BIOGEME Version 1.4 [Sat Dec 17 12:19:10 GMT 2005]

Author: Michel Bierlaire, EPFL (2001-2005)

This file has automatically been generated.

08/02/06 22:15:18

Telephone 3-2

Model: Mixed Multinomial Logit
Number of draws: 2000
Number of estimated parameters: 10
Number of observations: 434
Number of individuals: 434
Null log-likelihood: -560.25
Init log-likelihood: -479.112
Final log-likelihood: -469.909
Likelihood ratio test: 180.68
Rho-square: 0.16125
Adjusted rho-square: 0.143401
Final gradient norm: 5.01378e-006
Variance-covariance: from finite difference hessian

Utility parameters

Name Value Std err t-testRobust Std err Robust t-test
ASC1 -7.8681248e+003+3.6786916e+004-2.1388379e-001 *+1.4212079e+003-5.5362236e+000
ASC2 -5.9506945e+003+2.7826200e+004-2.1385221e-001 *+1.0755693e+003-5.5326000e+000
ASC3 -3.5823967e+003+1.6747253e+004-2.1390951e-001 *+6.4675177e+002-5.5390597e+000
ASC4 -2.4665571e+003+1.1530170e+004-2.1392201e-001 *+4.4538063e+002-5.5380880e+000
ASC5 +0.0000000e+000 fixed
LCOST -6.8975469e+003+3.2248551e+004-2.1388703e-001 *+1.2459134e+003-5.5361365e+000
sigma1 +3.1894376e+003+1.4908488e+004+2.1393435e-001 *+5.7579789e+002+5.5391617e+000
sigma2 +2.4794143e+003+1.1591224e+004+2.1390444e-001 *+4.4789941e+002+5.5356498e+000
sigma3 +9.4927580e+003+4.4375030e+004+2.1392116e-001 *+1.7138171e+003+5.5389563e+000
sigma4 -3.2712644e+003+1.5289157e+004-2.1395976e-001 *+5.9040901e+002-5.5406749e+000
sigma5 +4.4508082e+003+2.0806806e+004+2.1391117e-001 *+8.0395160e+002+5.5361643e+000

Scale parameters

Name Value Std err t-test 1Robust Std err Robust t-test 1
Scale1 +1.0000000e+000 fixed

Utility functions

1Alt1av1ASC1 [ sigma1 ] * one + LCOST * lcost1
2Alt2av2ASC2 [ sigma2 ] * one + LCOST * lcost2
3Alt3av3ASC3 [ sigma3 ] * one + LCOST * lcost3
4Alt4av4ASC4 [ sigma4 ] * one + LCOST * lcost4
5Alt5av5ASC5 [ sigma5 ] * one + LCOST * lcost5

Variance of random coefficients

NameValueStd errt-testRobust Std errRobust t-test
ASC1_sigma1+1.0172512e+007+9.5099384e+007+1.0696717e-001
ASC2_sigma2+6.1474952e+006+5.7478893e+007+1.0695222e-001
ASC3_sigma3+9.0112454e+007+8.4248284e+008+1.0696058e-001
ASC4_sigma4+1.0701171e+007+1.0002975e+008+1.0697988e-001
ASC5_sigma5+1.9809693e+007+1.8521420e+008+1.0695559e-001

Correlation of coefficients

Coefficient1 Coefficient2CovarianceCorrelationt-testRob. cov.Rob. corr.Rob. t-test
ASC3 sigma42.5604888e+0089.9999026e-001-2.1313281e-001*3.8184532e+0059.9999279e-001-5.5173491e+000
ASC2 sigma44.2543551e+0089.9999147e-001-2.1371612e-001*6.3502310e+0059.9999577e-001-5.5227103e+000
ASC2 ASC34.6601191e+0089.9999893e-001-2.1376473e-001*6.9562437e+0059.9999718e-001-5.5227984e+000
ASC2 ASC43.2083761e+0089.9999003e-001-2.1380025e-001*4.7903532e+0059.9999499e-001-5.5286879e+000
LCOST sigma44.9304941e+0089.9999240e-001-2.1381868e-001*7.3559666e+0059.9999747e-001-5.5320249e+000
ASC1 sigma45.6243642e+0089.9999199e-001-2.1382767e-001*8.3909120e+0059.9999670e-001-5.5330380e+000
sigma1 sigma53.1019739e+0089.9999801e-001-2.1384879e-001*4.6291158e+0059.9999555e-001-5.5283813e+000
ASC1 LCOST1.1863243e+0099.9999964e-001-2.1385627e-001*1.7707004e+0069.9999905e-001-5.5365376e+000
ASC3 LCOST5.4007372e+0089.9999829e-0012.1386192e-001*8.0579322e+0059.9999565e-0015.5329272e+000
ASC1 ASC36.1607910e+0089.9999890e-001-2.1386193e-001*9.1916621e+0059.9999725e-001-5.5338318e+000
ASC1 ASC44.2415529e+0089.9999036e-001-2.1386496e-001*6.3297589e+0059.9999590e-001-5.5353575e+000
ASC4 LCOST3.7182747e+0089.9998977e-0012.1386567e-001*5.5490261e+0059.9999440e-0015.5350240e+000
ASC3 ASC41.9309664e+0089.9998949e-001-2.1386593e-001*2.8804880e+0059.9999334e-001-5.5409469e+000
ASC2 sigma2-3.2253954e+008-9.9999945e-001-2.1386760e-001*-4.8174651e+005-9.9999932e-001-5.5334974e+000
ASC2 sigma5-5.7897333e+008-9.9999825e-001-2.1387753e-001*-8.6470247e+005-9.9999635e-001-5.5341296e+000
ASC2 sigma1-4.1484604e+008-9.9999874e-001-2.1388093e-001*-6.1930908e+005-9.9999769e-001-5.5348908e+000
ASC1 sigma2-4.2640520e+008-9.9999958e-001-2.1388875e-001*-6.3655786e+005-9.9999947e-001-5.5360866e+000
LCOST sigma2-3.7379999e+008-9.9999949e-001-2.1389166e-001*-5.5804337e+005-9.9999905e-001-5.5360089e+000
ASC1 sigma5-7.6541693e+008-9.9999833e-001-2.1389376e-001*-1.1425781e+006-9.9999628e-001-5.5362069e+000
ASC2 sigma3-1.2347873e+009-9.9999907e-001-2.1389464e-001*-1.8433260e+006-9.9999840e-001-5.5365075e+000
LCOST sigma5-6.7098889e+008-9.9999933e-001-2.1389653e-001*-1.0016528e+006-9.9999872e-001-5.5361491e+000
ASC1 sigma1-5.4843688e+008-9.9999926e-001-2.1389840e-001*-8.1832748e+005-9.9999872e-001-5.5370722e+000
LCOST sigma1-4.8077664e+008-9.9999897e-001-2.1390204e-001*-7.1739281e+005-9.9999788e-001-5.5370952e+000
ASC1 sigma3-1.6324192e+009-9.9999922e-001-2.1390426e-001*-2.4356871e+006-9.9999862e-001-5.5377194e+000
LCOST sigma3-1.4310295e+009-9.9999932e-001-2.1390683e-001*-2.1352645e+006-9.9999850e-001-5.5377714e+000
ASC3 sigma2-1.9412086e+008-9.9999844e-001-2.1390752e-001*-2.8967887e+005-9.9999699e-001-5.5376685e+000
ASC3 sigma5-3.4845559e+008-9.9999643e-001-2.1391062e-001*-5.1995280e+005-9.9999169e-001-5.5374665e+000
ASC4 sigma2-1.3364742e+008-9.9998984e-001-2.1391375e-001*-1.9948477e+005-9.9999522e-001-5.5368721e+000
sigma1 sigma36.6156380e+0089.9999879e-001-2.1391430e-001*9.8681005e+0059.9999775e-001-5.5388429e+000
ASC4 sigma5-2.3990330e+008-9.9998875e-001-2.1391559e-001*-3.5806171e+005-9.9999229e-001-5.5368599e+000
ASC3 sigma3-7.4315889e+008-9.9999872e-001-2.1391802e-001*-1.1084119e+006-9.9999790e-001-5.5389870e+000
sigma2 sigma52.4117597e+0089.9999842e-001-2.1391868e-001*3.6008819e+0059.9999651e-001-5.5367567e+000
ASC3 sigma1-2.4967564e+008-9.9999767e-001-2.1392133e-001*-3.7239642e+005-9.9999494e-001-5.5391147e+000
ASC4 sigma3-5.1164623e+008-9.9998945e-001-2.1392171e-001*-7.6329656e+005-9.9999427e-001-5.5387824e+000
sigma2 sigma35.1436059e+0089.9999938e-001-2.1392701e-001*7.6761704e+0059.9999918e-001-5.5401240e+000
sigma3 sigma59.2330121e+0089.9999847e-0012.1392944e-001*1.3778207e+0069.9999618e-0015.5413881e+000
ASC4 sigma1-1.7189565e+008-9.9998983e-001-2.1392950e-001*-2.5644796e+005-9.9999504e-001-5.5387002e+000
sigma3 sigma4-6.7845146e+008-9.9999214e-0012.1393137e-001*-1.0118497e+006-9.9999672e-0015.5394001e+000
sigma4 sigma5-3.1811611e+008-9.9999243e-001-2.1393215e-001*-4.7465897e+005-9.9999727e-001-5.5380779e+000
sigma2 sigma4-1.7721871e+008-9.9999246e-0012.1393630e-001*-2.6444310e+005-9.9999717e-0015.5385110e+000
sigma1 sigma4-2.2793648e+008-9.9999240e-0012.1394762e-001*-3.3995534e+005-9.9999727e-0015.5399315e+000
ASC1 ASC21.0236399e+0099.9999983e-001-2.1398138e-001*1.5286069e+0069.9999958e-001-5.5474699e+000
sigma1 sigma21.7280748e+0089.9999915e-0012.1403599e-001*2.5789917e+0059.9999857e-0015.5513353e+000
ASC4 sigma41.7628566e+0089.9999482e-0012.1406171e-001*2.6295561e+0059.9999570e-0015.5483207e+000
ASC2 LCOST8.9735430e+0089.9999962e-0012.1410242e-001*1.3400651e+0069.9999919e-0015.5582579e+000

Smallest singular value of the hessian: 1.5209569e-010

Unidentifiable model

The log-likelihood is (almost) flat along the following combinations of parameters

Sing. value=1.5209569e-010
-4.5368220e-001*ASC1
-3.4317230e-001*ASC2
-2.0653875e-001*ASC3
-1.4219693e-001*ASC4
-3.9771190e-001*LCOST
1.8386189e-001*sigma1
1.4295114e-001*sigma2
5.4726413e-001*sigma3
-1.8855542e-001*sigma4
2.5660399e-001*sigma5
-4.9129332e-003*Param[10]
-2.6964474e-003*Param[11]
-1.2890956e-003*Param[12]
-8.1915006e-004*Param[13]
-3.5701460e-003*Param[14]
8.0047649e-004*Param[15]
6.3982399e-004*Param[16]
1.9598839e-003*Param[17]
-1.1493235e-003*Param[18]
1.0673020e-003*Param[19]
1.6970016e-003*Param[20]
1.3586026e-003*Param[21]
8.8610123e-004*Param[22]
6.3677639e-004*Param[23]
1.5297722e-003*Param[24]
-1.1139616e-003*Param[25]
-8.2419844e-004*Param[26]
-1.2149527e-002*Param[27]
8.1837596e-004*Param[28]
-1.7223386e-003*Param[29]