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
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-test | | Robust 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 1 | | Robust Std err | Robust t-test 1 | |
Scale1 | +1.0000000e+000 | fixed |
Utility functions
1 | Alt1 | av1 | ASC1 [ sigma1 ] * one + LCOST * lcost1 |
2 | Alt2 | av2 | ASC2 [ sigma2 ] * one + LCOST * lcost2 |
3 | Alt3 | av3 | ASC3 [ sigma3 ] * one + LCOST * lcost3 |
4 | Alt4 | av4 | ASC4 [ sigma4 ] * one + LCOST * lcost4 |
5 | Alt5 | av5 | ASC5 [ sigma5 ] * one + LCOST * lcost5 |
Variance of random coefficients
Name | Value | Std err | t-test | Robust Std err | Robust 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 | Coefficient2 | Covariance | Correlation | t-test | | Rob. cov. | Rob. corr. | Rob. t-test |
ASC3 | sigma4 | 2.5604888e+008 | 9.9999026e-001 | -2.1313281e-001 | * | 3.8184532e+005 | 9.9999279e-001 | -5.5173491e+000 |
ASC2 | sigma4 | 4.2543551e+008 | 9.9999147e-001 | -2.1371612e-001 | * | 6.3502310e+005 | 9.9999577e-001 | -5.5227103e+000 |
ASC2 | ASC3 | 4.6601191e+008 | 9.9999893e-001 | -2.1376473e-001 | * | 6.9562437e+005 | 9.9999718e-001 | -5.5227984e+000 |
ASC2 | ASC4 | 3.2083761e+008 | 9.9999003e-001 | -2.1380025e-001 | * | 4.7903532e+005 | 9.9999499e-001 | -5.5286879e+000 |
LCOST | sigma4 | 4.9304941e+008 | 9.9999240e-001 | -2.1381868e-001 | * | 7.3559666e+005 | 9.9999747e-001 | -5.5320249e+000 |
ASC1 | sigma4 | 5.6243642e+008 | 9.9999199e-001 | -2.1382767e-001 | * | 8.3909120e+005 | 9.9999670e-001 | -5.5330380e+000 |
sigma1 | sigma5 | 3.1019739e+008 | 9.9999801e-001 | -2.1384879e-001 | * | 4.6291158e+005 | 9.9999555e-001 | -5.5283813e+000 |
ASC1 | LCOST | 1.1863243e+009 | 9.9999964e-001 | -2.1385627e-001 | * | 1.7707004e+006 | 9.9999905e-001 | -5.5365376e+000 |
ASC3 | LCOST | 5.4007372e+008 | 9.9999829e-001 | 2.1386192e-001 | * | 8.0579322e+005 | 9.9999565e-001 | 5.5329272e+000 |
ASC1 | ASC3 | 6.1607910e+008 | 9.9999890e-001 | -2.1386193e-001 | * | 9.1916621e+005 | 9.9999725e-001 | -5.5338318e+000 |
ASC1 | ASC4 | 4.2415529e+008 | 9.9999036e-001 | -2.1386496e-001 | * | 6.3297589e+005 | 9.9999590e-001 | -5.5353575e+000 |
ASC4 | LCOST | 3.7182747e+008 | 9.9998977e-001 | 2.1386567e-001 | * | 5.5490261e+005 | 9.9999440e-001 | 5.5350240e+000 |
ASC3 | ASC4 | 1.9309664e+008 | 9.9998949e-001 | -2.1386593e-001 | * | 2.8804880e+005 | 9.9999334e-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 | sigma3 | 6.6156380e+008 | 9.9999879e-001 | -2.1391430e-001 | * | 9.8681005e+005 | 9.9999775e-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 | sigma5 | 2.4117597e+008 | 9.9999842e-001 | -2.1391868e-001 | * | 3.6008819e+005 | 9.9999651e-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 | sigma3 | 5.1436059e+008 | 9.9999938e-001 | -2.1392701e-001 | * | 7.6761704e+005 | 9.9999918e-001 | -5.5401240e+000 |
sigma3 | sigma5 | 9.2330121e+008 | 9.9999847e-001 | 2.1392944e-001 | * | 1.3778207e+006 | 9.9999618e-001 | 5.5413881e+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-001 | 2.1393137e-001 | * | -1.0118497e+006 | -9.9999672e-001 | 5.5394001e+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-001 | 2.1393630e-001 | * | -2.6444310e+005 | -9.9999717e-001 | 5.5385110e+000 |
sigma1 | sigma4 | -2.2793648e+008 | -9.9999240e-001 | 2.1394762e-001 | * | -3.3995534e+005 | -9.9999727e-001 | 5.5399315e+000 |
ASC1 | ASC2 | 1.0236399e+009 | 9.9999983e-001 | -2.1398138e-001 | * | 1.5286069e+006 | 9.9999958e-001 | -5.5474699e+000 |
sigma1 | sigma2 | 1.7280748e+008 | 9.9999915e-001 | 2.1403599e-001 | * | 2.5789917e+005 | 9.9999857e-001 | 5.5513353e+000 |
ASC4 | sigma4 | 1.7628566e+008 | 9.9999482e-001 | 2.1406171e-001 | * | 2.6295561e+005 | 9.9999570e-001 | 5.5483207e+000 |
ASC2 | LCOST | 8.9735430e+008 | 9.9999962e-001 | 2.1410242e-001 | * | 1.3400651e+006 | 9.9999919e-001 | 5.5582579e+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] |