biogeme 2.5 [Dim 19 jui 2016 17:58:58 CEST]

Michel Bierlaire, EPFL

This file has automatically been generated.

Thu Jul 7 17:44:57 2016

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:	-4359.824
Final log likelihood:	-4306.211
Likelihood ratio test:	5316.904
Rho-square:	0.382
Adjusted rho-square:	0.380
Final gradient norm:	+5.038e-05
Diagnostic:	Normal termination. Obj: 6.05545e-06 Const: 6.05545e-06
Iterations:	34
Run time:	02h 52:13
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	0.0799	-21.13	0.00		0.292	-5.77	0.00
B_TIME	-3.72	0.451	-8.26	0.00		0.459	-8.11	0.00
B_TIME_S	9.89	0.871	11.35	0.00		0.965	10.25	0.00
SMP1	0.233	0.166	1.40	0.16	*	0.147	1.58	0.11	*
SMP2	-0.629	0.141	-4.45	0.00		0.111	-5.65	0.00
SMP3	-0.357	0.126	-2.83	0.00		0.115	-3.11	0.00
SMP4	0.874	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	97.9	17.2	5.68

Correlation of coefficients

Coefficient1	Coefficient2	Covariance	Correlation	t-test	p-value		Rob. cov.	Rob. corr.	Rob. t-test	p-value
ASC_TRAIN	SMP2	-0.000585	-0.0484	0.14	0.89	*	-0.00177	-0.103	0.11	0.91	*
ASC_CAR	SMP1	-0.000645	-0.0657	0.35	0.72	*	-0.00303	-0.179	0.31	0.75	*
ASC_TRAIN	SMP3	-5.48e-05	-0.00507	-1.62	0.10	*	-0.000150	-0.00844	-1.28	0.20	*
SMP2	SMP3	-0.00375	-0.210	-1.30	0.19	*	-0.00516	-0.403	-1.43	0.15	*
SMP1	SMP3	-0.0175	-0.837	2.11	0.04		-0.0141	-0.833	2.35	0.02
SMP1	SMP4	-0.00126	-0.0419	-2.56	0.01		-0.00939	-0.392	-2.48	0.01
ASC_CAR	SMP4	0.000957	0.0893	-3.11	0.00		0.00317	0.170	-3.16	0.00
B_COST	SMP2	0.000336	0.0298	-6.61	0.00		-0.00110	-0.0337	-3.35	0.00
ASC_TRAIN	B_COST	0.000888	0.130	9.90	0.00		0.00991	0.219	3.62	0.00
ASC_TRAIN	SMP1	-0.000821	-0.0578	-4.39	0.00		-0.00222	-0.0974	-3.75	0.00
ASC_CAR	SMP3	5.67e-05	0.00758	4.70	0.00		0.000696	0.0526	4.13	0.00
B_COST	SMP3	-0.000241	-0.0239	-8.80	0.00		0.000337	0.0100	-4.25	0.00
B_COST	B_TIME	0.00295	0.0819	4.51	0.00		0.0500	0.373	4.60	0.00
SMP1	SMP2	-0.00154	-0.0657	3.83	0.00		0.00416	0.253	5.36	0.00
B_COST	SMP1	-0.000248	-0.0187	-10.35	0.00		-0.00618	-0.143	-5.56	0.00
ASC_CAR	SMP2	-0.000321	-0.0383	5.96	0.00		-0.000972	-0.0760	5.58	0.00
SMP2	SMP4	-0.0227	-0.889	-4.80	0.00		-0.0154	-0.853	-5.69	0.00
B_TIME	SMP2	-0.0279	-0.438	-5.86	0.00		-0.0270	-0.528	-5.88	0.00
ASC_TRAIN	B_TIME	-0.00321	-0.0832	6.70	0.00		-0.00561	-0.0790	6.29	0.00
ASC_CAR	B_COST	0.000840	0.178	21.91	0.00		0.00575	0.171	6.72	0.00
B_TIME	SMP1	-0.0541	-0.723	-6.80	0.00		-0.0503	-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		0.00538	0.214	-7.44	0.00
SMP3	SMP4	0.00404	0.177	-6.11	0.00		0.00696	0.372	-7.67	0.00
B_COST	SMP4	0.000192	0.0133	-13.01	0.00		0.00850	0.179	-8.32	0.00
ASC_CAR	B_TIME	-0.00236	-0.0886	8.75	0.00		-0.00397	-0.0753	8.35	0.00
B_TIME	SMP3	0.0432	0.758	-9.24	0.00		0.0382	0.723	-8.76	0.00
B_TIME_S	SMP1	-0.0675	-0.467	10.06	0.00		-0.0893	-0.627	9.08	0.00
ASC_CAR	B_TIME_S	0.00632	0.122	-11.08	0.00		0.0213	0.192	-10.10	0.00
B_TIME_S	SMP2	-0.0781	-0.635	10.88	0.00		-0.0652	-0.607	10.15	0.00
B_TIME_S	SMP4	0.0973	0.617	11.67	0.00		0.0938	0.597	10.27	0.00
ASC_TRAIN	B_TIME_S	0.00278	0.0373	-12.03	0.00		0.00637	0.0427	-10.81	0.00
B_COST	B_TIME_S	-0.00831	-0.119	-13.09	0.00		-0.0535	-0.190	-10.92	0.00
B_TIME_S	SMP3	0.0666	0.604	12.79	0.00		0.0723	0.651	11.45	0.00
B_TIME	SMP4	0.0454	0.557	-12.07	0.00		0.0491	0.658	-12.33	0.00
B_TIME	B_TIME_S	0.213	0.542	-18.59	0.00		0.196	0.441	-15.71	0.00

Smallest singular value of the hessian: 0.315356