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Sun Dec 18 15:27:10 2011
Tip: click on the columns headers to sort a table [Credits]
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 assoviated with each mass point are W_0 and W_OTHER, respectively. |
Model: | Multinomial 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: | 00:01 |
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 | 1.80e+308 | -0.00 | 1.00 | * | ||||
W_0 | 0.251 | 2.79e+07 | 0.00 | 1.00 | * | ||||
W_OTHER | 0.749 | 2.79e+07 | 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 | B_TIME_OTHER | 2.92e-12 | 0.00 | 0.00 | 1.00 | * | |||||
ASC_TRAIN | B_TIME_OTHER | -2.29e-06 | 0.00 | 0.00 | 1.00 | * | |||||
B_COST | B_TIME_OTHER | 3.47e-05 | 0.00 | 0.00 | 1.00 | * | |||||
ASC_CAR | W_0 | 1.74e-13 | 2.48e-19 | -0.00 | 1.00 | * | |||||
W_0 | W_OTHER | -7.79e+14 | -1.00 | -0.00 | 1.00 | * | |||||
ASC_CAR | W_OTHER | -1.29e-13 | -1.84e-19 | -0.00 | 1.00 | * | |||||
ASC_TRAIN | W_0 | 1.00e-05 | 1.39e-11 | -0.00 | 1.00 | * | |||||
ASC_TRAIN | W_OTHER | -1.00e-05 | -1.39e-11 | -0.00 | 1.00 | * | |||||
B_COST | W_0 | -0.000152 | -1.40e-10 | -0.00 | 1.00 | * | |||||
B_COST | W_OTHER | 0.000152 | 1.40e-10 | -0.00 | 1.00 | * | |||||
B_TIME_OTHER | W_0 | 1.70e+13 | 0.00 | -0.00 | 1.00 | * | |||||
B_TIME_OTHER | W_OTHER | -1.70e+13 | 0.00 | -0.00 | 1.00 | * | |||||
ASC_CAR | ASC_TRAIN | 0.000257 | 0.395 | 18.61 | 0.00 | ||||||
ASC_TRAIN | B_COST | 0.000219 | 0.219 | 20.84 | 0.00 | ||||||
ASC_CAR | B_COST | 0.000328 | 0.337 | 36.15 | 0.00 |
1*W_0 + 1*W_OTHER = 1 [1 = 1]
Smallest singular value of the hessian: 2.73863e-16
The log-likelihood is (almost) flat along the following combinations of parameters
Sing. value | = | 2.73863e-16 |
-0.0101352 | * | B_TIME_OTHER |
-0.463163 | * | W_0 |
0.463163 | * | W_OTHER |
-0.00188832 | * | Param[9] |
-0.462432 | * | Param[10] |
0.267549 | * | Param[11] |
0.00141656 | * | Param[15] |
0.267549 | * | Param[16] |
-0.462432 | * | Param[17] |
Sing. value | = | 5.79646e-08 |
-0.97388 | * | B_TIME_OTHER |
0.00482018 | * | W_0 |
-0.00482018 | * | W_OTHER |
-0.181446 | * | Param[9] |
0.00481256 | * | Param[10] |
-0.0027844 | * | Param[11] |
0.136115 | * | Param[15] |
-0.0027844 | * | Param[16] |
0.00481256 | * | Param[17] |