Model run using Apollo for R, version 0.2.5 on Windows by sac111 
www.ApolloChoiceModelling.com

Model name                       : INT_MXL_PREF_LN_EXC
Model description                : MXL model with interaction, pref, ln-norm, with exc
Model run at                     : 2021-10-29 16:42:13
Estimation method                : bfgs
Model diagnosis                  : successful convergence 
Number of individuals            : 686
Number of rows in database       : 5488
Number of modelled outcomes      : 5488

Number of cores used             :  8 
Number of inter-individual draws : 1000 (sobolOwenFaureTezuka)

LL(start)                        : -3448.26
LL(0)                            : -3803.992
LL(C)                            : Not applicable
LL(final)                        : -2678.167
Rho-square (0)                   :  0.296 
Adj.Rho-square (0)               :  0.2923 
AIC                              :  5384.33 
BIC                              :  5476.88 


Estimated parameters             :  14
Time taken (hh:mm:ss)            :  00:08:1.3 
     pre-estimation              :  00:02:6.97 
     estimation                  :  00:02:46.64 
     post-estimation             :  00:03:7.69 
Iterations                       :  58  
Min abs eigenvalue of Hessian    :  0.13294 

Estimates:
                 Estimate        s.e.   t.rat.(0)  p(2-sided)    t.rat(1)  p(2-sided)    Rob.s.e. Rob.t.rat.(0)  p(2-sided) Rob.t.rat.(1)
mu.fee           -1.64399      0.1619    -10.1569    0.000000  -16.335096     0.00000      0.1746       -9.4174    0.000000    -15.145742
mu.disc          -6.46698      1.5291     -4.2293   2.344e-05   -4.883306   1.043e-06      1.5490       -4.1749   2.981e-05     -4.820462
mu.anon           0.61466      0.2315      2.6550    0.007932   -1.664451     0.09602      0.2300        2.6730    0.007519     -1.675735
mu.hh             0.15960      0.2132      0.7487    0.454010   -3.942690   8.057e-05      0.2167        0.7365    0.461396     -3.878468
mu.daily          0.99841      0.1713      5.8274   5.629e-09   -0.009255     0.99262      0.1754        5.6925   1.252e-08     -0.009041
mu.anon.hh        0.71064      0.4166      1.7059    0.088028   -0.694607     0.48730      0.4233        1.6788    0.093196     -0.683566
mu.anon.daily    -0.60605      0.3095     -1.9584    0.050177   -5.189928   2.104e-07      0.2946       -2.0569    0.039696     -5.450826
sg.fee           -2.30613      0.2920     -7.8977   2.887e-15  -11.322363     0.00000      0.3081       -7.4845   7.172e-14    -10.729983
sg.disc          -8.30521      2.2953     -3.6184  2.9646e-04   -4.054053   5.034e-05      2.2725       -3.6546  2.5760e-04     -4.094623
sg.anon           1.48642      0.1146     12.9686    0.000000    4.243902   2.197e-05      0.1212       12.2599    0.000000      4.011957
sg.hh            -0.57124      0.1205     -4.7412   2.124e-06  -13.041119     0.00000      0.1218       -4.6905   2.725e-06    -12.901693
sg.daily          0.22741      0.3950      0.5757    0.564791   -1.956020     0.05046      0.3177        0.7158    0.474116     -2.431856
sg.anon.hh        0.06847      0.4640      0.1476    0.882685   -2.007488     0.04470      0.2111        0.3244    0.745657     -4.412725
sg.anon.daily    -0.44334      0.6118     -0.7247    0.468661   -2.359221     0.01831      0.5787       -0.7661    0.443638     -2.494017
               p(2-sided)
mu.fee            0.00000
mu.disc         1.432e-06
mu.anon           0.09379
mu.hh          1.0512e-04
mu.daily          0.99279
mu.anon.hh        0.49425
mu.anon.daily   5.014e-08
sg.fee            0.00000
sg.disc         4.229e-05
sg.anon         6.022e-05
sg.hh             0.00000
sg.daily          0.01502
sg.anon.hh      1.021e-05
sg.anon.daily     0.01263


Overview of choices for MNL model component :
                                       1       2
Times available                  5488.00 5488.00
Times chosen                     3097.00 2391.00
Percentage chosen overall          56.43   43.57
Percentage chosen when available   56.43   43.57


Classical covariance matrix:
                     mu.fee       mu.disc       mu.anon         mu.hh      mu.daily    mu.anon.hh mu.anon.daily        sg.fee       sg.disc
mu.fee             0.026199     -0.027381      0.005808      0.003720     -0.006872     -0.004962      0.014739     -0.001018     -0.051739
mu.disc           -0.027381      2.338097      0.007770     -0.006948      0.075612      0.025455     -0.091691     -0.013385      3.407407
mu.anon            0.005808      0.007770      0.053599      0.043084      0.005178     -0.086827     -0.041190      0.006206      0.006051
mu.hh              0.003720     -0.006948      0.043084      0.045435      0.003770     -0.083802     -0.034718      0.008337     -0.014040
mu.daily          -0.006872      0.075612      0.005178      0.003770      0.029354    1.5706e-04     -0.039359     -0.007938      0.109094
mu.anon.hh        -0.004962      0.025455     -0.086827     -0.083802    1.5706e-04      0.173539      0.066758     -0.014266      0.037277
mu.anon.daily      0.014739     -0.091691     -0.041190     -0.034718     -0.039359      0.066758      0.095763      0.011217     -0.136708
sg.fee            -0.001018     -0.013385      0.006206      0.008337     -0.007938     -0.014266      0.011217      0.085264     -0.015419
sg.disc           -0.051739      3.407407      0.006051     -0.014040      0.109094      0.037277     -0.136708     -0.015419      5.268338
sg.anon           -0.001545      0.020445    2.5753e-04    1.1959e-04      0.003138      0.001929     -0.002993      0.003872      0.032789
sg.hh             -0.001428     -0.009816     -0.001673    -3.521e-05     -0.003066   -9.9578e-04      0.003066   -5.5951e-04     -0.014055
sg.daily           0.012456     -0.043122      0.001013   -2.8921e-04     -0.003386      0.003490      0.013417     -0.012374     -0.068533
sg.anon.hh        -0.008912      0.004424     7.699e-05    1.9020e-04      0.003757      0.002059     -0.007071      0.005692      0.067307
sg.anon.daily      0.012307     -0.046392     -0.001261   -4.7029e-04     -0.008339      0.002477      0.024192     -0.017804     -0.088134
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee            -0.001545     -0.001428      0.012456     -0.008912      0.012307
mu.disc            0.020445     -0.009816     -0.043122      0.004424     -0.046392
mu.anon          2.5753e-04     -0.001673      0.001013     7.699e-05     -0.001261
mu.hh            1.1959e-04    -3.521e-05   -2.8921e-04    1.9020e-04   -4.7029e-04
mu.daily           0.003138     -0.003066     -0.003386      0.003757     -0.008339
mu.anon.hh         0.001929   -9.9578e-04      0.003490      0.002059      0.002477
mu.anon.daily     -0.002993      0.003066      0.013417     -0.007071      0.024192
sg.fee             0.003872   -5.5951e-04     -0.012374      0.005692     -0.017804
sg.disc            0.032789     -0.014055     -0.068533      0.067307     -0.088134
sg.anon            0.013137     -0.003509      0.002725      0.004333     -0.006938
sg.hh             -0.003509      0.014516     -0.003228      0.005666      0.001396
sg.daily           0.002725     -0.003228      0.156011     -0.021850      0.131656
sg.anon.hh         0.004333      0.005666     -0.021850      0.215320     -0.031436
sg.anon.daily     -0.006938      0.001396      0.131656     -0.031436      0.374281

Robust covariance matrix:
                     mu.fee       mu.disc       mu.anon         mu.hh      mu.daily    mu.anon.hh mu.anon.daily        sg.fee       sg.disc
mu.fee             0.030475   -4.4279e-04      0.005939      0.003464     -0.007194     -0.005089      0.014834     -0.009294     -0.037501
mu.disc         -4.4279e-04      2.399458      0.018027     -0.004935      0.076334      0.012737     -0.115791     -0.048659      3.444564
mu.anon            0.005939      0.018027      0.052879      0.043333      0.002698     -0.087501     -0.036497      0.009072      0.028735
mu.hh              0.003464     -0.004935      0.043333      0.046952      0.003307     -0.085953     -0.032026      0.008472     -0.007499
mu.daily          -0.007194      0.076334      0.002698      0.003307      0.030763      0.005130     -0.037442     -0.004204      0.106735
mu.anon.hh        -0.005089      0.012737     -0.087501     -0.085953      0.005130      0.179190      0.059027     -0.015563      0.011959
mu.anon.daily      0.014834     -0.115791     -0.036497     -0.032026     -0.037442      0.059027      0.086815   -3.6431e-04     -0.170122
sg.fee            -0.009294     -0.048659      0.009072      0.008472     -0.004204     -0.015563   -3.6431e-04      0.094938     -0.046180
sg.disc           -0.037501      3.444564      0.028735     -0.007499      0.106735      0.011959     -0.170122     -0.046180      5.164456
sg.anon           -0.004023      0.021654      0.004275      0.001999      0.003749     -0.001592     -0.005309      0.007153      0.036768
sg.hh             -0.002409     -0.012418     -0.002807     -0.001750     -0.003620    2.4085e-04      0.003082    6.1911e-04     -0.020423
sg.daily           0.012367     -0.045142   -9.2613e-04    3.1378e-04     -0.002759      0.003963      0.013402     -0.017377     -0.071795
sg.anon.hh        -0.018083     -0.025171      0.003971      0.001276      0.001358     -0.003910     -0.008098      0.016671      0.025814
sg.anon.daily      0.018229     -0.070468     -0.006033     -0.004295     -0.010381      0.007371      0.032244     -0.037495     -0.152963
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee            -0.004023     -0.002409      0.012367     -0.018083      0.018229
mu.disc            0.021654     -0.012418     -0.045142     -0.025171     -0.070468
mu.anon            0.004275     -0.002807   -9.2613e-04      0.003971     -0.006033
mu.hh              0.001999     -0.001750    3.1378e-04      0.001276     -0.004295
mu.daily           0.003749     -0.003620     -0.002759      0.001358     -0.010381
mu.anon.hh        -0.001592    2.4085e-04      0.003963     -0.003910      0.007371
mu.anon.daily     -0.005309      0.003082      0.013402     -0.008098      0.032244
sg.fee             0.007153    6.1911e-04     -0.017377      0.016671     -0.037495
sg.disc            0.036768     -0.020423     -0.071795      0.025814     -0.152963
sg.anon            0.014700     -0.003928    4.6459e-04      0.008647     -0.012441
sg.hh             -0.003928      0.014832     -0.007067   -1.2662e-04     -0.002809
sg.daily         4.6459e-04     -0.007067      0.100931     -0.017785      0.073012
sg.anon.hh         0.008647   -1.2662e-04     -0.017785      0.044563     -0.048827
sg.anon.daily     -0.012441     -0.002809      0.073012     -0.048827      0.334916

Classical correlation matrix:
                     mu.fee       mu.disc       mu.anon         mu.hh      mu.daily    mu.anon.hh mu.anon.daily        sg.fee       sg.disc
mu.fee              1.00000     -0.110631      0.154997      0.107825     -0.247816     -0.073585       0.29427      -0.02153      -0.13926
mu.disc            -0.11063      1.000000      0.021949     -0.021318      0.288620      0.039962      -0.19377      -0.02998       0.97086
mu.anon             0.15500      0.021949      1.000000      0.873066      0.130553     -0.900289      -0.57493       0.09181       0.01139
mu.hh               0.10783     -0.021318      0.873066      1.000000      0.103238     -0.943759      -0.52634       0.13394      -0.02870
mu.daily           -0.24782      0.288620      0.130553      0.103238      1.000000      0.002201      -0.74236      -0.15867       0.27742
mu.anon.hh         -0.07358      0.039962     -0.900289     -0.943759      0.002201      1.000000       0.51786      -0.11728       0.03899
mu.anon.daily       0.29427     -0.193775     -0.574934     -0.526339     -0.742359      0.517856       1.00000       0.12414      -0.19247
sg.fee             -0.02153     -0.029977      0.091808      0.133943     -0.158668     -0.117277       0.12414       1.00000      -0.02301
sg.disc            -0.13926      0.970859      0.011386     -0.028697      0.277416      0.038985      -0.19247      -0.02301       1.00000
sg.anon            -0.08331      0.116657      0.009705      0.004895      0.159814      0.040409      -0.08439       0.11570       0.12463
sg.hh              -0.07324     -0.053284     -0.059973     -0.001371     -0.148535     -0.019840       0.08224      -0.01590      -0.05082
sg.daily            0.19483     -0.071399      0.011075     -0.003435     -0.050042      0.021209       0.10977      -0.10729      -0.07559
sg.anon.hh         -0.11866      0.006235    7.1665e-04      0.001923      0.047259      0.010652      -0.04924       0.04201       0.06319
sg.anon.daily       0.12428     -0.049592     -0.008903     -0.003606     -0.079554      0.009719       0.12778      -0.09966      -0.06276
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee            -0.083306     -0.073237      0.194826     -0.118655      0.124279
mu.disc            0.116657     -0.053284     -0.071399      0.006235     -0.049592
mu.anon            0.009705     -0.059973      0.011075    7.1665e-04     -0.008903
mu.hh              0.004895     -0.001371     -0.003435      0.001923     -0.003606
mu.daily           0.159814     -0.148535     -0.050042      0.047259     -0.079554
mu.anon.hh         0.040409     -0.019840      0.021209      0.010652      0.009719
mu.anon.daily     -0.084389      0.082245      0.109773     -0.049240      0.127784
sg.fee             0.115703     -0.015904     -0.107291      0.042007     -0.099663
sg.disc            0.124635     -0.050824     -0.075594      0.063195     -0.062763
sg.anon            1.000000     -0.254074      0.060196      0.081479     -0.098939
sg.hh             -0.254074      1.000000     -0.067829      0.101340      0.018934
sg.daily           0.060196     -0.067829      1.000000     -0.119217      0.544833
sg.anon.hh         0.081479      0.101340     -0.119217      1.000000     -0.110736
sg.anon.daily     -0.098939      0.018934      0.544833     -0.110736      1.000000

Robust correlation matrix:
                     mu.fee       mu.disc       mu.anon         mu.hh      mu.daily    mu.anon.hh mu.anon.daily        sg.fee       sg.disc
mu.fee             1.000000     -0.001637       0.14795      0.091567      -0.23496     -0.068865      0.288402     -0.172790      -0.09453
mu.disc           -0.001637      1.000000       0.05061     -0.014704       0.28096      0.019425     -0.253700     -0.101950       0.97851
mu.anon            0.147947      0.050608       1.00000      0.869663       0.06689     -0.898907     -0.538668      0.128040       0.05499
mu.hh              0.091567     -0.014704       0.86966      1.000000       0.08702     -0.937079     -0.501625      0.126899      -0.01523
mu.daily          -0.234958      0.280962       0.06689      0.087016       1.00000      0.069095     -0.724511     -0.077790       0.26778
mu.anon.hh        -0.068865      0.019425      -0.89891     -0.937079       0.06910      1.000000      0.473254     -0.119320       0.01243
mu.anon.daily      0.288402     -0.253700      -0.53867     -0.501625      -0.72451      0.473254      1.000000     -0.004013      -0.25407
sg.fee            -0.172790     -0.101950       0.12804      0.126899      -0.07779     -0.119320     -0.004013      1.000000      -0.06595
sg.disc           -0.094527      0.978510       0.05499     -0.015229       0.26778      0.012432     -0.254068     -0.065951       1.00000
sg.anon           -0.190075      0.115299       0.15332      0.076100       0.17632     -0.031024     -0.148612      0.191487       0.13344
sg.hh             -0.113290     -0.065827      -0.10023     -0.066317      -0.16946      0.004672      0.085902      0.016499      -0.07379
sg.daily           0.222992     -0.091729      -0.01268      0.004558      -0.04951      0.029466      0.143174     -0.177519      -0.09944
sg.anon.hh        -0.490703     -0.076976       0.08179      0.027902       0.03669     -0.043753     -0.130192      0.256299       0.05381
sg.anon.daily      0.180436     -0.078609      -0.04533     -0.034255      -0.10227      0.030089      0.189098     -0.210276      -0.11631
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee             -0.19008     -0.113290      0.222992     -0.490703       0.18044
mu.disc             0.11530     -0.065827     -0.091729     -0.076976      -0.07861
mu.anon             0.15332     -0.100227     -0.012677      0.081794      -0.04533
mu.hh               0.07610     -0.066317      0.004558      0.027902      -0.03425
mu.daily            0.17632     -0.169459     -0.049510      0.036687      -0.10227
mu.anon.hh         -0.03102      0.004672      0.029466     -0.043753       0.03009
mu.anon.daily      -0.14861      0.085902      0.143174     -0.130192       0.18910
sg.fee              0.19149      0.016499     -0.177519      0.256299      -0.21028
sg.disc             0.13344     -0.073791     -0.099442      0.053810      -0.11631
sg.anon             1.00000     -0.265997      0.012062      0.337831      -0.17730
sg.hh              -0.26600      1.000000     -0.182653     -0.004925      -0.03985
sg.daily            0.01206     -0.182653      1.000000     -0.265192       0.39711
sg.anon.hh          0.33783     -0.004925     -0.265192      1.000000      -0.39967
sg.anon.daily      -0.17730     -0.039849      0.397111     -0.399675       1.00000

 20 worst outliers in terms of lowest average per choice prediction:
    ID Avg prob per choice
 10990           0.3188296
 10358           0.3391353
 10875           0.3443945
 10741           0.3463345
 10196           0.3474413
 10209           0.3490624
 10316           0.3508732
 10858           0.3513275
 10843           0.3517620
 10810           0.3563728
 10828           0.3565612
 10007           0.3566141
 10909           0.3571949
 10654           0.3634155
 10670           0.3639050
 10972           0.3643995
 10749           0.3685276
 10450           0.3685631
 10115           0.3687519
 10050           0.3732653

Changes in parameter estimates from starting values:
                  Initial    Estimate  Difference
mu.fee             -3.000    -1.64399     1.35601
mu.disc            -3.000    -6.46698    -3.46698
mu.anon             0.000     0.61466     0.61466
mu.hh               0.000     0.15960     0.15960
mu.daily            0.000     0.99841     0.99841
mu.anon.hh          0.000     0.71064     0.71064
mu.anon.daily       0.000    -0.60605    -0.60605
sg.fee              0.000    -2.30613    -2.30613
sg.disc             0.000    -8.30521    -8.30521
sg.anon             0.000     1.48642     1.48642
sg.hh               0.000    -0.57124    -0.57124
sg.daily            0.000     0.22741     0.22741
sg.anon.hh          0.000     0.06847     0.06847
sg.anon.daily       0.000    -0.44334    -0.44334

Settings and functions used in model definition:

apollo_control
--------------
                       Value                                                
modelName              "INT_MXL_PREF_LN_EXC"                                
modelDescr             "MXL model with interaction, pref, ln-norm, with exc"
indivID                "ID"                                                 
panelData              "TRUE"                                               
mixing                 "TRUE"                                               
nCores                 "8"                                                  
seed                   "423543"                                             
debug                  "FALSE"                                              
workInLogs             "FALSE"                                              
HB                     "FALSE"                                              
noValidation           "FALSE"                                              
noDiagnostics          "FALSE"                                              
outputDirectory        ""                                                   
analyticGrad           "TRUE"                                               
analyticGrad_manualSet "FALSE"                                              

Hessian routines attempted
--------------
numerical jacobian of LL analytical gradient

Scaling in estimation
--------------
                   Value
mu.fee        1.64399180
mu.disc       6.46690690
mu.anon       0.61465807
mu.hh         0.15959825
mu.daily      0.99842058
mu.anon.hh    0.71063942
mu.anon.daily 0.60605340
sg.fee        2.30610188
sg.disc       8.30533860
sg.anon       1.48643230
sg.hh         0.57124275
sg.daily      0.22740688
sg.anon.hh    0.06847472
sg.anon.daily 0.44333507

Scaling used in computing Hessian
--------------
                   Value
mu.fee        1.64399432
mu.disc       6.46698443
mu.anon       0.61465721
mu.hh         0.15959846
mu.daily      0.99841435
mu.anon.hh    0.71064051
mu.anon.daily 0.60605361
sg.fee        2.30612569
sg.disc       8.30521029
sg.anon       1.48642194
sg.hh         0.57124156
sg.daily      0.22740698
sg.anon.hh    0.06847472
sg.anon.daily 0.44333573


apollo_randCoeff
----------------
function(apollo_beta, apollo_inputs){
  randcoeff = list()
  randcoeff[["a.fee"]] = -exp(mu.fee + sg.fee*draws.fee)
  randcoeff[["a.disc"]] =  exp(mu.disc + sg.disc*draws.disc)
  randcoeff[["b.anon"]] = mu.anon + sg.anon*draws.anon
  randcoeff[["b.hh"]] =  mu.hh + sg.hh*draws.hh
  randcoeff[["b.daily"]] =  mu.daily + sg.daily*draws.daily 
  randcoeff[["b.anon.hh"]] =  mu.anon.hh + sg.anon.hh*draws.anon.hh
  randcoeff[["b.anon.daily"]] =  mu.anon.daily + sg.anon.daily*draws.anon.daily
  
  return(randcoeff)


apollo_probabilities
--------------------
function(apollo_beta, apollo_inputs, functionality="estimate"){
  
  ### Attach inputs and detach after function exit
  apollo_attach(apollo_beta, apollo_inputs)
  on.exit(apollo_detach(apollo_beta, apollo_inputs))
  P = list()
  V = list()
  V[['1']]  = a.fee*FeeP_1 + a.disc*DiscP_1 + b.anon*(Anon_1==1) +
    b.hh*(HH_1==1) + b.daily*(Daily_1==1) +
    b.anon.hh*(HH_1==1 & Anon_1==1) + b.anon.daily*(Daily_1==1 & Anon_1==1)
  V[['2']]  = a.fee*FeeP_2 + a.disc*DiscP_2 + b.anon*(Anon_2==1) +
    b.hh*(HH_2==1) + b.daily*(Daily_2==1) +
    b.anon.hh*(HH_2==1 & Anon_2==1) + b.anon.daily*(Daily_2==1 & Anon_2==1)

  mnl_settings = list(
    alternatives  = c("1"=1, "2"=2),
    avail         = list("1"=av_1, "2"=av_2), 
    choiceVar     = choice,
    V             = V
  )
  
  ### Compute probabilities using MNL model
  P[['model']] = apollo_mnl(mnl_settings, functionality)
  
  ### Take product across observation for same individual
  P = apollo_panelProd(P, apollo_inputs, functionality)
  ### Average across inter-individual draws
  P = apollo_avgInterDraws(P, apollo_inputs, functionality)
  ### Prepare and return outputs of function
  P = apollo_prepareProb(P, apollo_inputs, functionality)
  return(P)
