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

Model name                       : INT_MXL_WTP_LN_IN
Model description                : MXL model with interaction, wtp, log-norm, in
Model run at                     : 2021-10-30 16:11:35
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)                        : -3518.235
LL(0)                            : -3803.992
LL(C)                            : Not applicable
LL(final)                        : -3046.096
Rho-square (0)                   :  0.1992 
Adj.Rho-square (0)               :  0.1956 
AIC                              :  6120.19 
BIC                              :  6212.74 


Estimated parameters             :  14
Time taken (hh:mm:ss)            :  00:16:18.38 
     pre-estimation              :  00:02:17.84 
     estimation                  :  00:10:16.74 
     post-estimation             :  00:03:43.8 
Iterations                       :  110  

Estimates:
                 Estimate        s.e.   t.rat.(0)  p(2-sided)    Rob.s.e. Rob.t.rat.(0)  p(2-sided)
mu.fee          -1.781381     0.35986     -4.9501   7.416e-07     1.06159      -1.67804    0.093340
mu.disc        -17.115075     1.53747    -11.1320     0.00000     6.28044      -2.72514    0.006427
mu.anon         -0.222940         NaN         NaN         NaN     9.28575      -0.02401    0.980846
mu.hh           -0.222928         NaN         NaN         NaN     9.28575      -0.02401    0.980847
mu.daily         0.812726     0.48142      1.6882     0.09138     2.94268       0.27619    0.782405
mu.anon.hh       0.587906     0.17066      3.4448  5.7144e-04    19.08559       0.03080    0.975426
mu.anon.daily   -0.577027         NaN         NaN         NaN     6.36135      -0.09071    0.927724
sg.fee          -7.230074     0.75350     -9.5953     0.00000     3.96565      -1.82318    0.068277
sg.disc          0.139633     0.84378      0.1655     0.86856    10.78265       0.01295    0.989668
sg.anon        -8.650e-06   1.283e-06     -6.7447   1.533e-11   5.711e-06      -1.51478    0.129828
sg.hh          -1.455e-06         NaN         NaN         NaN   5.003e-06      -0.29089    0.771138
sg.daily         0.005410     0.01156      0.4681     0.63973     0.02897       0.18676    0.851851
sg.anon.hh       0.256827     0.15233      1.6859     0.09181     0.94407       0.27204    0.785589
sg.anon.daily   -0.003665     0.01009     -0.3634     0.71633     0.02594      -0.14133    0.887612


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             0.129503     -0.216798      0.010018      0.010012     -0.032571     -0.025719       0.02170      0.012038      0.363413
mu.disc           -0.216798      2.363806     -1.928867     -1.928854      0.668903      3.976291       1.25128      1.012354      0.337731
mu.anon            0.010018     -1.928867     -0.015803     -0.015856     -0.122309      0.010294       0.13482     -0.212319      3.388680
mu.hh              0.010012     -1.928854     -0.015856     -0.015909     -0.122292      0.010403       0.13486     -0.212296      3.388684
mu.daily          -0.032571      0.668903     -0.122309     -0.122292      0.231770      0.285141      -0.10554      0.197060     -1.041514
mu.anon.hh        -0.025719      3.976291      0.010294      0.010403      0.285141      0.029126      -0.28820      0.459144     -6.962348
mu.anon.daily      0.021699      1.251285      0.134821      0.134857     -0.105539     -0.288203      -0.02932      0.018968     -2.327797
sg.fee             0.012038      1.012354     -0.212319     -0.212296      0.197060      0.459144       0.01897      0.567765     -1.399520
sg.disc            0.363413      0.337731      3.388680      3.388684     -1.041514     -6.962348      -2.32780     -1.399520      0.711973
sg.anon           1.856e-07    -1.758e-06     1.668e-06     1.668e-06    -5.417e-07    -3.433e-06    -1.115e-06    -7.055e-07     1.268e-06
sg.hh            -1.695e-07     3.154e-07    -1.570e-06    -1.570e-06     4.929e-07     3.227e-06     1.069e-06     6.861e-07     4.171e-07
sg.daily        -2.5049e-04     -0.005238   -7.1015e-04   -7.1031e-04      0.001382      0.001643   -4.0514e-04    8.8922e-04      0.010316
sg.anon.hh        -0.010291      0.214354     -0.038702     -0.038697      0.073306      0.090232      -0.03343      0.062471     -0.334370
sg.anon.daily      0.001028      0.001787      0.004899      0.004899     -0.005480     -0.010750    3.8859e-04     -0.004453     -0.007311
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee            1.856e-07    -1.695e-07   -2.5049e-04     -0.010291      0.001028
mu.disc          -1.758e-06     3.154e-07     -0.005238      0.214354      0.001787
mu.anon           1.668e-06    -1.570e-06   -7.1015e-04     -0.038702      0.004899
mu.hh             1.668e-06    -1.570e-06   -7.1031e-04     -0.038697      0.004899
mu.daily         -5.417e-07     4.929e-07      0.001382      0.073306     -0.005480
mu.anon.hh       -3.433e-06     3.227e-06      0.001643      0.090232     -0.010750
mu.anon.daily    -1.115e-06     1.069e-06   -4.0514e-04     -0.033431    3.8859e-04
sg.fee           -7.055e-07     6.861e-07    8.8922e-04      0.062471     -0.004453
sg.disc           1.268e-06     4.171e-07      0.010316     -0.334370     -0.007311
sg.anon           1.645e-12    -7.710e-13     6.926e-09    -1.743e-07    -5.222e-09
sg.hh            -7.710e-13    -1.841e-13    -4.297e-09     1.581e-07     2.630e-09
sg.daily          6.926e-09    -4.297e-09    1.3358e-04    4.0178e-04    -7.583e-05
sg.anon.hh       -1.743e-07     1.581e-07    4.0178e-04      0.023206     -0.001721
sg.anon.daily    -5.222e-09     2.630e-09    -7.583e-05     -0.001721    1.0175e-04

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              1.12697      -1.82783        9.2741        9.2741      -2.91478      -19.0657       -6.3079      -3.84790      -0.85842
mu.disc            -1.82783      39.44393      -14.6291      -14.6281       7.07094       30.5057        7.5389      10.18427     -63.03663
mu.anon             9.27411     -14.62912       86.2252       86.2252     -26.87202     -177.2220      -58.8699     -36.02643     -11.90000
mu.hh               9.27410     -14.62810       86.2252       86.2252     -26.87196     -177.2220      -58.8700     -36.02633     -11.90181
mu.daily           -2.91478       7.07094      -26.8720      -26.8720       8.65936       55.2808       18.0679      11.51536      -0.71199
mu.anon.hh        -19.06571      30.50567     -177.2220     -177.2220      55.28080      364.2598      120.9489      74.09671      23.68790
mu.anon.daily      -6.30790       7.53887      -58.8699      -58.8700      18.06785      120.9489       40.4668      24.31632      12.43496
sg.fee             -3.84790      10.18427      -36.0264      -36.0263      11.51536       74.0967       24.3163      15.72634      -2.08105
sg.disc            -0.85842     -63.03660      -11.9000      -11.9018      -0.71199       23.6879       12.4350      -2.08104     116.26562
sg.anon           2.418e-06    -3.546e-05     2.043e-05     2.043e-05    -8.526e-06    -4.237e-05    -1.185e-05    -1.195e-05     5.356e-05
sg.hh             5.046e-07     2.900e-05     6.539e-06     6.540e-06     9.683e-09    -1.308e-05    -6.461e-06     5.481e-07    -5.393e-05
sg.daily            0.02778      -0.03028        0.2594        0.2594      -0.07920       -0.5329       -0.1786      -0.10688      -0.06006
sg.anon.hh         -0.93545       2.25836       -8.6251       -8.6250       2.77807       17.7432        5.8005       3.69482      -0.20879
sg.anon.daily      -0.01754      -0.06535       -0.1711       -0.1711       0.04419        0.3500        0.1256       0.06068       0.18966
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee            2.418e-06     5.046e-07       0.02778      -0.93545      -0.01754
mu.disc          -3.546e-05     2.900e-05      -0.03028       2.25836      -0.06535
mu.anon           2.043e-05     6.539e-06       0.25939      -8.62507      -0.17108
mu.hh             2.043e-05     6.540e-06       0.25939      -8.62505      -0.17108
mu.daily         -8.526e-06     9.684e-09      -0.07920       2.77807       0.04419
mu.anon.hh       -4.237e-05    -1.308e-05      -0.53286      17.74316       0.35003
mu.anon.daily    -1.185e-05    -6.461e-06      -0.17859       5.80046       0.12565
sg.fee           -1.195e-05     5.481e-07      -0.10688       3.69482       0.06068
sg.disc           5.356e-05    -5.393e-05      -0.06006      -0.20879       0.18966
sg.anon           3.261e-11    -2.453e-11     4.930e-08    -2.727e-06     4.096e-08
sg.hh            -2.453e-11     2.503e-11     3.082e-08    -6.009e-09    -8.981e-08
sg.daily          4.930e-08     3.082e-08    8.3909e-04      -0.02544   -6.0292e-04
sg.anon.hh       -2.727e-06    -6.009e-09      -0.02544       0.89126       0.01423
sg.anon.daily     4.096e-08    -8.981e-08   -6.0292e-04       0.01423    6.7266e-04

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       -0.3918           NaN           NaN       -0.1880       -0.4188           NaN       0.04440        1.1968
mu.disc            -0.39184        1.0000           NaN           NaN        0.9037       15.1541           NaN       0.87386        0.2603
mu.anon                 NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
mu.hh                   NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
mu.daily           -0.18800        0.9037           NaN           NaN        1.0000        3.4705           NaN       0.54323       -2.5639
mu.anon.hh         -0.41877       15.1541           NaN           NaN        3.4705        1.0000           NaN       3.57046      -48.3485
mu.anon.daily           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
sg.fee              0.04440        0.8739           NaN           NaN        0.5432        3.5705           NaN       1.00000       -2.2012
sg.disc             1.19682        0.2603           NaN           NaN       -2.5639      -48.3485           NaN      -2.20122        1.0000
sg.anon             0.40213       -0.8914           NaN           NaN       -0.8774      -15.6827           NaN      -0.73008        1.1717
sg.hh                   NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
sg.daily           -0.06023       -0.2948           NaN           NaN        0.2483        0.8329           NaN       0.10211        1.0579
sg.anon.hh         -0.18773        0.9152           NaN           NaN        0.9996        3.4708           NaN       0.54425       -2.6014
sg.anon.daily       0.28307        0.1152           NaN           NaN       -1.1284       -6.2444           NaN      -0.58591       -0.8589
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee               0.4021           NaN      -0.06023       -0.1877        0.2831
mu.disc             -0.8914           NaN      -0.29476        0.9152        0.1152
mu.anon                 NaN           NaN           NaN           NaN           NaN
mu.hh                   NaN           NaN           NaN           NaN           NaN
mu.daily            -0.8774           NaN       0.24829        0.9996       -1.1284
mu.anon.hh         -15.6827           NaN       0.83290        3.4708       -6.2444
mu.anon.daily           NaN           NaN           NaN           NaN           NaN
sg.fee              -0.7301           NaN       0.10211        0.5442       -0.5859
sg.disc              1.1717           NaN       1.05788       -2.6014       -0.8589
sg.anon              1.0000           NaN       0.46727       -0.8924       -0.4037
sg.hh                   NaN           NaN           NaN           NaN           NaN
sg.daily             0.4673           NaN       1.00000        0.2282       -0.6504
sg.anon.hh          -0.8924           NaN       0.22821        1.0000       -1.1203
sg.anon.daily       -0.4037           NaN      -0.65043       -1.1203        1.0000

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              1.00000       -0.2742        0.9408        0.9408      -0.93305       -0.9410       -0.9341      -0.91402      -0.07499
mu.disc            -0.27415        1.0000       -0.2508       -0.2508       0.38260        0.2545        0.1887       0.40891      -0.93084
mu.anon             0.94080       -0.2508        1.0000        1.0000      -0.98342       -1.0000       -0.9966      -0.97834      -0.11885
mu.hh               0.94080       -0.2508        1.0000        1.0000      -0.98342       -1.0000       -0.9966      -0.97834      -0.11887
mu.daily           -0.93305        0.3826       -0.9834       -0.9834       1.00000        0.9843        0.9652       0.98678      -0.02244
mu.anon.hh         -0.94100        0.2545       -1.0000       -1.0000       0.98430        1.0000        0.9962       0.97899       0.11511
mu.anon.daily      -0.93407        0.1887       -0.9966       -0.9966       0.96519        0.9962        1.0000       0.96391       0.18129
sg.fee             -0.91402        0.4089       -0.9783       -0.9783       0.98678        0.9790        0.9639       1.00000      -0.04867
sg.disc            -0.07499       -0.9308       -0.1189       -0.1189      -0.02244        0.1151        0.1813      -0.04867       1.00000
sg.anon             0.39888       -0.9888        0.3853        0.3853      -0.50735       -0.3888       -0.3261      -0.52775       0.86983
sg.hh               0.09500        0.9228        0.1407        0.1408    6.5768e-04       -0.1370       -0.2030       0.02762      -0.99970
sg.daily            0.90349       -0.1664        0.9644        0.9644      -0.92911       -0.9638       -0.9692      -0.93040      -0.19228
sg.anon.hh         -0.93339        0.3809       -0.9839       -0.9839       0.99999        0.9847        0.9659       0.98691      -0.02051
sg.anon.daily      -0.63710       -0.4012       -0.7104       -0.7104       0.57896        0.7071        0.7616       0.59002       0.67819
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee               0.3989      0.095004        0.9035     -0.933389       -0.6371
mu.disc             -0.9888      0.922813       -0.1664      0.380891       -0.4012
mu.anon              0.3853      0.140738        0.9644     -0.983883       -0.7104
mu.hh                0.3853      0.140756        0.9644     -0.983880       -0.7104
mu.daily            -0.5074    6.5770e-04       -0.9291      0.999994        0.5790
mu.anon.hh          -0.3888     -0.136999       -0.9638      0.984744        0.7071
mu.anon.daily       -0.3261     -0.202991       -0.9692      0.965854        0.7616
sg.fee              -0.5278      0.027621       -0.9304      0.986910        0.5900
sg.disc              0.8698     -0.999703       -0.1923     -0.020510        0.6782
sg.anon              1.0000     -0.858565        0.2980     -0.505783        0.2766
sg.hh               -0.8586      1.000000        0.2127     -0.001272       -0.6921
sg.daily             0.2980      0.212660        1.0000     -0.930333       -0.8025
sg.anon.hh          -0.5058     -0.001272       -0.9303      1.000000        0.5814
sg.anon.daily        0.2766     -0.692063       -0.8025      0.581359        1.0000

 20 worst outliers in terms of lowest average per choice prediction:
    ID Avg prob per choice
 10111           0.4415295
 10966           0.4415501
 10283           0.4415907
 10032           0.4416407
 10441           0.4416860
 10225           0.4422846
 10508           0.4423184
 10204           0.4424353
 10149           0.4424933
 10358           0.4426213
 10773           0.4426458
 10482           0.4426945
 11048           0.4427418
 10402           0.4427486
 10244           0.4427597
 10088           0.4428132
 10334           0.4428369
 10511           0.4428955
 10427           0.4429008
 10988           0.4429025

Changes in parameter estimates from starting values:
                  Initial    Estimate  Difference
mu.fee             -3.000   -1.781381    1.218619
mu.disc            -3.000  -17.115075  -14.115075
mu.anon             0.000   -0.222940   -0.222940
mu.hh               0.000   -0.222928   -0.222928
mu.daily            0.000    0.812726    0.812726
mu.anon.hh          0.000    0.587906    0.587906
mu.anon.daily       0.000   -0.577027   -0.577027
sg.fee              0.000   -7.230074   -7.230074
sg.disc             0.000    0.139633    0.139633
sg.anon             0.000  -8.650e-06  -8.650e-06
sg.hh               0.000  -1.455e-06  -1.455e-06
sg.daily            0.000    0.005410    0.005410
sg.anon.hh          0.000    0.256827    0.256827
sg.anon.daily       0.000   -0.003665   -0.003665

Settings and functions used in model definition:

apollo_control
--------------
                       Value                                          
modelName              "INT_MXL_WTP_LN_IN"                            
modelDescr             "MXL model with interaction, wtp, log-norm, in"
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        1.781381e+00
mu.disc       1.711507e+01
mu.anon       2.229401e-01
mu.hh         2.229282e-01
mu.daily      8.127259e-01
mu.anon.hh    5.879058e-01
mu.anon.daily 5.770270e-01
sg.fee        7.230074e+00
sg.disc       1.396328e-01
sg.anon       8.650232e-06
sg.hh         1.455445e-06
sg.daily      5.409806e-03
sg.anon.hh    2.568268e-01
sg.anon.daily 3.665403e-03

Scaling used in computing Hessian
--------------
                     Value
mu.fee        1.781381e+00
mu.disc       1.711507e+01
mu.anon       2.229401e-01
mu.hh         2.229282e-01
mu.daily      8.127259e-01
mu.anon.hh    5.879058e-01
mu.anon.daily 5.770270e-01
sg.fee        7.230074e+00
sg.disc       1.396328e-01
sg.anon       8.650232e-06
sg.hh         1.455445e-06
sg.daily      5.409806e-03
sg.anon.hh    2.568268e-01
sg.anon.daily 3.665403e-03


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)
