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

Model name                       : INT_MXL_WTA_LNO_EXC
Model description                : MXL model with interaction, wta, ln-norm, with exc
Model run at                     : 2021-10-29 16:22:39
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)                        : -2891.412
Rho-square (0)                   :  0.2399 
Adj.Rho-square (0)               :  0.2362 
AIC                              :  5810.82 
BIC                              :  5903.37 


Estimated parameters             :  14
Time taken (hh:mm:ss)            :  00:12:50.59 
     pre-estimation              :  00:02:9.46 
     estimation                  :  00:07:4.73 
     post-estimation             :  00:03:36.39 
Iterations                       :  105  

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         -19.899469         NaN         NaN         NaN         NaN         NaN     15.3319      -1.29791     0.19432      -1.36313
mu.disc        -15.240005         NaN         NaN         NaN         NaN         NaN      7.6090      -2.00289     0.04519      -2.13431
mu.anon        -10.004827         NaN         NaN         NaN         NaN         NaN    163.7135      -0.06111     0.95127      -0.06722
mu.hh          -14.779448         NaN         NaN         NaN         NaN         NaN    163.3373      -0.09048     0.92790      -0.09661
mu.daily        18.019983    6.757710      2.6666    0.007663       2.519     0.01178      5.0651       3.55767  3.7416e-04       3.36024
mu.anon.hh      29.363388    3.593598      8.1710   2.220e-16       7.893   2.887e-15    326.4687       0.08994     0.92833       0.08688
mu.anon.daily  -31.940182         NaN         NaN         NaN         NaN         NaN     26.9426      -1.18549     0.23582      -1.22261
sg.fee         -34.102438         NaN         NaN         NaN         NaN         NaN     21.1185      -1.61481     0.10635      -1.66216
sg.disc        -25.278947         NaN         NaN         NaN         NaN         NaN     12.7198      -1.98738     0.04688      -2.06599
sg.anon         -0.117420         NaN         NaN         NaN         NaN         NaN      0.2355      -0.49862     0.61805      -4.74511
sg.hh            0.004944    0.034556      0.1431    0.886224     -28.795     0.00000      0.2038       0.02427     0.98064      -4.88338
sg.daily         0.796664         NaN         NaN         NaN         NaN         NaN      3.2723       0.24346     0.80765      -0.06214
sg.anon.hh       0.230664    0.006288     36.6818    0.000000    -122.345     0.00000      0.3982       0.57930     0.56239      -1.93213
sg.anon.daily   -5.447513         NaN         NaN         NaN         NaN         NaN     16.0340      -0.33975     0.73405      -0.40211
               p(2-sided)
mu.fee            0.17284
mu.disc           0.03282
mu.anon           0.94641
mu.hh             0.92304
mu.daily       7.7875e-04
mu.anon.hh        0.93077
mu.anon.daily     0.22148
sg.fee            0.09648
sg.disc           0.03883
sg.anon         2.084e-06
sg.hh           1.043e-06
sg.daily          0.95045
sg.anon.hh        0.05334
sg.anon.daily     0.68760


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            -65.59134       33.9064   -391.244329   -391.027368      -4.61342     782.44175       -1.2340   -104.033753       48.2951
mu.disc            33.90641      -12.1621   -106.869365   -107.246522      -4.23280     214.73117      -43.5363     37.551180      -16.0606
mu.anon          -391.24433     -106.8694     -0.162117     -1.346747      48.62712      -3.08279      816.5823   -484.111564     -206.7170
mu.hh            -391.02737     -107.2465     -1.346747     -2.534831      48.54110      -0.69694      816.2284   -483.895057     -207.2241
mu.daily           -4.61342       -4.2328     48.627121     48.541096      45.66664     -97.22975      -39.3948     -5.930232      -10.7708
mu.anon.hh        782.44175      214.7312     -3.082786     -0.696945     -97.22975      12.91395    -1632.4441    968.469678      414.9276
mu.anon.daily      -1.23399      -43.5363    816.582250    816.228360     -39.39480   -1632.44409     -288.8734    -44.726039      -68.9806
sg.fee           -104.03375       37.5512   -484.111564   -483.895057      -5.93023     968.46968      -44.7260   -181.793663       56.2393
sg.disc            48.29507      -16.0606   -206.716993   -207.224095     -10.77079     414.92764      -68.9806     56.239266      -16.5241
sg.anon             0.17990        0.1998     -4.248715     -4.235595      -0.08190       8.45850        0.3184      0.392815        0.3671
sg.hh               0.21009        0.1782     -7.429653     -7.399035      -0.13152      14.77851        0.8324      0.557261        0.3832
sg.daily            0.75413        5.4997   -102.955005   -102.852803      -0.50052     205.67467       37.9438      6.298782        9.2264
sg.anon.hh          0.06413       -0.3548     -0.007336     -0.009050      -0.03869       0.02620       -0.1405      0.007627       -0.5185
sg.anon.daily      -3.49045      -27.8540    507.992365    507.753740       3.95662   -1015.61183     -190.8130    -29.635250      -46.5518
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee              0.17990      0.210093       0.75413      0.064127      -3.49045
mu.disc             0.19981      0.178173       5.49971     -0.354793     -27.85401
mu.anon            -4.24871     -7.429653    -102.95501     -0.007336     507.99237
mu.hh              -4.23560     -7.399035    -102.85280     -0.009050     507.75374
mu.daily           -0.08190     -0.131521      -0.50052     -0.038694       3.95662
mu.anon.hh          8.45850     14.778510     205.67467      0.026201   -1015.61183
mu.anon.daily       0.31837      0.832434      37.94383     -0.140468    -190.81299
sg.fee              0.39282      0.557261       6.29878      0.007627     -29.63525
sg.disc             0.36711      0.383158       9.22643     -0.518471     -46.55176
sg.anon            -0.01160     -0.013809      -0.05954      0.011381       0.11665
sg.hh              -0.01381      0.001194      -0.09297      0.027608       0.38211
sg.daily           -0.05954     -0.092966      -5.27180      0.070090      21.31678
sg.anon.hh          0.01138      0.027608       0.07009     3.954e-05      -0.08693
sg.anon.daily       0.11665      0.382109      21.31678     -0.086926    -108.64785

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             235.0679       25.5213     -1248.900     -1246.558      -47.4501      2493.287      -228.775      312.4527      71.05094
mu.disc             25.5213       57.8972      -681.311      -680.426      -18.1654      1361.402         7.917       55.0264      92.96271
mu.anon          -1248.9005     -681.3112     2.680e+04     2.674e+04      655.5749    -5.345e+04     -1238.705    -2377.4115   -1410.65909
mu.hh            -1246.5579     -680.4264     2.674e+04     2.668e+04      653.9948    -5.332e+04     -1234.493    -2372.3842   -1408.20117
mu.daily           -47.4501      -18.1654       655.575       653.995       25.6553     -1307.401         1.778      -79.7141     -42.74444
mu.anon.hh        2493.2873     1361.4016    -5.345e+04    -5.332e+04    -1307.4007     1.066e+05      2462.891     4743.6805    2816.76530
mu.anon.daily     -228.7748        7.9172     -1238.705     -1234.493        1.7781      2462.891       725.904     -203.3258      -3.12861
sg.fee             312.4527       55.0264     -2377.411     -2372.384      -79.7141      4743.680      -203.326      445.9916     135.46880
sg.disc             71.0509       92.9627     -1410.659     -1408.201      -42.7444      2816.765        -3.129      135.4688     161.79240
sg.anon              0.2069        0.2046        24.440        24.358        0.4374       -48.634        -4.389       -0.7016      -0.01248
sg.hh                2.1648        0.5196        -4.126        -4.119       -0.3805         8.270        -4.015        2.5982       1.09127
sg.daily            30.5241        0.5723       109.527       109.123       -2.1381      -217.534       -87.399       29.5508       3.74947
sg.anon.hh           1.8466        0.5296       -55.048       -54.879       -1.3592       109.638         4.485        4.2090       1.78222
sg.anon.daily     -165.2284       -7.1669      -272.456      -271.099       17.8984       539.087       422.538     -172.3120     -29.86479
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee              0.20694       2.16481       30.5241       1.84656      -165.228
mu.disc             0.20460       0.51959        0.5723       0.52962        -7.167
mu.anon            24.43979      -4.12569      109.5274     -55.04801      -272.456
mu.hh              24.35784      -4.11912      109.1234     -54.87926      -271.099
mu.daily            0.43740      -0.38047       -2.1381      -1.35924        17.898
mu.anon.hh        -48.63402       8.26958     -217.5344     109.63805       539.087
mu.anon.daily      -4.38852      -4.01542      -87.3989       4.48506       422.538
sg.fee             -0.70158       2.59823       29.5508       4.20905      -172.312
sg.disc            -0.01248       1.09127        3.7495       1.78222       -29.865
sg.anon             0.05545       0.02313        0.5124      -0.08140        -2.235
sg.hh               0.02313       0.04152        0.5273    -7.379e-05        -2.584
sg.daily            0.51240       0.52733       10.7078      -0.45360       -52.112
sg.anon.hh         -0.08140    -7.379e-05       -0.4536       0.15855         1.663
sg.anon.daily      -2.23501      -2.58412      -52.1125       1.66251       257.089

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                  NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
mu.disc                 NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
mu.anon                 NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
mu.hh                   NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
mu.daily                NaN           NaN           NaN           NaN        1.0000        -4.004           NaN           NaN           NaN
mu.anon.hh              NaN           NaN           NaN           NaN       -4.0038         1.000           NaN           NaN           NaN
mu.anon.daily           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
sg.fee                  NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
sg.disc                 NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
sg.anon                 NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
sg.hh                   NaN           NaN           NaN           NaN       -0.5632       119.007           NaN           NaN           NaN
sg.daily                NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
sg.anon.hh              NaN           NaN           NaN           NaN       -0.9106         1.159           NaN           NaN           NaN
sg.anon.daily           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN           NaN
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee                  NaN           NaN           NaN           NaN           NaN
mu.disc                 NaN           NaN           NaN           NaN           NaN
mu.anon                 NaN           NaN           NaN           NaN           NaN
mu.hh                   NaN           NaN           NaN           NaN           NaN
mu.daily                NaN       -0.5632           NaN       -0.9106           NaN
mu.anon.hh              NaN      119.0067           NaN        1.1595           NaN
mu.anon.daily           NaN           NaN           NaN           NaN           NaN
sg.fee                  NaN           NaN           NaN           NaN           NaN
sg.disc                 NaN           NaN           NaN           NaN           NaN
sg.anon                 NaN           NaN           NaN           NaN           NaN
sg.hh                   NaN        1.0000           NaN      127.0505           NaN
sg.daily                NaN           NaN           NaN           NaN           NaN
sg.anon.hh              NaN      127.0505           NaN        1.0000           NaN
sg.anon.daily           NaN           NaN           NaN           NaN           NaN

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       0.21876       -0.4976       -0.4978      -0.61101        0.4981     -0.553824        0.9650      0.364329
mu.disc             0.21876       1.00000       -0.5469       -0.5475      -0.47133        0.5480      0.038619        0.3424      0.960508
mu.anon            -0.49756      -0.54693        1.0000        1.0000       0.79059       -1.0000     -0.280830       -0.6876     -0.677421
mu.hh              -0.49777      -0.54748        1.0000        1.0000       0.79050       -1.0000     -0.280520       -0.6878     -0.677798
mu.daily           -0.61101      -0.47133        0.7906        0.7905       1.00000       -0.7906      0.013029       -0.7452     -0.663456
mu.anon.hh          0.49812       0.54804       -1.0000       -1.0000      -0.79064        1.0000      0.280004        0.6880      0.678313
mu.anon.daily      -0.55382       0.03862       -0.2808       -0.2805       0.01303        0.2800      1.000000       -0.3573     -0.009129
sg.fee              0.96499       0.34244       -0.6876       -0.6878      -0.74522        0.6880     -0.357347        1.0000      0.504309
sg.disc             0.36433       0.96051       -0.6774       -0.6778      -0.66346        0.6783     -0.009129        0.5043      1.000000
sg.anon             0.05732       0.11418        0.6339        0.6333       0.36671       -0.6326     -0.691685       -0.1411     -0.004165
sg.hh               0.69294       0.33512       -0.1237       -0.1238      -0.36865        0.1243     -0.731416        0.6038      0.421041
sg.daily            0.60841       0.02298        0.2045        0.2042      -0.12900       -0.2036     -0.991325        0.4276      0.090082
sg.anon.hh          0.30247       0.17481       -0.8445       -0.8438      -0.67395        0.8434      0.418071        0.5005      0.351887
sg.anon.daily      -0.67212      -0.05874       -0.1038       -0.1035       0.22039        0.1030      0.978101       -0.5089     -0.146433
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee             0.057315        0.6929       0.60841        0.3025      -0.67212
mu.disc            0.114183        0.3351       0.02298        0.1748      -0.05874
mu.anon            0.633933       -0.1237       0.20445       -0.8445      -0.10379
mu.hh              0.633262       -0.1238       0.20417       -0.8438      -0.10351
mu.daily           0.366710       -0.3686      -0.12900       -0.6740       0.22039
mu.anon.hh        -0.632599        0.1243      -0.20363        0.8434       0.10299
mu.anon.daily     -0.691685       -0.7314      -0.99133        0.4181       0.97810
sg.fee            -0.141073        0.6038       0.42762        0.5005      -0.50887
sg.disc           -0.004165        0.4210       0.09008        0.3519      -0.14643
sg.anon            1.000000        0.4820       0.66495       -0.8681      -0.59193
sg.hh              0.482029        1.0000       0.79087   -9.0946e-04      -0.79094
sg.daily           0.664953        0.7909       1.00000       -0.3481      -0.99323
sg.anon.hh        -0.868129   -9.0946e-04      -0.34813        1.0000       0.26040
sg.anon.daily     -0.591926       -0.7909      -0.99323        0.2604       1.00000

 20 worst outliers in terms of lowest average per choice prediction:
    ID Avg prob per choice
 10966           0.4518609
 10283           0.4521448
 10111           0.4521524
 10817           0.4522473
 10508           0.4522485
 10726           0.4522644
 10032           0.4523044
 10693           0.4523943
 10988           0.4524060
 10243           0.4524658
 10407           0.4525061
 10294           0.4525062
 10103           0.4525204
 10441           0.4525222
 10057           0.4525449
 10116           0.4525556
 10510           0.4525696
 10059           0.4525734
 10613           0.4525834
 10358           0.4526005

Changes in parameter estimates from starting values:
                  Initial    Estimate  Difference
mu.fee             -3.000  -19.899469  -16.899469
mu.disc            -3.000  -15.240005  -12.240005
mu.anon             0.000  -10.004827  -10.004827
mu.hh               0.000  -14.779448  -14.779448
mu.daily            0.000   18.019983   18.019983
mu.anon.hh          0.000   29.363388   29.363388
mu.anon.daily       0.000  -31.940182  -31.940182
sg.fee              0.000  -34.102438  -34.102438
sg.disc             0.000  -25.278947  -25.278947
sg.anon             0.000   -0.117420   -0.117420
sg.hh               0.000    0.004944    0.004944
sg.daily            0.000    0.796664    0.796664
sg.anon.hh          0.000    0.230664    0.230664
sg.anon.daily       0.000   -5.447513   -5.447513

Settings and functions used in model definition:

apollo_control
--------------
                       Value                                               
modelName              "INT_MXL_WTA_LNO_EXC"                               
modelDescr             "MXL model with interaction, wta, 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        19.899482933
mu.disc       15.240010234
mu.anon       10.004728651
mu.hh         14.779689152
mu.daily      18.019999806
mu.anon.hh    29.363330035
mu.anon.daily 31.940152391
sg.fee        34.102467745
sg.disc       25.278924384
sg.anon        0.117419807
sg.hh          0.004944457
sg.daily       0.796663919
sg.anon.hh     0.230663732
sg.anon.daily  5.447515888

Scaling used in computing Hessian
--------------
                     Value
mu.fee        19.899469252
mu.disc       15.240005126
mu.anon       10.004826734
mu.hh         14.779447800
mu.daily      18.019983400
mu.anon.hh    29.363388333
mu.anon.daily 31.940181826
sg.fee        34.102437614
sg.disc       25.278947059
sg.anon        0.117419817
sg.hh          0.004944457
sg.daily       0.796663893
sg.anon.hh     0.230663656
sg.anon.daily  5.447513171


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)
