biogeme 2.6a [Mon Apr 17 15:32:48 CEST 2017]
Michel Bierlaire, EPFL
This file has automatically been generated.
Tue Apr 18 19:04:55 2017
Tip: click on the columns headers to sort a table [Credits]
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Example of a cross nested logit model 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 a nest called EXISTING involving Car and Train
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and a nest called PUBLIC involving Swissmetro and Train
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Note that the alternative Train belongs to the two nests.
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| Model: | Cross-Nested Logit |
| Number of estimated parameters: | 8 |
| Number of observations: | 6768 |
| Number of individuals: | 6768 |
| Null log likelihood: | -6964.663 |
| Init log likelihood: | -6964.663 |
| Final log likelihood: | -5214.049 |
| Likelihood ratio test: | 3501.228 |
| Rho-square: | 0.251 |
| Adjusted rho-square: | 0.250 |
| Final gradient norm: | +5.747e-04 |
| Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
| Iterations: | 27 |
| Run time: | 00:02 |
| 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 | -0.240 | 0.0384 | -6.26 | 0.00 | | | | | |
| ASC_SM | 0.00 | fixed | | | | | | | |
| ASC_TRAIN | 0.0983 | 0.0563 | 1.74 | 0.08 | * | | | | |
| B_COST | -0.819 | 0.0446 | -18.36 | 0.00 | | | | | |
| B_TIME | -0.777 | 0.0558 | -13.93 | 0.00 | | | | | |
Model parameters
| Name | Value | Std err | t-test 0 | p-value | t-test 1 | p-value | | Robust Std err | Robust t-test 0 | p-value | Robust t-test 1 | p-value | |
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| EXISTING | 2.51 | 0.175 | 14.40 | 0.00 | 8.68 | 0.00 | | | | | | | |
| PUBLIC | 4.11 | 0.569 | 7.23 | 0.00 | 5.48 | 0.00 | | | | | | | |
| EXISTING_A1_TRAIN | 0.495 | 0.0289 | 17.11 | 0.00 | -17.46 | 0.00 | | | | | | | |
| EXISTING_A3_Car | 1.00 | fixed | | | | | | | | | | | |
| PUBLIC_A1_TRAIN | 0.505 | 0.0289 | 17.46 | 0.00 | -17.11 | 0.00 | | | | | | | |
| PUBLIC_A2_SM | 1.00 | 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 |
| 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 |
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 | 0.000650 | 0.300 | -5.85 | 0.00 | | |
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ASC_CAR | B_COST | -0.000103 | -0.0601 | 9.54 | 0.00 | | |
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ASC_CAR | B_TIME | -0.00132 | -0.614 | 6.31 | 0.00 | | |
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ASC_TRAIN | B_COST | 0.00104 | 0.413 | 16.50 | 0.00 | | |
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ASC_TRAIN | B_TIME | -0.000275 | -0.0876 | 10.59 | 0.00 | | |
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B_COST | B_TIME | 0.00115 | 0.460 | -0.79 | 0.43 | * | |
User defined linear constraints
1*EXISTING_A1_TRAIN + 1*PUBLIC_A1_TRAIN = 1 [1 = 1]
Smallest singular value of the hessian: 0.674134