Model run using Apollo for R, version 0.0.4 
www.cmc.leeds.ac.uk

Model name                       : MMNL
Model description                : Mixed logit model with inter and intra draws
Model run at                     : 2019-03-10 22:18:45
Estimation method                : bfgs
Model diagnosis                  : successful convergence 
Number of individuals            : 100
Number of observations           : 1400
Estimated parameters             : 8
Number of inter-person draws     : 10 (halton)
Number of intra-person draws     : 10 (mlhs)

LL(start)                        : -1066.482
LL(0)                            : -1636.718
LL(final)                        : -1066.479
Rho-square (0)                   :  0.3484 
Adj.Rho-square (0)               :  0.3435 
AIC                              :  2148.96 
BIC                              :  2190.91 
Time taken (hh:mm:ss)            :  00:01:28.42 
Iterations                       :  6 
Number of cores used             :  2 

Estimates:
          Estimate Std.err. t.ratio(0) Rob.std.err. Rob.t.ratio(0)
asc_car     0.0000       NA         NA           NA             NA
asc_bus    -2.5111   0.2167     -11.59       0.2391         -10.50
asc_air     0.1133   0.4408       0.26       0.4444           0.25
asc_rail   -0.3724   0.2541      -1.47       0.2499          -1.49
b_tt_mu    -0.0144   0.0018      -8.09       0.0017          -8.37
b_tt_sgBe   0.0059   0.0008       7.58       0.0008           7.03
b_tt_sgWi  -0.0032   0.0015      -2.18       0.0014          -2.21
b_access   -0.0271   0.0061      -4.43       0.0062          -4.36
b_cost     -0.0673   0.0042     -16.14       0.0057         -11.89


Overview of choices for MNL model component: 
                                     car     bus     air    rail 
Times available                  1078.00 1204.00 1064.00 1260.00 
Times chosen                      385.00   50.00  308.00  657.00 
Percentage chosen overall          27.50    3.57   22.00   46.93 
Percentage chosen when available   35.71    4.15   28.95   52.14 
 

Classical covariance matrix:
            asc_bus   asc_air  asc_rail   b_tt_mu b_tt_sgBe b_tt_sgWi  b_access
asc_bus    0.046956  0.001262 -0.003098 -0.000036  -3.2e-05   8.6e-05 -0.000306
asc_air    0.001262  0.194276  0.100656  0.000448  -2.8e-05   4.6e-05 -0.001674
asc_rail  -0.003098  0.100656  0.064542  0.000323  -1.8e-05   3.2e-05 -0.000521
b_tt_mu   -0.000036  0.000448  0.000323  0.000003  -1.0e-06   1.0e-06  0.000001
b_tt_sgBe -0.000032 -0.000028 -0.000018 -0.000001   1.0e-06   0.0e+00 -0.000001
b_tt_sgWi  0.000086  0.000046  0.000032  0.000001   0.0e+00   2.0e-06  0.000002
b_access  -0.000306 -0.001674 -0.000521  0.000001  -1.0e-06   2.0e-06  0.000037
b_cost     0.000224 -0.000088  0.000098  0.000004  -1.0e-06   3.0e-06  0.000006
             b_cost
asc_bus    0.000224
asc_air   -0.000088
asc_rail   0.000098
b_tt_mu    0.000004
b_tt_sgBe -0.000001
b_tt_sgWi  0.000003
b_access   0.000006
b_cost     0.000017

Robust covariance matrix:
            asc_bus   asc_air  asc_rail   b_tt_mu b_tt_sgBe b_tt_sgWi  b_access
asc_bus    0.057174 -0.000777 -0.004287 -0.000035  -8.0e-06  0.000129 -0.000212
asc_air   -0.000777  0.197455  0.099314  0.000381   3.9e-05  0.000065 -0.001777
asc_rail  -0.004287  0.099314  0.062430  0.000278   1.0e-06  0.000046 -0.000595
b_tt_mu   -0.000035  0.000381  0.000278  0.000003  -1.0e-06  0.000001  0.000002
b_tt_sgBe -0.000008  0.000039  0.000001 -0.000001   1.0e-06  0.000000 -0.000002
b_tt_sgWi  0.000129  0.000065  0.000046  0.000001   0.0e+00  0.000002  0.000002
b_access  -0.000212 -0.001777 -0.000595  0.000002  -2.0e-06  0.000002  0.000039
b_cost     0.000351  0.000162  0.000195  0.000005   0.0e+00  0.000004  0.000007
            b_cost
asc_bus   0.000351
asc_air   0.000162
asc_rail  0.000195
b_tt_mu   0.000005
b_tt_sgBe 0.000000
b_tt_sgWi 0.000004
b_access  0.000007
b_cost    0.000032

Classical correlation matrix:
            asc_bus   asc_air  asc_rail   b_tt_mu b_tt_sgBe b_tt_sgWi  b_access
asc_bus    1.000000  0.013217 -0.056271 -0.092387 -0.187440  0.273145 -0.230602
asc_air    0.013217  1.000000  0.898895  0.568883 -0.082431  0.071973 -0.620569
asc_rail  -0.056271  0.898895  1.000000  0.710998 -0.092315  0.086050 -0.334818
b_tt_mu   -0.092387  0.568883  0.710998  1.000000 -0.366105  0.420360  0.118145
b_tt_sgBe -0.187440 -0.082431 -0.092315 -0.366105  1.000000 -0.327272 -0.111674
b_tt_sgWi  0.273145  0.071973  0.086050  0.420360 -0.327272  1.000000  0.195113
b_access  -0.230602 -0.620569 -0.334818  0.118145 -0.111674  0.195113  1.000000
b_cost     0.247667 -0.047679  0.092024  0.485497 -0.306895  0.451498  0.250988
             b_cost
asc_bus    0.247667
asc_air   -0.047679
asc_rail   0.092024
b_tt_mu    0.485497
b_tt_sgBe -0.306895
b_tt_sgWi  0.451498
b_access   0.250988
b_cost     1.000000

Robust correlation matrix:
            asc_bus   asc_air  asc_rail   b_tt_mu b_tt_sgBe b_tt_sgWi  b_access
asc_bus    1.000000 -0.007311 -0.071760 -0.085794 -0.041959  0.375847 -0.142475
asc_air   -0.007311  1.000000  0.894502  0.496703  0.103875  0.102103 -0.642973
asc_rail  -0.071760  0.894502  1.000000  0.645658  0.002477  0.127752 -0.383040
b_tt_mu   -0.085794  0.496703  0.645658  1.000000 -0.512083  0.483005  0.193253
b_tt_sgBe -0.041959  0.103875  0.002477 -0.512083  1.000000 -0.337061 -0.426497
b_tt_sgWi  0.375847  0.102103  0.127752  0.483005 -0.337061  1.000000  0.222520
b_access  -0.142475 -0.642973 -0.383040  0.193253 -0.426497  0.222520  1.000000
b_cost     0.259130  0.064508  0.137496  0.465470 -0.066122  0.526784  0.201816
             b_cost
asc_bus    0.259130
asc_air    0.064508
asc_rail   0.137496
b_tt_mu    0.465470
b_tt_sgBe -0.066122
b_tt_sgWi  0.526784
b_access   0.201816
b_cost     1.000000

20 worst outliers in terms of lowest average per choice prediction:
 ID Avg prob per choice
 77           0.2490989
 82           0.2684602
 74           0.2781098
 25           0.2832889
 23           0.2848679
 61           0.3122410
 18           0.3191802
 12           0.3239212
 80           0.3299794
  7           0.3336905
 86           0.3374899
 59           0.3426630
 84           0.3426928
 48           0.3434681
 35           0.3509370
 47           0.3547532
 73           0.3568783
 27           0.3594586
 19           0.3664104
 76           0.3671699

Changes in parameter estimates from starting values:
          Initial Estimate Difference
asc_car    0.0000   0.0000          0
asc_bus   -2.5111  -2.5111          0
asc_air    0.1133   0.1133          0
asc_rail  -0.3724  -0.3724          0
b_tt_mu   -0.0144  -0.0144          0
b_tt_sgBe  0.0059   0.0059          0
b_tt_sgWi -0.0032  -0.0032          0
b_access  -0.0271  -0.0271          0
b_cost    -0.0673  -0.0673          0
