||
| ASC_TRAIN | B_COST | 0.000219 | 0.219 | 20.84 | 0.00 | ||||||
| ASC_TRAIN | B_TIME_OTHER | 0.000108 | 3.29e-10 | 0.00 | 1.00 | * | |||||
| ASC_TRAIN | W_0 | -0.000442 | -1.60e-10 | -0.00 | 1.00 | * | |||||
| ASC_TRAIN | W_OTHER | 0.000442 | 1.60e-10 | -0.00 | 1.00 | * | |||||
| B_COST | B_TIME_OTHER | -0.00166 | -3.37e-09 | 0.00 | 1.00 | * | |||||
| B_COST | W_0 | 0.00679 | 1.65e-09 | -0.00 | 1.00 | * | |||||
| B_COST | W_OTHER | -0.00679 | -1.65e-09 | -0.00 | 1.00 | * | |||||
| B_TIME_OTHER | W_0 | -6.60e+14 | -0.488 | -0.00 | 1.00 | * | |||||
| B_TIME_OTHER | W_OTHER | 6.60e+14 | 0.488 | -0.00 | 1.00 | * | |||||
| W_0 | W_OTHER | -1.14e+16 | -1.00 | -0.00 | 1.00 | * |
1*W_0 + 1*W_OTHER = 1 [1 = 1]
Smallest singular value of the hessian: 1.87584e-17
The log likelihood is (almost) flat along the following combinations of parameters
| Sing. value | = | 1.87584e-17 |
| -0.0269223 | * | B_TIME_OTHER |
| 0.463012 | * | W_0 |
| -0.463012 | * | W_OTHER |
| -0.00501595 | * | Param[9] |
| 0.46228 | * | Param[10] |
| -0.267461 | * | Param[11] |
| 0.00376281 | * | Param[15] |
| -0.267461 | * | Param[16] |
| 0.46228 | * | Param[17] |