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

Model name                       : MNL2Cores
Model description                : Simple MNL model on mode choice RP data
Model run at                     : 2019-03-10 22:20:38
Estimation method                : bfgs
Model diagnosis                  : successful convergence 
Number of individuals            : 500
Number of observations           : 1000
Estimated parameters             : 9
Model with no mixing

LL(start)                        : -1170.86
LL(0)                            : -1170.86
LL(final)                        : -1025.756
Rho-square (0)                   :  0.1239 
Adj.Rho-square (0)               :  0.1162 
AIC                              :  2069.51 
BIC                              :  2113.68 
Time taken (hh:mm:ss)            :  00:00:30.02 
Iterations                       :  16 
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     0.4747   1.0187       0.47       0.9896           0.48
asc_air     1.6291   0.8274       1.97       0.8167           1.99
asc_rail    0.9445   0.8036       1.18       0.7944           1.19
b_tt_car   -0.0036   0.0016      -2.35       0.0016          -2.33
b_tt_bus   -0.0088   0.0026      -3.37       0.0026          -3.38
b_tt_air   -0.0207   0.0066      -3.13       0.0064          -3.22
b_tt_rail  -0.0112   0.0044      -2.56       0.0045          -2.52
b_access   -0.0115   0.0064      -1.78       0.0063          -1.82
b_cost     -0.0339   0.0033     -10.30       0.0032         -10.69


Overview of choices for MNL model component: 
                                    car    bus    air   rail 
Times available                  778.00 902.00 752.00 874.00 
Times chosen                     332.00 126.00 215.00 327.00 
Percentage chosen overall         33.20  12.60  21.50  32.70 
Percentage chosen when available  42.67  13.97  28.59  37.41 
 

Classical covariance matrix:
            asc_bus   asc_air  asc_rail b_tt_car  b_tt_bus  b_tt_air b_tt_rail
asc_bus    1.037694  0.202768  0.172024 0.000565 -0.002324 -0.000075  0.000086
asc_air    0.202768  0.684650  0.263731 0.000746  0.000168 -0.004045  0.000160
asc_rail   0.172024  0.263731  0.645694 0.000765  0.000173 -0.000176 -0.002788
b_tt_car   0.000565  0.000746  0.000765 0.000002  0.000001  0.000000  0.000000
b_tt_bus  -0.002324  0.000168  0.000173 0.000001  0.000007  0.000000  0.000000
b_tt_air  -0.000075 -0.004045 -0.000176 0.000000  0.000000  0.000044 -0.000002
b_tt_rail  0.000086  0.000160 -0.002788 0.000000  0.000000 -0.000002  0.000019
b_access  -0.000418 -0.003063 -0.000089 0.000000  0.000000  0.000015 -0.000004
b_cost    -0.000016 -0.000597 -0.000241 0.000001  0.000001  0.000005  0.000002
           b_access    b_cost
asc_bus   -0.000418 -0.000016
asc_air   -0.003063 -0.000597
asc_rail  -0.000089 -0.000241
b_tt_car   0.000000  0.000001
b_tt_bus   0.000000  0.000001
b_tt_air   0.000015  0.000005
b_tt_rail -0.000004  0.000002
b_access   0.000041  0.000003
b_cost     0.000003  0.000011

Robust covariance matrix:
            asc_bus   asc_air  asc_rail  b_tt_car  b_tt_bus  b_tt_air b_tt_rail
asc_bus    0.979329  0.194002  0.119352  0.000489 -0.002216 -0.000278  0.000307
asc_air    0.194002  0.666992  0.246199  0.000755  0.000217 -0.003767  0.000306
asc_rail   0.119352  0.246199  0.631016  0.000705  0.000294  0.000005 -0.002761
b_tt_car   0.000489  0.000755  0.000705  0.000002  0.000001  0.000000  0.000000
b_tt_bus  -0.002216  0.000217  0.000294  0.000001  0.000007  0.000000  0.000000
b_tt_air  -0.000278 -0.003767  0.000005  0.000000  0.000000  0.000041 -0.000003
b_tt_rail  0.000307  0.000306 -0.002761  0.000000  0.000000 -0.000003  0.000020
b_access  -0.000311 -0.003084 -0.000444 -0.000001 -0.000001  0.000014 -0.000002
b_cost    -0.000040 -0.000543 -0.000168  0.000001  0.000001  0.000005  0.000002
           b_access    b_cost
asc_bus   -0.000311 -0.000040
asc_air   -0.003084 -0.000543
asc_rail  -0.000444 -0.000168
b_tt_car  -0.000001  0.000001
b_tt_bus  -0.000001  0.000001
b_tt_air   0.000014  0.000005
b_tt_rail -0.000002  0.000002
b_access   0.000040  0.000004
b_cost     0.000004  0.000010

Classical correlation matrix:
            asc_bus   asc_air  asc_rail  b_tt_car  b_tt_bus  b_tt_air b_tt_rail
asc_bus    1.000000  0.240563  0.210156  0.356572 -0.869282 -0.011174  0.019239
asc_air    0.240563  1.000000  0.396656  0.580156  0.077232 -0.740858  0.044161
asc_rail   0.210156  0.396656  1.000000  0.612818  0.081932 -0.033237 -0.791141
b_tt_car   0.356572  0.580156  0.612818  1.000000  0.128909 -0.044037 -0.033754
b_tt_bus  -0.869282  0.077232  0.081932  0.128909  1.000000 -0.027186 -0.014442
b_tt_air  -0.011174 -0.740858 -0.033237 -0.044037 -0.027186  1.000000 -0.060079
b_tt_rail  0.019239  0.044161 -0.791141 -0.033754 -0.014442 -0.060079  1.000000
b_access  -0.063845 -0.575631 -0.017140 -0.009332 -0.020915  0.344585 -0.144482
b_cost    -0.004835 -0.218874 -0.091075  0.183049  0.143544  0.246160  0.162237
           b_access    b_cost
asc_bus   -0.063845 -0.004835
asc_air   -0.575631 -0.218874
asc_rail  -0.017140 -0.091075
b_tt_car  -0.009332  0.183049
b_tt_bus  -0.020915  0.143544
b_tt_air   0.344585  0.246160
b_tt_rail -0.144482  0.162237
b_access   1.000000  0.133489
b_cost     0.133489  1.000000

Robust correlation matrix:
            asc_bus   asc_air  asc_rail  b_tt_car  b_tt_bus  b_tt_air b_tt_rail
asc_bus    1.000000  0.240039  0.151826  0.315143 -0.856709 -0.043771  0.069546
asc_air    0.240039  1.000000  0.379496  0.590286  0.101799 -0.718834  0.083985
asc_rail   0.151826  0.379496  1.000000  0.566483  0.141802  0.000890 -0.778694
b_tt_car   0.315143  0.590286  0.566483  1.000000  0.199051 -0.026924  0.044804
b_tt_bus  -0.856709  0.101799  0.141802  0.199051  1.000000  0.012637 -0.035221
b_tt_air  -0.043771 -0.718834  0.000890 -0.026924  0.012637  1.000000 -0.087981
b_tt_rail  0.069546  0.083985 -0.778694  0.044804 -0.035221 -0.087981  1.000000
b_access  -0.049930 -0.600337 -0.088863 -0.054403 -0.058611  0.337220 -0.082518
b_cost    -0.012700 -0.209462 -0.066455  0.213204  0.153562  0.223180  0.138540
           b_access    b_cost
asc_bus   -0.049930 -0.012700
asc_air   -0.600337 -0.209462
asc_rail  -0.088863 -0.066455
b_tt_car  -0.054403  0.213204
b_tt_bus  -0.058611  0.153562
b_tt_air   0.337220  0.223180
b_tt_rail -0.082518  0.138540
b_access   1.000000  0.200684
b_cost     0.200684  1.000000

20 worst outliers in terms of lowest average per choice prediction:
  ID Avg prob per choice
 227          0.09402451
 166          0.10679187
 253          0.11808357
 462          0.12224800
 112          0.12893178
   2          0.13175097
 317          0.13889401
 381          0.14516199
 267          0.14935514
 231          0.15478013
  86          0.15515144
 300          0.15877769
  43          0.15898082
 453          0.16107142
 417          0.16181148
 125          0.16343231
  76          0.16384970
 287          0.16583607
  35          0.16655629
 413          0.16790034

Changes in parameter estimates from starting values:
          Initial Estimate Difference
asc_car         0   0.0000     0.0000
asc_bus         0   0.4747     0.4747
asc_air         0   1.6291     1.6291
asc_rail        0   0.9445     0.9445
b_tt_car        0  -0.0036    -0.0036
b_tt_bus        0  -0.0088    -0.0088
b_tt_air        0  -0.0207    -0.0207
b_tt_rail       0  -0.0112    -0.0112
b_access        0  -0.0115    -0.0115
b_cost          0  -0.0339    -0.0339
