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

Model name                       : INT_MXL_WTP_LN
Model description                : MXL model with interaction, wtp, log-norm, control
Model run at                     : 2021-10-30 15:05:50
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)                        : -2771.506
Rho-square (0)                   :  0.2714 
Adj.Rho-square (0)               :  0.2677 
AIC                              :  5571.01 
BIC                              :  5663.56 


Estimated parameters             :  14
Time taken (hh:mm:ss)            :  00:08:52.52 
     pre-estimation              :  00:02:12.18 
     estimation                  :  00:03:0.26 
     post-estimation             :  00:03:40.08 
Iterations                       :  63  
Min abs eigenvalue of Hessian    :  0.07424 

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            -1.7788      0.1049    -16.9624    0.000000   -26.49846    0.000000      0.1322      -13.4579    0.000000     -21.02380
mu.disc           -5.2845      0.9261     -5.7062   1.156e-08    -6.78595   1.153e-11      1.0024       -5.2717   1.352e-07      -6.26926
mu.anon           -3.5067      1.5674     -2.2373    0.025265    -2.87535    0.004036      1.5992       -2.1928    0.028325      -2.81806
mu.hh             -1.5295      1.4103     -1.0846    0.278107    -1.79367    0.072866      1.4685       -1.0416    0.297605      -1.72256
mu.daily          -7.0444      1.6984     -4.1478   3.357e-05    -4.73662   2.173e-06      2.5533       -2.7590    0.005798      -3.15065
mu.anon.hh        -3.3555      2.7765     -1.2085    0.226839    -1.56871    0.116716      2.8228       -1.1887    0.234550      -1.54297
mu.anon.daily      8.0971      2.5821      3.1359    0.001713     2.74861    0.005985      3.4082        2.3758    0.017511       2.08238
sg.fee            -0.9073      0.1226     -7.3993   1.370e-13   -15.55489    0.000000      0.1336       -6.7897   1.124e-11     -14.27336
sg.disc           -6.9317      1.2875     -5.3839   7.288e-08    -6.16063   7.246e-10      1.4319       -4.8410   1.292e-06      -5.53943
sg.anon           12.1364      1.0464     11.5979    0.000000    10.64226    0.000000      1.4228        8.5300    0.000000       7.82714
sg.hh             -4.9269      0.7190     -6.8522   7.271e-12    -8.24300   2.220e-16      0.9197       -5.3570   8.462e-08      -6.44427
sg.daily          -0.2771      1.0695     -0.2591    0.795551    -1.19409    0.232443      0.5556       -0.4988    0.617955      -2.29846
sg.anon.hh         0.8388      2.4240      0.3461    0.729296    -0.06648    0.946993      2.6832        0.3126    0.754563      -0.06006
sg.anon.daily      9.1552      1.2769      7.1697   7.518e-13     6.38655   1.697e-10      1.1712        7.8171   5.329e-15       6.96325
               p(2-sided)
mu.fee           0.000000
mu.disc         3.628e-10
mu.anon          0.004831
mu.hh            0.084969
mu.daily         0.001629
mu.anon.hh       0.122837
mu.anon.daily    0.037307
sg.fee           0.000000
sg.disc         3.035e-08
sg.anon         4.885e-15
sg.hh           1.162e-10
sg.daily         0.021535
sg.anon.hh       0.952107
sg.anon.daily   3.325e-12


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             0.010997      -0.02709     -0.019631     -0.020045       0.10992       0.05904      -0.13725     -0.005514      -0.05203
mu.disc           -0.027094       0.85768     -0.059841      0.033966      -0.48746      -0.19771       0.53668      0.054329       1.14873
mu.anon           -0.019631      -0.05984      2.456622      1.775218       0.06168      -3.71231      -1.70606      0.007379      -0.02489
mu.hh             -0.020045       0.03397      1.775218      1.988852       0.04120      -3.64104      -1.35714      0.009325       0.05856
mu.daily           0.109917      -0.48746      0.061679      0.041200       2.88440       0.57125      -3.65381     -0.057065      -0.75548
mu.anon.hh         0.059035      -0.19771     -3.712311     -3.641038       0.57125       7.70904       2.18822     -0.034001      -0.30793
mu.anon.daily     -0.137252       0.53668     -1.706059     -1.357143      -3.65381       2.18822       6.66712      0.054720       0.81235
sg.fee            -0.005514       0.05433      0.007379      0.009325      -0.05706      -0.03400       0.05472      0.015034       0.10188
sg.disc           -0.052027       1.14873     -0.024889      0.058565      -0.75548      -0.30793       0.81235      0.101875       1.65762
sg.anon           -0.070674       0.19494      0.252908      0.151177      -1.15775      -0.52241       1.45336      0.030660       0.31098
sg.hh              0.023159      -0.07112     -0.062557      0.018944       0.49110       0.12060      -0.62686     -0.017920      -0.11781
sg.daily           0.010804      -0.03384      0.097342      0.096738       0.29535      -0.18008      -0.42649      0.005849      -0.03060
sg.anon.hh        -0.062303      -0.19548      0.238093      0.097715      -2.09900      -0.29471       2.66562     -0.035536      -0.24453
sg.anon.daily     -0.019565       0.08110      0.268534      0.217926      -0.38441      -0.53072       0.83649      0.020727       0.14995
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee             -0.07067       0.02316      0.010804      -0.06230      -0.01956
mu.disc             0.19494      -0.07112     -0.033844      -0.19548       0.08110
mu.anon             0.25291      -0.06256      0.097342       0.23809       0.26853
mu.hh               0.15118       0.01894      0.096738       0.09772       0.21793
mu.daily           -1.15775       0.49110      0.295354      -2.09900      -0.38441
mu.anon.hh         -0.52241       0.12060     -0.180079      -0.29471      -0.53072
mu.anon.daily       1.45336      -0.62686     -0.426491       2.66562       0.83649
sg.fee              0.03066      -0.01792      0.005849      -0.03554       0.02073
sg.disc             0.31098      -0.11781     -0.030601      -0.24453       0.14995
sg.anon             1.09503      -0.34850     -0.184567       0.84926       0.15882
sg.hh              -0.34850       0.51699      0.068585      -0.31473      -0.04272
sg.daily           -0.18457       0.06858      1.143919      -0.59054       0.40694
sg.anon.hh          0.84926      -0.31473     -0.590539       5.87562       0.11078
sg.anon.daily       0.15882      -0.04272      0.406944       0.11078       1.63057

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             0.017469      -0.04587      -0.04698      -0.02610       0.26410       0.10313       -0.3023     -0.007953      -0.08370
mu.disc           -0.045867       1.00488       0.05208       0.12901      -1.00614      -0.37866        1.2360      0.095769       1.40526
mu.anon           -0.046984       0.05208       2.55751       1.78953      -0.49775      -3.81116       -1.0169      0.023393       0.17580
mu.hh             -0.026100       0.12901       1.78953       2.15645      -0.03101      -3.73747       -1.1877      0.013856       0.19618
mu.daily           0.264100      -1.00614      -0.49775      -0.03101       6.51916       1.42133       -7.9289     -0.129442      -1.61458
mu.anon.hh         0.103128      -0.37866      -3.81116      -3.73747       1.42133       7.96830        1.2769     -0.071222      -0.65772
mu.anon.daily     -0.302346       1.23600      -1.01691      -1.18774      -7.92895       1.27695       11.6156      0.124143       1.88149
sg.fee            -0.007953       0.09577       0.02339       0.01386      -0.12944      -0.07122        0.1241      0.017855       0.15814
sg.disc           -0.083704       1.40526       0.17580       0.19618      -1.61458      -0.65772        1.8815      0.158139       2.05024
sg.anon           -0.145448       0.43116       0.27829       0.07293      -2.83223      -0.72667        3.3193      0.062601       0.68019
sg.hh              0.052932      -0.13160      -0.12707       0.22467       1.22416       0.10692       -1.4121     -0.034309      -0.23484
sg.daily           0.029258      -0.07625       0.07965       0.03998       0.73208      -0.07072       -0.9759      0.002410      -0.08700
sg.anon.hh        -0.206580       0.09470       0.76916       0.19024      -5.52262      -0.89213        6.8779     -0.007416       0.23595
sg.anon.daily     -0.032817       0.23164       0.38962       0.13895      -0.87114      -0.53046        1.2832      0.034701       0.39536
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee             -0.14545      0.052932      0.029258     -0.206580     -0.032817
mu.disc             0.43116     -0.131600     -0.076247      0.094703      0.231636
mu.anon             0.27829     -0.127067      0.079650      0.769162      0.389616
mu.hh               0.07293      0.224666      0.039983      0.190239      0.138951
mu.daily           -2.83223      1.224161      0.732079     -5.522622     -0.871138
mu.anon.hh         -0.72667      0.106916     -0.070717     -0.892131     -0.530461
mu.anon.daily       3.31931     -1.412050     -0.975913      6.877893      1.283231
sg.fee              0.06260     -0.034309      0.002410     -0.007416      0.034701
sg.disc             0.68019     -0.234840     -0.086999      0.235948      0.395362
sg.anon             2.02435     -0.767461     -0.435441      2.385823      0.100711
sg.hh              -0.76746      0.845876      0.170676     -1.002405     -0.007443
sg.daily           -0.43544      0.170676      0.308740     -0.911156      0.278157
sg.anon.hh          2.38582     -1.002405     -0.911156      7.199550      0.466551
sg.anon.daily       0.10071     -0.007443      0.278157      0.466551      1.371670

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      -0.27898      -0.11944      -0.13554       0.61718       0.20276       -0.5069      -0.42885      -0.38535
mu.disc            -0.27898       1.00000      -0.04123       0.02601      -0.30992      -0.07689        0.2244       0.47844       0.96342
mu.anon            -0.11944      -0.04123       1.00000       0.80312       0.02317      -0.85305       -0.4216       0.03840      -0.01233
mu.hh              -0.13554       0.02601       0.80312       1.00000       0.01720      -0.92987       -0.3727       0.05393       0.03225
mu.daily            0.61718      -0.30992       0.02317       0.01720       1.00000       0.12114       -0.8332      -0.27403      -0.34550
mu.anon.hh          0.20276      -0.07689      -0.85305      -0.92987       0.12114       1.00000        0.3052      -0.09987      -0.08614
mu.anon.daily      -0.50690       0.22443      -0.42156      -0.37270      -0.83320       0.30523        1.0000       0.17284       0.24436
sg.fee             -0.42885       0.47844       0.03840       0.05393      -0.27403      -0.09987        0.1728       1.00000       0.64533
sg.disc            -0.38535       0.96342      -0.01233       0.03225      -0.34550      -0.08614        0.2444       0.64533       1.00000
sg.anon            -0.64405       0.20115       0.15420       0.10244      -0.65144      -0.17980        0.5379       0.23895       0.23083
sg.hh               0.30714      -0.10681      -0.05551       0.01868       0.40216       0.06041       -0.3376      -0.20326      -0.12727
sg.daily            0.09633      -0.03417       0.05807       0.06414       0.16260      -0.06064       -0.1544       0.04460      -0.02222
sg.anon.hh         -0.24510      -0.08708       0.06267       0.02858      -0.50987      -0.04379        0.4259      -0.11956      -0.07836
sg.anon.daily      -0.14611       0.06857       0.13417       0.12101      -0.17725      -0.14969        0.2537       0.13238       0.09121
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee              -0.6440       0.30714       0.09633      -0.24510      -0.14611
mu.disc              0.2012      -0.10681      -0.03417      -0.08708       0.06857
mu.anon              0.1542      -0.05551       0.05807       0.06267       0.13417
mu.hh                0.1024       0.01868       0.06414       0.02858       0.12101
mu.daily            -0.6514       0.40216       0.16260      -0.50987      -0.17725
mu.anon.hh          -0.1798       0.06041      -0.06064      -0.04379      -0.14969
mu.anon.daily        0.5379      -0.33764      -0.15443       0.42589       0.25370
sg.fee               0.2390      -0.20326       0.04460      -0.11956       0.13238
sg.disc              0.2308      -0.12727      -0.02222      -0.07836       0.09121
sg.anon              1.0000      -0.46318      -0.16491       0.33481       0.11886
sg.hh               -0.4632       1.00000       0.08918      -0.18058      -0.04652
sg.daily            -0.1649       0.08918       1.00000      -0.22778       0.29797
sg.anon.hh           0.3348      -0.18058      -0.22778       1.00000       0.03579
sg.anon.daily        0.1189      -0.04652       0.29797       0.03579       1.00000

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               1.0000      -0.34618      -0.22228     -0.134470      0.782588       0.27641       -0.6712      -0.45031      -0.44229
mu.disc             -0.3462       1.00000       0.03249      0.087642     -0.393101      -0.13382        0.3618       0.71496       0.97903
mu.anon             -0.2223       0.03249       1.00000      0.762012     -0.121902      -0.84424       -0.1866       0.10947       0.07677
mu.hh               -0.1345       0.08764       0.76201      1.000000     -0.008270      -0.90162       -0.2373       0.07061       0.09330
mu.daily             0.7826      -0.39310      -0.12190     -0.008270      1.000000       0.19720       -0.9112      -0.37940      -0.44163
mu.anon.hh           0.2764      -0.13382      -0.84424     -0.901624      0.197204       1.00000        0.1327      -0.18882      -0.16272
mu.anon.daily       -0.6712       0.36178      -0.18658     -0.237317     -0.911169       0.13273        1.0000       0.27259       0.38555
sg.fee              -0.4503       0.71496       0.10947      0.070611     -0.379397      -0.18882        0.2726       1.00000       0.82652
sg.disc             -0.4423       0.97903       0.07677      0.093301     -0.441633      -0.16272        0.3855       0.82652       1.00000
sg.anon             -0.7734       0.30230       0.12231      0.034904     -0.779632      -0.18093        0.6845       0.32927       0.33388
sg.hh                0.4354      -0.14274      -0.08639      0.166347      0.521302       0.04118       -0.4505      -0.27917      -0.17833
sg.daily             0.3984      -0.13689       0.08964      0.049001      0.516018      -0.04509       -0.5153       0.03246      -0.10935
sg.anon.hh          -0.5825       0.03521       0.17925      0.048281     -0.806115      -0.11779        0.7521      -0.02068       0.06141
sg.anon.daily       -0.2120       0.19730       0.20802      0.080792     -0.291317      -0.16045        0.3215       0.22174       0.23576
                    sg.anon         sg.hh      sg.daily    sg.anon.hh sg.anon.daily
mu.fee             -0.77344      0.435434       0.39839      -0.58250     -0.212002
mu.disc             0.30230     -0.142740      -0.13689       0.03521      0.197298
mu.anon             0.12231     -0.086391       0.08964       0.17925      0.208019
mu.hh               0.03490      0.166347       0.04900       0.04828      0.080792
mu.daily           -0.77963      0.521302       0.51602      -0.80611     -0.291317
mu.anon.hh         -0.18093      0.041182      -0.04509      -0.11779     -0.160452
mu.anon.daily       0.68452     -0.450481      -0.51534       0.75211      0.321484
sg.fee              0.32927     -0.279168       0.03246      -0.02068      0.221736
sg.disc             0.33388     -0.178327      -0.10935       0.06141      0.235759
sg.anon             1.00000     -0.586489      -0.55079       0.62495      0.060438
sg.hh              -0.58649      1.000000       0.33398      -0.40620     -0.006909
sg.daily           -0.55079      0.333982       1.00000      -0.61114      0.427433
sg.anon.hh          0.62495     -0.406197      -0.61114       1.00000      0.148464
sg.anon.daily       0.06044     -0.006909       0.42743       0.14846      1.000000

 20 worst outliers in terms of lowest average per choice prediction:
    ID Avg prob per choice
 10358           0.3244949
 10196           0.3272176
 10007           0.3376153
 10990           0.3442417
 10858           0.3446344
 10749           0.3450376
 10670           0.3452020
 10316           0.3459543
 10828           0.3469817
 10654           0.3553429
 10442           0.3556507
 10243           0.3566993
 10875           0.3579197
 10972           0.3596014
 10209           0.3600792
 10115           0.3625565
 10741           0.3638756
 10185           0.3654049
 10516           0.3656460
 10165           0.3698295

Changes in parameter estimates from starting values:
                  Initial    Estimate  Difference
mu.fee             -3.000     -1.7788      1.2212
mu.disc            -3.000     -5.2845     -2.2845
mu.anon             0.000     -3.5067     -3.5067
mu.hh               0.000     -1.5295     -1.5295
mu.daily            0.000     -7.0444     -7.0444
mu.anon.hh          0.000     -3.3555     -3.3555
mu.anon.daily       0.000      8.0971      8.0971
sg.fee              0.000     -0.9073     -0.9073
sg.disc             0.000     -6.9317     -6.9317
sg.anon             0.000     12.1364     12.1364
sg.hh               0.000     -4.9269     -4.9269
sg.daily            0.000     -0.2771     -0.2771
sg.anon.hh          0.000      0.8388      0.8388
sg.anon.daily       0.000      9.1552      9.1552

Settings and functions used in model definition:

apollo_control
--------------
                       Value                                               
modelName              "INT_MXL_WTP_LN"                                    
modelDescr             "MXL model with interaction, wtp, log-norm, control"
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         1.7787566
mu.disc        5.2845714
mu.anon        3.5067054
mu.hh          1.5295471
mu.daily       7.0444302
mu.anon.hh     3.3555322
mu.anon.daily  8.0971450
sg.fee         0.9072620
sg.disc        6.9316785
sg.anon       12.1363610
sg.hh          4.9269001
sg.daily       0.2771280
sg.anon.hh     0.8388451
sg.anon.daily  9.1552421

Scaling used in computing Hessian
--------------
                   Value
mu.fee         1.7787561
mu.disc        5.2845379
mu.anon        3.5067096
mu.hh          1.5295490
mu.daily       7.0444489
mu.anon.hh     3.3555369
mu.anon.daily  8.0971134
sg.fee         0.9072614
sg.disc        6.9317235
sg.anon       12.1364367
sg.hh          4.9268954
sg.daily       0.2771280
sg.anon.hh     0.8388451
sg.anon.daily  9.1552397


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.disc*DiscP_1 + a.fee*(FeeP_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.disc*DiscP_2 + a.fee*(FeeP_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)
