biogeme 2.5 [Dim 19 jui 2016 17:58:58 CEST]
Michel Bierlaire, EPFL
This file has automatically been generated.
Wed Jul 6 20:06:12 2016
Tip: click on the columns headers to sort a table [Credits]
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Example of a 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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A Box-Cox transform is applied to the travel time variable
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| Model: | 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: | -5292.095 |
| Likelihood ratio test: | 3345.135 |
| Rho-square: | 0.240 |
| Adjusted rho-square: | 0.239 |
| Final gradient norm: | +6.878e-04 |
| Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
| Iterations: | 17 |
| 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 | -0.00462 | 0.0471 | -0.10 | 0.92 | * | 0.0480 | -0.10 | 0.92 | * |
| ASC_SM | 0.00 | fixed | | | | | | | |
| ASC_TRAIN | -0.485 | 0.0614 | -7.90 | 0.00 | | 0.0644 | -7.53 | 0.00 | |
| B_COST | -1.08 | 0.0520 | -20.74 | 0.00 | | 0.0680 | -15.86 | 0.00 | |
| B_TIME | -1.67 | 0.0744 | -22.51 | 0.00 | | 0.0766 | -21.88 | 0.00 | |
| LAMBDA | 0.510 | 0.0519 | 9.83 | 0.00 | | 0.0773 | 6.60 | 0.00 | |
Utility functions
| Id | Name | Availability | Specification |
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| 1 | A1_TRAIN | TRAIN_AV_SP | ASC_TRAIN * one + B_COST * TRAIN_COST_SCALED + ( B_TIME * ( ( TRAIN_TT_SCALED ** LAMBDA ) - 1 ) ) / LAMBDA |
| 2 | A2_SM | SM_AV | ASC_SM * one + B_COST * SM_COST_SCALED + ( B_TIME * ( ( SM_TT_SCALED ** LAMBDA ) - 1 ) ) / LAMBDA |
| 3 | A3_Car | CAR_AV_SP | ASC_CAR * one + B_COST * CAR_CO_SCALED + ( B_TIME * ( ( CAR_TT_SCALED ** LAMBDA ) - 1 ) ) / LAMBDA |
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 | LAMBDA | -0.000543 | -0.222 | -6.65 | 0.00 | | 0.000428 | 0.115 | -5.97 | 0.00 | |
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ASC_TRAIN | B_COST | 2.88e-06 | 0.000901 | 7.38 | 0.00 | | -0.000245 | -0.0560 | 6.17 | 0.00 | |
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B_COST | B_TIME | 0.000575 | 0.149 | 7.08 | 0.00 | | 0.00131 | 0.251 | 6.72 | 0.00 | |
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ASC_TRAIN | B_TIME | -0.00357 | -0.782 | 9.28 | 0.00 | | -0.00387 | -0.786 | 8.93 | 0.00 | |
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ASC_CAR | ASC_TRAIN | 0.00188 | 0.651 | 10.19 | 0.00 | | 0.00218 | 0.705 | 10.50 | 0.00 | |
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ASC_TRAIN | LAMBDA | -0.000715 | -0.224 | -11.20 | 0.00 | | 0.00116 | 0.233 | -11.26 | 0.00 | |
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ASC_CAR | B_COST | 0.000481 | 0.197 | 17.07 | 0.00 | | 0.000436 | 0.133 | 13.80 | 0.00 | |
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B_COST | LAMBDA | -0.000157 | -0.0582 | -21.02 | 0.00 | | -0.000985 | -0.187 | -14.17 | 0.00 | |
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ASC_CAR | B_TIME | -0.00231 | -0.661 | 15.01 | 0.00 | | -0.00245 | -0.668 | 14.61 | 0.00 | |
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B_TIME | LAMBDA | 0.00142 | 0.367 | -29.75 | 0.00 | | -0.000703 | -0.119 | -18.99 | 0.00 | |
Smallest singular value of the hessian: 1.42687