Model run using Apollo for R, version 0.2.5 on Linux by ecubero 
www.ApolloChoiceModelling.com

Model name                       : MMNL_NoLux_100_v9_CY
Model description                : MMNL model with Normal distributions for everything besides price
Model run at                     : 2021-11-09 10:57:14
Estimation method                : bfgs
Model diagnosis                  : successful convergence 
Number of individuals            : 135
Number of rows in database       : 1620
Number of modelled outcomes      : 1620

Number of cores used             :  6 
Number of inter-individual draws : 100 (mlhs)

LL(start)                        : -4114.163
LL(0)                            : -2245.797
LL(C)                            : Not applicable
LL(final)                        : -1584.95
Rho-square (0)                   :  0.2943 
Adj.Rho-square (0)               :  0.2871 
AIC                              :  3201.9 
BIC                              :  3288.14 


Estimated parameters             :  16
Time taken (hh:mm:ss)            :  00:04:56.94 
     pre-estimation              :  00:00:15.59 
     estimation                  :  00:03:24.87 
     post-estimation             :  00:01:16.48 
Iterations                       :  75  
Min abs eigenvalue of Hessian    :  0.394581 

Estimates:
                Estimate        s.e.   t.rat.(0)  p(1-sided)    Rob.s.e. Rob.t.rat.(0)  p(1-sided)
asc_ref           0.0000          NA          NA          NA          NA            NA          NA
asc_alt          -0.6950      0.3929     -1.7688    0.038462      0.6607       -1.0520    0.146400
asc_nn           -5.6019      1.3911     -4.0271   2.824e-05      3.0021       -1.8660    0.031023
b_price_mu       -3.6204      0.5213     -6.9443   1.901e-12      1.2338       -2.9344    0.001671
b_price_sig       1.2779      0.4361      2.9305    0.001692      1.0511        1.2158    0.112026
b_transp_mu       0.1124      0.1473      0.7636    0.222539      0.1686        0.6668    0.252463
b_transp_sig      0.7812      0.1164      6.7116   9.628e-12      0.1555        5.0237   2.535e-07
b_enrich_mu       0.1245      0.1470      0.8475    0.198352      0.2069        0.6019    0.273631
b_enrich_sig      0.2900      0.1746      1.6611    0.048345      0.2792        1.0386    0.149495
b_stun_mu         0.1567      0.1385      1.1313    0.128954      0.1383        1.1335    0.128502
b_stun_sig        1.2060      0.1305      9.2442    0.000000      0.2142        5.6312   8.948e-09
b_out_mu          0.7151      0.2858      2.5022    0.006171      0.3339        2.1417    0.016111
b_out_sig         1.9999      0.1845     10.8377    0.000000      0.3028        6.6049   1.989e-11
b_ins_mu         -0.3505      0.2633     -1.3310    0.091591      0.3160       -1.1092    0.133674
b_ins_sig         1.2664      0.2203      5.7473   4.534e-09      0.2848        4.4465   4.364e-06
b_org_mu          1.3625      0.2145      6.3529   1.057e-10      0.3464        3.9331   4.193e-05
b_org_sig         1.8648      0.2155      8.6547    0.000000      0.4569        4.0816   2.236e-05


Overview of choices for MNL model component :
                                     ref    alt1    alt2    none
Times available                  1620.00 1620.00 1620.00 1620.00
Times chosen                      514.00  477.00  456.00  173.00
Percentage chosen overall          31.73   29.44   28.15   10.68
Percentage chosen when available   31.73   29.44   28.15   10.68


Classical covariance matrix:
                  asc_alt       asc_nn   b_price_mu  b_price_sig  b_transp_mu b_transp_sig  b_enrich_mu b_enrich_sig    b_stun_mu
asc_alt          0.154403    -0.436855     0.164226    -0.132155    -0.040065    -0.001206    -0.047369    -0.001277    -0.028421
asc_nn          -0.436855     1.935046    -0.695127     0.547070     0.103447   4.7753e-04     0.125997     0.030620     0.074969
b_price_mu       0.164226    -0.695127     0.271798    -0.223798    -0.037988   2.8715e-04    -0.047310    -0.015390    -0.027783
b_price_sig     -0.132155     0.547070    -0.223798     0.190172     0.030005  -1.0930e-04     0.038027     0.014826     0.022910
b_transp_mu     -0.040065     0.103447    -0.037988     0.030005     0.021683    -0.004241     0.011875    -0.001954     0.003671
b_transp_sig    -0.001206   4.7753e-04   2.8715e-04  -1.0930e-04    -0.004241     0.013547     0.001021  -1.5671e-04   2.6522e-04
b_enrich_mu     -0.047369     0.125997    -0.047310     0.038027     0.011875     0.001021     0.021595    -0.002690     0.008517
b_enrich_sig    -0.001277     0.030620    -0.015390     0.014826    -0.001954  -1.5671e-04    -0.002690     0.030483    -0.001071
b_stun_mu       -0.028421     0.074969    -0.027783     0.022910     0.003671   2.6522e-04     0.008517    -0.001071     0.019190
b_stun_sig     7.4727e-04    -0.009915     0.004447    -0.003825  -3.6566e-04   7.9271e-04  -5.6311e-04     0.001547    -0.002876
b_out_mu        -0.083742     0.227192    -0.082955     0.068007     0.019740     0.001751     0.023133     0.005463     0.016278
b_out_sig       -0.020353     0.071630    -0.035123     0.035261     0.004037     0.001666     0.006552     0.001480     0.003551
b_ins_mu        -0.075903     0.194636    -0.073659     0.060352     0.018425     0.001814     0.021291     0.004223     0.012092
b_ins_sig       -0.009721     0.045268    -0.019237     0.015869     0.005303    -0.002593     0.003767    -0.002850  -7.2362e-04
b_org_mu         0.020523    -0.088855     0.032615    -0.025303    -0.004277  -3.5978e-04    -0.007311  -1.7984e-04    -0.004186
b_org_sig        0.017702    -0.092775     0.040615    -0.034342    -0.003217     0.001450    -0.005014    -0.007753    -0.002038
               b_stun_sig     b_out_mu    b_out_sig     b_ins_mu    b_ins_sig     b_org_mu    b_org_sig
asc_alt        7.4727e-04    -0.083742    -0.020353    -0.075903    -0.009721     0.020523     0.017702
asc_nn          -0.009915     0.227192     0.071630     0.194636     0.045268    -0.088855    -0.092775
b_price_mu       0.004447    -0.082955    -0.035123    -0.073659    -0.019237     0.032615     0.040615
b_price_sig     -0.003825     0.068007     0.035261     0.060352     0.015869    -0.025303    -0.034342
b_transp_mu   -3.6566e-04     0.019740     0.004037     0.018425     0.005303    -0.004277    -0.003217
b_transp_sig   7.9271e-04     0.001751     0.001666     0.001814    -0.002593  -3.5978e-04     0.001450
b_enrich_mu   -5.6311e-04     0.023133     0.006552     0.021291     0.003767    -0.007311    -0.005014
b_enrich_sig     0.001547     0.005463     0.001480     0.004223    -0.002850  -1.7984e-04    -0.007753
b_stun_mu       -0.002876     0.016278     0.003551     0.012092  -7.2362e-04    -0.004186    -0.002038
b_stun_sig       0.017020     0.003251  -2.6371e-04   7.8120e-04    -0.003440     0.006519     0.005749
b_out_mu         0.003251     0.081679     0.006461     0.046584     0.001486    -0.021577    -0.003999
b_out_sig     -2.6371e-04     0.006461     0.034051     0.012585     0.001815   9.4143e-04    -0.002792
b_ins_mu       7.8120e-04     0.046584     0.012585     0.069341    -0.013523    -0.008238    -0.006983
b_ins_sig       -0.003440     0.001486     0.001815    -0.013523     0.048552    -0.003005    -0.003798
b_org_mu         0.006519    -0.021577   9.4143e-04    -0.008238    -0.003005     0.045999     0.010230
b_org_sig        0.005749    -0.003999    -0.002792    -0.006983    -0.003798     0.010230     0.046424

Robust covariance matrix:
                  asc_alt       asc_nn   b_price_mu  b_price_sig  b_transp_mu b_transp_sig  b_enrich_mu b_enrich_sig    b_stun_mu
asc_alt           0.43651     -1.50732      0.62566     -0.52137    -0.082462    -0.021954    -0.125291    -0.021454    -0.048541
asc_nn           -1.50732      9.01281     -3.62025      3.00635     0.234044     0.065731     0.431300     0.356806     0.103293
b_price_mu        0.62566     -3.62025      1.52216     -1.28963    -0.093517    -0.028375    -0.178872    -0.166427    -0.043150
b_price_sig      -0.52137      3.00635     -1.28963      1.10480     0.074574     0.025474     0.148256     0.150186     0.037191
b_transp_mu      -0.08246      0.23404     -0.09352      0.07457     0.028442    -0.005580     0.023331    -0.004348     0.006034
b_transp_sig     -0.02195      0.06573     -0.02837      0.02547    -0.005580     0.024179     0.009003    -0.002812     0.005966
b_enrich_mu      -0.12529      0.43130     -0.17887      0.14826     0.023331     0.009003     0.042820    -0.002419     0.014985
b_enrich_sig     -0.02145      0.35681     -0.16643      0.15019    -0.004348    -0.002812    -0.002419     0.077976    -0.010596
b_stun_mu        -0.04854      0.10329     -0.04315      0.03719     0.006034     0.005966     0.014985    -0.010596     0.019117
b_stun_sig        0.01648     -0.12782      0.05609     -0.04772    -0.007708  -1.9208e-04    -0.009319    -0.003272     0.003640
b_out_mu         -0.16797      0.56353     -0.21626      0.17636     0.031713     0.007180     0.046622     0.010639     0.023203
b_out_sig        -0.12683      0.60333     -0.26959      0.23898     0.011508     0.017287     0.034676     0.031718     0.010147
b_ins_mu         -0.16978      0.61676     -0.25608      0.21478     0.033621     0.008475     0.049244     0.013806     0.018412
b_ins_sig        -0.09517      0.32090     -0.13619      0.11170     0.024643    -0.004355     0.030463    -0.003554     0.003568
b_org_mu          0.11677     -0.61585      0.26036     -0.21731    -0.024601    -0.004629    -0.038301    -0.022659    -0.006288
b_org_sig         0.16631     -0.89140      0.40605     -0.35203    -0.031043    -0.002766    -0.052922    -0.058473    -0.006643
               b_stun_sig     b_out_mu    b_out_sig     b_ins_mu    b_ins_sig     b_org_mu    b_org_sig
asc_alt          0.016485    -0.167969    -0.126832    -0.169780    -0.095174     0.116768     0.166308
asc_nn          -0.127817     0.563529     0.603330     0.616762     0.320900    -0.615851    -0.891403
b_price_mu       0.056094    -0.216258    -0.269592    -0.256078    -0.136189     0.260357     0.406053
b_price_sig     -0.047718     0.176363     0.238982     0.214779     0.111698    -0.217306    -0.352030
b_transp_mu     -0.007708     0.031713     0.011508     0.033621     0.024643    -0.024601    -0.031043
b_transp_sig  -1.9208e-04     0.007180     0.017287     0.008475    -0.004355    -0.004629    -0.002766
b_enrich_mu     -0.009319     0.046622     0.034676     0.049244     0.030463    -0.038301    -0.052922
b_enrich_sig    -0.003272     0.010639     0.031718     0.013806    -0.003554    -0.022659    -0.058473
b_stun_mu        0.003640     0.023203     0.010147     0.018412     0.003568    -0.006288    -0.006643
b_stun_sig       0.045866     0.003584    -0.004763    -0.003697    -0.023877     0.035272     0.041239
b_out_mu         0.003584     0.111498     0.042543     0.076148     0.024817    -0.044583    -0.042103
b_out_sig       -0.004763     0.042543     0.091678     0.053200     0.022386    -0.039905    -0.068891
b_ins_mu        -0.003697     0.076148     0.053200     0.099851     0.019155    -0.050512    -0.074484
b_ins_sig       -0.023877     0.024817     0.022386     0.019155     0.081115    -0.035104    -0.042227
b_org_mu         0.035272    -0.044583    -0.039905    -0.050512    -0.035104     0.120012     0.109210
b_org_sig        0.041239    -0.042103    -0.068891    -0.074484    -0.042227     0.109210     0.208729

Classical correlation matrix:
                  asc_alt       asc_nn   b_price_mu  b_price_sig  b_transp_mu b_transp_sig  b_enrich_mu b_enrich_sig    b_stun_mu
asc_alt           1.00000    -0.799217     0.801661    -0.771228     -0.69242    -0.026377     -0.82034    -0.018608     -0.52212
asc_nn           -0.79922     1.000000    -0.958507     0.901829      0.50502     0.002949      0.61637     0.126075      0.38904
b_price_mu        0.80166    -0.958507     1.000000    -0.984374     -0.49483     0.004732     -0.61753    -0.169075     -0.38469
b_price_sig      -0.77123     0.901829    -0.984374     1.000000      0.46726    -0.002153      0.59340     0.194730      0.37924
b_transp_mu      -0.69242     0.505022    -0.494832     0.467260      1.00000    -0.247458      0.54880    -0.076020      0.17998
b_transp_sig     -0.02638     0.002949     0.004732    -0.002153     -0.24746     1.000000      0.05971    -0.007712      0.01645
b_enrich_mu      -0.82034     0.616371    -0.617533     0.593405      0.54880     0.059715      1.00000    -0.104836      0.41838
b_enrich_sig     -0.01861     0.126075    -0.169075     0.194730     -0.07602    -0.007712     -0.10484     1.000000     -0.04428
b_stun_mu        -0.52212     0.389040    -0.384689     0.379238      0.17998     0.016450      0.41838    -0.044279      1.00000
b_stun_sig        0.01458    -0.054636     0.065376    -0.067235     -0.01903     0.052206     -0.02937     0.067928     -0.15913
b_out_mu         -0.74569     0.571468    -0.556756     0.545661      0.46905     0.052627      0.55081     0.109478      0.41116
b_out_sig        -0.28070     0.279052    -0.365097     0.438184      0.14856     0.077552      0.24164     0.045952      0.13892
b_ins_mu         -0.73356     0.531351    -0.536543     0.525557      0.47518     0.059173      0.55020     0.091856      0.33148
b_ins_sig        -0.11227     0.147687    -0.167459     0.165149      0.16345    -0.101094      0.11633    -0.074073     -0.02371
b_org_mu          0.24352    -0.297826     0.291691    -0.270532     -0.13541    -0.014413     -0.23198    -0.004803     -0.14091
b_org_sig         0.20909    -0.309539     0.361567    -0.365491     -0.10140     0.057802     -0.15835    -0.206085     -0.06826
               b_stun_sig     b_out_mu    b_out_sig     b_ins_mu    b_ins_sig     b_org_mu    b_org_sig
asc_alt           0.01458     -0.74569     -0.28070     -0.73356     -0.11227     0.243525      0.20909
asc_nn           -0.05464      0.57147      0.27905      0.53135      0.14769    -0.297826     -0.30954
b_price_mu        0.06538     -0.55676     -0.36510     -0.53654     -0.16746     0.291691      0.36157
b_price_sig      -0.06723      0.54566      0.43818      0.52556      0.16515    -0.270532     -0.36549
b_transp_mu      -0.01903      0.46905      0.14856      0.47518      0.16345    -0.135411     -0.10140
b_transp_sig      0.05221      0.05263      0.07755      0.05917     -0.10109    -0.014413      0.05780
b_enrich_mu      -0.02937      0.55081      0.24164      0.55020      0.11633    -0.231980     -0.15835
b_enrich_sig      0.06793      0.10948      0.04595      0.09186     -0.07407    -0.004803     -0.20608
b_stun_mu        -0.15913      0.41116      0.13892      0.33148     -0.02371    -0.140906     -0.06826
b_stun_sig        1.00000      0.08718     -0.01095      0.02274     -0.11967     0.232990      0.20452
b_out_mu          0.08718      1.00000      0.12251      0.61900      0.02360    -0.352010     -0.06494
b_out_sig        -0.01095      0.12251      1.00000      0.25899      0.04463     0.023788     -0.07022
b_ins_mu          0.02274      0.61900      0.25899      1.00000     -0.23306    -0.145869     -0.12308
b_ins_sig        -0.11967      0.02360      0.04463     -0.23306      1.00000    -0.063597     -0.08000
b_org_mu          0.23299     -0.35201      0.02379     -0.14587     -0.06360     1.000000      0.22138
b_org_sig         0.20452     -0.06494     -0.07022     -0.12308     -0.08000     0.221382      1.00000

Robust correlation matrix:
                  asc_alt       asc_nn   b_price_mu  b_price_sig  b_transp_mu b_transp_sig  b_enrich_mu b_enrich_sig    b_stun_mu
asc_alt            1.0000      -0.7599       0.7676      -0.7508     -0.74007    -0.213694     -0.91643     -0.11629     -0.53137
asc_nn            -0.7599       1.0000      -0.9774       0.9527      0.46226     0.140806      0.69427      0.42562      0.24884
b_price_mu         0.7676      -0.9774       1.0000      -0.9945     -0.44944    -0.147905     -0.70063     -0.48307     -0.25295
b_price_sig       -0.7508       0.9527      -0.9945       1.0000      0.42069     0.155858      0.68163      0.51169      0.25591
b_transp_mu       -0.7401       0.4623      -0.4494       0.4207      1.00000    -0.212779      0.66852     -0.09232      0.25877
b_transp_sig      -0.2137       0.1408      -0.1479       0.1559     -0.21278     1.000000      0.27979     -0.06476      0.27748
b_enrich_mu       -0.9164       0.6943      -0.7006       0.6816      0.66852     0.279788      1.00000     -0.04186      0.52375
b_enrich_sig      -0.1163       0.4256      -0.4831       0.5117     -0.09232    -0.064764     -0.04186      1.00000     -0.27443
b_stun_mu         -0.5314       0.2488      -0.2530       0.2559      0.25877     0.277484      0.52375     -0.27443      1.00000
b_stun_sig         0.1165      -0.1988       0.2123      -0.2120     -0.21342    -0.005768     -0.21027     -0.05471      0.12291
b_out_mu          -0.7614       0.5622      -0.5249       0.5025      0.56314     0.138289      0.67474      0.11409      0.50257
b_out_sig         -0.6340       0.6637      -0.7217       0.7509      0.22537     0.367172      0.55344      0.37514      0.24238
b_ins_mu          -0.8132       0.6501      -0.6569       0.6467      0.63088     0.172484      0.75310      0.15646      0.42142
b_ins_sig         -0.5058       0.3753      -0.3876       0.3731      0.51306    -0.098345      0.51690     -0.04469      0.09061
b_org_mu           0.5102      -0.5922       0.6092      -0.5968     -0.42107    -0.085932     -0.53428     -0.23424     -0.13129
b_org_sig          0.5510      -0.6499       0.7204      -0.7331     -0.40290    -0.038938     -0.55979     -0.45833     -0.10516
               b_stun_sig     b_out_mu    b_out_sig     b_ins_mu    b_ins_sig     b_org_mu    b_org_sig
asc_alt          0.116505     -0.76138     -0.63401     -0.81323     -0.50579      0.51017      0.55097
asc_nn          -0.198799      0.56215      0.66373      0.65015      0.37531     -0.59215     -0.64991
b_price_mu       0.212294     -0.52494     -0.72168     -0.65685     -0.38758      0.60915      0.72038
b_price_sig     -0.211979      0.50250      0.75092      0.64666      0.37313     -0.59678     -0.73307
b_transp_mu     -0.213420      0.56314      0.22537      0.63088      0.51306     -0.42107     -0.40290
b_transp_sig    -0.005768      0.13829      0.36717      0.17248     -0.09835     -0.08593     -0.03894
b_enrich_mu     -0.210271      0.67474      0.55344      0.75310      0.51690     -0.53428     -0.55979
b_enrich_sig    -0.054706      0.11409      0.37514      0.15646     -0.04469     -0.23424     -0.45833
b_stun_mu        0.122909      0.50257      0.24238      0.42142      0.09061     -0.13129     -0.10516
b_stun_sig       1.000000      0.05012     -0.07346     -0.05463     -0.39145      0.47541      0.42147
b_out_mu         0.050121      1.00000      0.42078      0.72169      0.26095     -0.38541     -0.27599
b_out_sig       -0.073457      0.42078      1.00000      0.55604      0.25959     -0.38044     -0.49801
b_ins_mu        -0.054625      0.72169      0.55604      1.00000      0.21285     -0.46143     -0.51594
b_ins_sig       -0.391450      0.26095      0.25959      0.21285      1.00000     -0.35579     -0.32452
b_org_mu         0.475412     -0.38541     -0.38044     -0.46143     -0.35579      1.00000      0.69001
b_org_sig        0.421472     -0.27599     -0.49801     -0.51594     -0.32452      0.69001      1.00000

 20 worst outliers in terms of lowest average per choice prediction:
   ID Avg prob per choice
  748           0.1366770
 3140           0.1674947
 3286           0.1764371
 2493           0.1765387
 6403           0.1767919
 5786           0.1934074
 2936           0.1935521
  131           0.1962094
 2063           0.1993166
 6941           0.2060678
 4408           0.2069819
 4375           0.2070269
 2275           0.2122168
 6890           0.2147972
 2296           0.2148408
 6876           0.2155090
 7166           0.2173872
 2453           0.2242528
   53           0.2262082
 4053           0.2266792

Changes in parameter estimates from starting values:
                 Initial    Estimate  Difference
asc_ref          0.00000      0.0000     0.00000
asc_alt         -0.75665     -0.6950     0.06161
asc_nn          -2.09305     -5.6019    -3.50882
b_price_mu      -3.00000     -3.6204    -0.62038
b_price_sig      0.01016      1.2779     1.26779
b_transp_mu      0.16236      0.1124    -0.04991
b_transp_sig     0.14688      0.7812     0.63428
b_enrich_mu      1.00000      0.1245    -0.87546
b_enrich_sig     0.15519      0.2900     0.13483
b_stun_mu        0.20265      0.1567    -0.04593
b_stun_sig       0.13396      1.2060     1.07204
b_out_mu         0.58544      0.7151     0.12969
b_out_sig        0.26446      1.9999     1.73540
b_ins_mu        -0.02439     -0.3505    -0.32610
b_ins_sig        0.21938      1.2664     1.04702
b_org_mu         0.68338      1.3625     0.67915
b_org_sig        0.11812      1.8648     1.74665

Settings and functions used in model definition:

apollo_control
--------------
                       Value                                                              
modelName              "MMNL_NoLux_100_v9_CY"                                             
modelDescr             "MMNL model with Normal distributions for everything besides price"
indivID                "id"                                                               
mixing                 "TRUE"                                                             
nCores                 "6"                                                                
workInLogs             "TRUE"                                                             
debug                  "FALSE"                                                            
seed                   "13"                                                               
HB                     "FALSE"                                                            
noValidation           "FALSE"                                                            
noDiagnostics          "FALSE"                                                            
outputDirectory        ""                                                                 
panelData              "TRUE"                                                             
analyticGrad           "FALSE"                                                            
analyticGrad_manualSet "FALSE"                                                            

Hessian routines attempted
--------------
numerical second derivative of LL (using maxLik)

Scaling in estimation
--------------
                 Value
asc_alt      0.6950415
asc_nn       5.6018684
b_price_mu   3.6203817
b_price_sig  1.2779456
b_transp_mu  0.1124483
b_transp_sig 0.7811617
b_enrich_mu  0.1245446
b_enrich_sig 0.2900217
b_stun_mu    0.1567243
b_stun_sig   1.2060012
b_out_mu     0.7151279
b_out_sig    1.9998611
b_ins_mu     0.3504943
b_ins_sig    1.2663955
b_org_mu     1.3625264
b_org_sig    1.8647661

Scaling used in computing Hessian
--------------
                 Value
asc_alt      0.6950415
asc_nn       5.6018711
b_price_mu   3.6203796
b_price_sig  1.2779461
b_transp_mu  0.1124483
b_transp_sig 0.7811617
b_enrich_mu  0.1245446
b_enrich_sig 0.2900217
b_stun_mu    0.1567243
b_stun_sig   1.2060013
b_out_mu     0.7151278
b_out_sig    1.9998614
b_ins_mu     0.3504944
b_ins_sig    1.2663952
b_org_mu     1.3625263
b_org_sig    1.8647653


apollo_randCoeff
----------------
function(apollo_beta, apollo_inputs){
  randcoeff = list()
  
  randcoeff[["b_price"]] =    -exp(b_price_mu + b_price_sig * draws_price)
  randcoeff[["b_transp"]] =   b_transp_mu + b_transp_sig * draws_transp
  randcoeff[["b_enrich"]] =   b_enrich_mu + b_enrich_sig * draws_enrich
  randcoeff[["b_stun"]] =     b_stun_mu + b_stun_sig * draws_stun
  randcoeff[["b_out"]] =      b_out_mu + b_out_sig * draws_out
  randcoeff[["b_ins"]] =      b_ins_mu + b_ins_sig * draws_ins
  randcoeff[["b_org"]] =      b_org_mu + b_org_sig * draws_org
  
  return(randcoeff)


apollo_probabilities
--------------------
function(apollo_beta, apollo_inputs, functionality="estimate"){
  
  ### Function initialisation: do not change the following three commands
  ### Attach inputs and detach after function exit
  apollo_attach(apollo_beta, apollo_inputs)
  on.exit(apollo_detach(apollo_beta, apollo_inputs))
  
  ### Create list of probabilities P
  P = list()
  ### Create coefficients using interactions among vars
  
  ### List of utilities: these must use the same names as in mnl_settings, order is irrelevant
  V = list()
  V[['ref']]   = asc_ref + b_price * price_ref + b_transp * transp_ref + b_enrich * enrich_ref + b_stun * stun_ref + b_out * out_ref + b_ins * ins_ref + b_org * org_ref       
  V[['alt1']]  = asc_alt + b_price * price_1   + b_transp * transp_1   + b_enrich * enrich_1   + b_stun * stun_1   + b_out * out_1   + b_ins * ins_1   + b_org * org_1 
  V[['alt2']]  = asc_alt + b_price * price_2   + b_transp * transp_2   + b_enrich * enrich_2   + b_stun * stun_2   + b_out * out_2   + b_ins * ins_2   + b_org * org_2 
  V[['none']]  = asc_nn 
  
  ### Define settings for MNL model component
  mnl_settings = list(
    alternatives  = c(ref=1, alt1=2, alt2=3, none=4), 
    avail         = list(ref=av_ref, alt1=av_alt1, alt2=av_alt2, none=av_nn), 
    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)
