biogeme 2.6a [Mon Apr 17 15:32:48 CEST 2017]

Michel Bierlaire, EPFL

This file has automatically been generated.

Tue Apr 18 19:40:20 2017

Tip: click on the columns headers to sort a table [Credits]

Example of a mixture of logit model with panel data for a transportation mode choice with 3 alternatives:

- Train

- Car

- Swissmetro, an hypothetical high-speed train

The time coefficient is normally distributed. This is an example of a mixture of logit model.

The syntax for a distributed coefficient is B_TIME [ B_TIME_S ], where

B_TIME is the mean and B_TIME_S squared is the variance.

The square brackets are associated with a normal distribution.

For seminonparametric terms are included to test the distribution of the error component for the Train alternative (see Fosgerau and Bierlaire, 2007)

Model:	Mixed Logit for panel data
Number of Hess-Train draws:	500
Number of estimated parameters:	9
Number of observations:	6768
Number of individuals:	752
Null log likelihood:	-6964.663
Init log likelihood:	-4360.066
Final log likelihood:	-4306.556
Likelihood ratio test:	5316.213
Rho-square:	0.382
Adjusted rho-square:	0.380
Final gradient norm:	+1.085e-04
Diagnostic:	Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations:	34
Run time:	06:04
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
ASC_CAR	0.297	0.0592	5.01	0.00		0.115	2.58	0.01
ASC_SM	0.00	fixed
ASC_TRAIN	-0.606	0.0856	-7.08	0.00		0.155	-3.92	0.00
B_COST	-1.69	0.0798	-21.13	0.00		0.292	-5.78	0.00
B_TIME	-3.73	0.451	-8.26	0.00		0.459	-8.12	0.00
B_TIME_S	9.90	0.872	11.35	0.00		0.968	10.23	0.00
SMP1	0.234	0.166	1.41	0.16	*	0.148	1.58	0.11	*
SMP2	-0.630	0.142	-4.44	0.00		0.111	-5.65	0.00
SMP3	-0.358	0.126	-2.83	0.00		0.115	-3.11	0.00
SMP4	0.875	0.181	4.83	0.00		0.163	5.38	0.00

Utility functions

Id	Name	Availability	Specification
1	A1_TRAIN	TRAIN_AV_SP	ASC_TRAIN * one + B_TIME [ B_TIME_S ] * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
2	A2_SM	SM_AV	ASC_SM * one + B_TIME [ B_TIME_S ] * SM_TT_SCALED + B_COST * SM_COST_SCALED
3	A3_Car	CAR_AV_SP	ASC_CAR * one + B_TIME [ B_TIME_S ] * CAR_TT_SCALED + B_COST * CAR_CO_SCALED

Seminonparametric transform

Base parameter: B_TIME_B_TIME_S

List of terms:

Term of order Coefficient

1 SMP1

2 SMP2

3 SMP3

4 SMP4

Term of order	Coefficient
1	SMP1
2	SMP2
3	SMP3
4	SMP4

Variance of random coefficients

Name	Value	Std err	t-test	Robust Std err	Robust t-test
B_TIME_B_TIME_S	98.0	17.3	5.67

Correlation of coefficients

Coefficient1	Coefficient2	Covariance	Correlation	t-test	p-value		Rob. cov.	Rob. corr.	Rob. t-test	p-value
ASC_TRAIN	SMP2	-0.000587	-0.0483	0.14	0.89	*	-0.00176	-0.102	0.12	0.90	*
ASC_CAR	SMP1	-0.000655	-0.0665	0.35	0.73	*	-0.00306	-0.180	0.31	0.76	*
ASC_TRAIN	SMP3	-4.99e-05	-0.00461	-1.62	0.11	*	-0.000147	-0.00828	-1.28	0.20	*
SMP2	SMP3	-0.00378	-0.211	-1.30	0.19	*	-0.00512	-0.399	-1.43	0.15	*
SMP1	SMP3	-0.0176	-0.835	2.11	0.03		-0.0142	-0.832	2.35	0.02
SMP1	SMP4	-0.00127	-0.0422	-2.55	0.01		-0.00939	-0.389	-2.47	0.01
ASC_CAR	SMP4	0.000960	0.0895	-3.12	0.00		0.00318	0.170	-3.17	0.00
B_COST	SMP2	0.000353	0.0312	-6.58	0.00		-0.000926	-0.0285	-3.35	0.00
ASC_TRAIN	B_COST	0.000888	0.130	9.89	0.00		0.00989	0.219	3.61	0.00
ASC_TRAIN	SMP1	-0.000834	-0.0586	-4.39	0.00		-0.00225	-0.0979	-3.74	0.00
ASC_CAR	SMP3	5.97e-05	0.00797	4.70	0.00		0.000705	0.0533	4.14	0.00
B_COST	SMP3	-0.000250	-0.0248	-8.79	0.00		0.000345	0.0103	-4.25	0.00
B_COST	B_TIME	0.00292	0.0812	4.52	0.00		0.0499	0.373	4.61	0.00
SMP1	SMP2	-0.00159	-0.0676	3.83	0.00		0.00409	0.247	5.33	0.00
B_COST	SMP1	-0.000243	-0.0183	-10.34	0.00		-0.00630	-0.145	-5.55	0.00
ASC_CAR	SMP2	-0.000319	-0.0380	5.95	0.00		-0.000965	-0.0754	5.58	0.00
SMP2	SMP4	-0.0228	-0.889	-4.79	0.00		-0.0154	-0.852	-5.70	0.00
B_TIME	SMP2	-0.0280	-0.439	-5.86	0.00		-0.0268	-0.524	-5.89	0.00
ASC_TRAIN	B_TIME	-0.00318	-0.0824	6.70	0.00		-0.00558	-0.0786	6.30	0.00
ASC_CAR	B_COST	0.000840	0.178	21.91	0.00		0.00574	0.171	6.73	0.00
B_TIME	SMP1	-0.0541	-0.722	-6.80	0.00		-0.0505	-0.742	-6.86	0.00
ASC_CAR	ASC_TRAIN	0.00330	0.650	13.85	0.00		0.0110	0.618	7.34	0.00
ASC_TRAIN	SMP4	0.00160	0.103	-7.70	0.00		0.00539	0.214	-7.44	0.00
SMP3	SMP4	0.00410	0.179	-6.12	0.00		0.00695	0.371	-7.68	0.00
B_COST	SMP4	0.000175	0.0121	-12.99	0.00		0.00836	0.176	-8.31	0.00
ASC_CAR	B_TIME	-0.00235	-0.0879	8.75	0.00		-0.00392	-0.0745	8.36	0.00
B_TIME	SMP3	0.0432	0.758	-9.24	0.00		0.0382	0.722	-8.77	0.00
B_TIME_S	SMP1	-0.0678	-0.467	10.05	0.00		-0.0902	-0.628	9.05	0.00
ASC_CAR	B_TIME_S	0.00634	0.123	-11.08	0.00		0.0214	0.192	-10.08	0.00
B_TIME_S	SMP2	-0.0783	-0.633	10.88	0.00		-0.0651	-0.604	10.13	0.00
B_TIME_S	SMP4	0.0974	0.616	11.66	0.00		0.0939	0.596	10.25	0.00
ASC_TRAIN	B_TIME_S	0.00283	0.0379	-12.03	0.00		0.00641	0.0428	-10.79	0.00
B_COST	B_TIME_S	-0.00842	-0.121	-13.08	0.00		-0.0538	-0.190	-10.90	0.00
B_TIME_S	SMP3	0.0669	0.606	12.79	0.00		0.0726	0.651	11.43	0.00
B_TIME	SMP4	0.0457	0.559	-12.09	0.00		0.0490	0.657	-12.34	0.00
B_TIME	B_TIME_S	0.214	0.543	-18.59	0.00		0.196	0.441	-15.67	0.00

Smallest singular value of the hessian: 0.299703