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Wed Jul 6 20:06:15 2016
Tip: click on the columns headers to sort a table [Credits]
| Example of a nested logit model for a transportation mode choice with 3 alternatives: |
| - Train |
| - Car |
| - Swissmetro, an hypothetical high-speed train |
| Alternatives Train and Car are grouped in the same nest, as their error terms are expected to share unobserved attributes associated with existing alternatives. |
| Although this should be discouraged, we illustrate here a normalization of the nested logit model from the bottom. |
| 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: | +3.112e-04 |
| Diagnostic: | Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06 |
| Iterations: | 20 |
| Run time: | 00:00 |
| Variance-covariance: | from finite difference hessian |
| Sample file: | ../swissmetro.dat |
| Name | Value | Std err | t-test | p-value | Robust Std err | Robust t-test | p-value | ||
|---|---|---|---|---|---|---|---|---|---|
| ASC_CAR | -0.343 | 0.0830 | -4.14 | 0.00 | 0.119 | -2.89 | 0.00 | ||
| ASC_SM | 0.00 | fixed | |||||||
| ASC_TRAIN | -1.05 | 0.103 | -10.21 | 0.00 | 0.165 | -6.37 | 0.00 | ||
| B_COST | -1.76 | 0.0999 | -17.61 | 0.00 | 0.149 | -11.79 | 0.00 | ||
| B_TIME | -1.85 | 0.101 | -18.22 | 0.00 | 0.226 | -8.18 | 0.00 |
| Value | Std err | t-test0 | p-value | t-test1 | p-value | Robust Std err | Robust t-test0 | p-value | Robust t-test1 | p-value | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.486839 | 0.0279 | 17.45 | 0.00 | -18.39 | 0.00 | 0.0389 | 12.51 | 0.00 | -13.1856 | 0.00 |
| 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 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| EXISTING | 1.00 | fixed | |||||||||||
| FUTURE | 1.00 | fixed |
| 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 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| B_COST | B_TIME | 0.00343 | 0.339 | 0.75 | 0.46 | * | 0.0162 | 0.482 | 0.43 | 0.67 | * |
| ASC_TRAIN | B_TIME | -0.00435 | -0.417 | 4.62 | 0.00 | -0.0262 | -0.705 | 2.20 | 0.03 | ||
| ASC_TRAIN | B_COST | 0.00331 | 0.321 | 5.99 | 0.00 | 0.00169 | 0.0684 | 3.30 | 0.00 | ||
| ASC_CAR | B_TIME | -0.00269 | -0.320 | 10.01 | 0.00 | -0.0159 | -0.594 | 4.83 | 0.00 | ||
| ASC_CAR | B_COST | 0.00305 | 0.368 | 13.66 | 0.00 | 0.00299 | 0.168 | 8.12 | 0.00 | ||
| ASC_CAR | ASC_TRAIN | 0.00706 | 0.826 | 12.20 | 0.00 | 0.0181 | 0.921 | 9.80 | 0.00 |
Smallest singular value of the hessian: 1.39506