biogeme 2.6a [Mon Apr 17 15:32:48 CEST 2017]
Michel Bierlaire, EPFL
This file has automatically been generated.
Tue Apr 18 19:04:52 2017
Tip: click on the columns headers to sort a table [Credits]
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Example of a 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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Alternatives Train and Car are grouped in the same nest, as their error terms are expected to share unobserved attributes associated with existing alternatives.
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| Model: | Nested Logit |
| Number of estimated parameters: | 5 |
| Number of observations: | 6768 |
| Number of individuals: | 6768 |
| Null log likelihood: | -6964.663 |
| Init log likelihood: | -6964.663 |
| Final log likelihood: | -5236.900 |
| Likelihood ratio test: | 3455.526 |
| Rho-square: | 0.248 |
| Adjusted rho-square: | 0.247 |
| Final gradient norm: | +2.505e-04 |
| Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
| Iterations: | 15 |
| Run time: | 00:01 |
| Variance-covariance: | from finite difference hessian |
| Sample file: | ../swissmetro.dat |
Utility parameters
| Name | Value | Std err | t-test | p-value | | Robust Std err | Robust t-test | p-value | |
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| ASC_CAR | -0.167 | 0.0371 | -4.50 | 0.00 | | 0.0545 | -3.07 | 0.00 | |
| ASC_SM | 0.00 | fixed | | | | | | | |
| ASC_TRAIN | -0.512 | 0.0452 | -11.33 | 0.00 | | 0.0791 | -6.47 | 0.00 | |
| B_COST | -0.857 | 0.0463 | -18.51 | 0.00 | | 0.0600 | -14.27 | 0.00 | |
| B_TIME | -0.899 | 0.0570 | -15.77 | 0.00 | | 0.107 | -8.39 | 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 | 2.05 | 0.118 | 17.45 | 0.00 | 8.96 | 0.00 | | 0.164 | 12.51 | 0.00 | 6.42 | 0.00 | |
| FUTURE | 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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B_COST | B_TIME | 0.00109 | 0.411 | 0.74 | 0.46 | * | 0.00268 | 0.417 | 0.43 | 0.67 | * |
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ASC_TRAIN | B_TIME | -0.00121 | -0.471 | 4.40 | 0.00 | | -0.00656 | -0.774 | 2.20 | 0.03 | |
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ASC_TRAIN | B_COST | 0.000322 | 0.154 | 5.79 | 0.00 | | -0.000263 | -0.0554 | 3.38 | 0.00 | |
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ASC_CAR | B_TIME | -0.00124 | -0.585 | 8.68 | 0.00 | | -0.00483 | -0.828 | 4.71 | 0.00 | |
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ASC_CAR | ASC_TRAIN | 0.00121 | 0.721 | 10.90 | 0.00 | | 0.00368 | 0.852 | 7.95 | 0.00 | |
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ASC_CAR | B_COST | 5.56e-05 | 0.0324 | 11.81 | 0.00 | | -0.000412 | -0.126 | 8.01 | 0.00 | |
Smallest singular value of the hessian: 2.0462