Model run using Apollo for R, version 0.2.3 on Darwin by stephane.hess www.ApolloChoiceModelling.com Model name : Apollo_example_25 Model description : ICLV model on drug choice data, using continuous measurement model for indicators Model run at : 2021-02-05 16:30:01 Estimation method : bfgs Model diagnosis : successful convergence Number of individuals : 1000 Number of rows in database : 10000 Number of modelled outcomes : 14000 choice: 10000 indic_dominance: 1000 indic_ingredients: 1000 indic_patent: 1000 indic_quality: 1000 Number of cores used : 5 Number of inter-individual draws : 100 (halton) LL(start) : -20881.08 LL(0, whole model) : Not applicable LL(final, whole model) : -17073.4 Rho-square (0) : Not applicable Adj.Rho-square (0) : Not applicable AIC : 34196.81 BIC : 34385.48 LL(0,indic_quality) : Not applicable LL(final,indic_quality) : -1597.301 LL(0,indic_ingredients) : Not applicable LL(final,indic_ingredients) : -1620.255 LL(0,indic_patent) : Not applicable LL(final,indic_patent) : -1636.335 LL(0,indic_dominance) : Not applicable LL(final,indic_dominance) : -1527.59 LL(0,choice) : -13862.94 LL(final,choice) : -10891.2 Estimated parameters : 25 Time taken (hh:mm:ss) : 00:06:13.87 pre-estimation : 00:00:34.27 estimation : 00:01:17.65 post-estimation : 00:04:21.95 Iterations : 38 Min abs eigenvalue of Hessian : 71.38174 Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) b_brand_Artemis 0.000000 NA NA NA NA b_brand_Novum -0.276728 0.03082 -8.979 0.03195 -8.662 b_brand_BestValue -0.580333 0.06615 -8.774 0.06433 -9.021 b_brand_Supermarket -0.266708 0.06726 -3.965 0.06624 -4.026 b_brand_PainAway -1.248770 0.06750 -18.499 0.06551 -19.063 b_country_CH 0.670161 0.03985 16.816 0.03881 17.269 b_country_DK 0.337698 0.03824 8.831 0.03757 8.990 b_country_USA 0.000000 NA NA NA NA b_country_IND -0.296318 0.05734 -5.168 0.05814 -5.097 b_country_RUS -0.893694 0.06171 -14.483 0.06115 -14.616 b_country_BRA -0.655527 0.06022 -10.886 0.06177 -10.612 b_char_standard 0.000000 NA NA NA NA b_char_fast 0.769947 0.02921 26.356 0.02889 26.647 b_char_double 1.212442 0.03777 32.102 0.03662 33.109 b_risk -0.001575 5.834e-05 -26.990 5.944e-05 -26.490 b_price -0.724328 0.01812 -39.966 0.01729 -41.888 lambda 0.659834 0.03260 20.239 0.03188 20.697 gamma_reg_user -0.741191 0.07947 -9.327 0.07972 -9.297 gamma_university -0.378841 0.07375 -5.137 0.07418 -5.107 gamma_age_50 0.673645 0.07593 8.872 0.07450 9.043 zeta_quality 0.534809 0.03940 13.573 0.03890 13.748 zeta_ingredient -0.503374 0.04020 -12.522 0.03966 -12.693 zeta_patent 0.606945 0.04097 14.814 0.03852 15.757 zeta_dominance -0.394531 0.03672 -10.743 0.03520 -11.207 sigma_qual 1.061415 0.02751 38.589 0.02703 39.274 sigma_ingr 1.108686 0.02786 39.791 0.02632 42.125 sigma_pate 1.084298 0.02912 37.231 0.02745 39.496 sigma_domi 1.045437 0.02530 41.319 0.02310 45.260 Summary statistics for NORMD model component indic_quality: Min. 1st Qu. Median Mean 3rd Qu. Max. -1.741 -0.741 0.259 0 0.259 2.259 Summary statistics for NORMD model component indic_ingredients: Min. 1st Qu. Median Mean 3rd Qu. Max. -2.232 -0.232 -0.232 0 0.768 1.768 Summary statistics for NORMD model component indic_patent: Min. 1st Qu. Median Mean 3rd Qu. Max. -1.806 -0.806 0.194 0 1.194 2.194 Summary statistics for NORMD model component indic_dominance: Min. 1st Qu. Median Mean 3rd Qu. Max. -2.164 -0.164 -0.164 0 0.836 1.836 Overview of choices for MNL model component choice: alt1 alt2 alt3 alt4 Times available 10000.00 10000.00 10000.00 10000.00 Times chosen 3403.00 3546.00 1517.00 1534.00 Percentage chosen overall 34.03 35.46 15.17 15.34 Percentage chosen when available 34.03 35.46 15.17 15.34 Classical covariance matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_PainAway b_brand_Novum 9.4984e-04 4.7298e-04 5.8289e-04 5.0844e-04 b_brand_BestValue 4.7298e-04 0.004375 0.003213 0.002956 b_brand_Supermarket 5.8289e-04 0.003213 0.004524 0.003024 b_brand_PainAway 5.0844e-04 0.002956 0.003024 0.004557 b_country_CH -6.662e-05 7.5558e-04 7.4268e-04 5.9612e-04 b_country_DK -5.572e-05 6.7075e-04 7.0616e-04 5.8379e-04 b_country_IND -5.871e-05 -0.001544 -0.001619 -0.001414 b_country_RUS -7.186e-05 -0.001565 -0.001638 -0.001334 b_country_BRA -1.231e-05 -0.001428 -0.001713 -0.001400 b_char_fast 1.038e-05 -8.326e-06 9.026e-05 -8.150e-05 b_char_double 7.626e-05 4.0853e-04 4.8187e-04 3.0581e-04 b_risk 2.678e-09 -7.058e-07 -7.571e-07 -2.166e-07 b_price 3.702e-05 3.4404e-04 3.1566e-04 4.0709e-04 lambda -1.245e-05 -1.7879e-04 -1.5613e-04 -2.3924e-04 gamma_reg_user 5.202e-06 4.1838e-04 4.3946e-04 4.0422e-04 gamma_university -6.183e-06 4.1409e-04 4.1830e-04 4.2857e-04 gamma_age_50 6.293e-07 3.6495e-04 3.5039e-04 3.7090e-04 zeta_quality -1.140e-06 9.688e-05 8.957e-05 9.623e-05 zeta_ingredient -3.335e-06 -1.0160e-04 -1.0144e-04 -1.0875e-04 zeta_patent 2.305e-06 1.0136e-04 1.1501e-04 1.0279e-04 zeta_dominance 6.312e-07 -6.585e-05 -7.290e-05 -6.808e-05 sigma_qual 9.189e-07 -3.267e-05 -2.588e-05 -3.297e-05 sigma_ingr -1.821e-06 -3.385e-05 -3.206e-05 -3.868e-05 sigma_pate -1.458e-06 -3.494e-05 -4.234e-05 -3.690e-05 sigma_domi 4.046e-07 -1.529e-05 -1.764e-05 -1.679e-05 b_country_CH b_country_DK b_country_IND b_country_RUS b_brand_Novum -6.662e-05 -5.572e-05 -5.871e-05 -7.186e-05 b_brand_BestValue 7.5558e-04 6.7075e-04 -0.001544 -0.001565 b_brand_Supermarket 7.4268e-04 7.0616e-04 -0.001619 -0.001638 b_brand_PainAway 5.9612e-04 5.8379e-04 -0.001414 -0.001334 b_country_CH 0.001588 7.5101e-04 1.669e-05 -7.883e-05 b_country_DK 7.5101e-04 0.001462 9.374e-05 1.283e-05 b_country_IND 1.669e-05 9.374e-05 0.003288 0.001564 b_country_RUS -7.883e-05 1.283e-05 0.001564 0.003808 b_country_BRA -7.943e-05 1.629e-06 0.001609 0.001576 b_char_fast 8.913e-05 3.847e-05 -9.387e-05 -1.1393e-04 b_char_double 1.3299e-04 3.007e-05 -5.707e-05 -7.893e-05 b_risk -1.506e-07 -6.191e-08 1.745e-07 2.191e-07 b_price -8.769e-05 -3.300e-05 2.507e-05 5.033e-05 lambda 5.051e-05 1.576e-05 3.646e-06 -8.944e-05 gamma_reg_user 1.999e-06 -8.959e-07 7.622e-06 -1.257e-05 gamma_university 1.702e-06 -7.787e-06 1.760e-05 -2.865e-06 gamma_age_50 -8.186e-06 3.464e-06 -2.345e-05 2.301e-05 zeta_quality 1.470e-06 -4.269e-06 1.305e-05 4.595e-06 zeta_ingredient 3.097e-06 -5.224e-07 2.007e-06 -1.955e-06 zeta_patent -1.274e-06 -5.568e-06 1.576e-05 -4.170e-06 zeta_dominance 6.117e-07 2.479e-06 -3.657e-06 -3.196e-06 sigma_qual -3.850e-07 2.368e-06 -6.799e-06 -4.683e-06 sigma_ingr 2.316e-06 -6.696e-07 2.659e-06 -2.574e-06 sigma_pate 1.653e-06 3.511e-06 -9.265e-06 9.197e-07 sigma_domi 6.188e-07 9.794e-07 -8.314e-07 -2.492e-06 b_country_BRA b_char_fast b_char_double b_risk b_brand_Novum -1.231e-05 1.038e-05 7.626e-05 2.678e-09 b_brand_BestValue -0.001428 -8.326e-06 4.0853e-04 -7.058e-07 b_brand_Supermarket -0.001713 9.026e-05 4.8187e-04 -7.571e-07 b_brand_PainAway -0.001400 -8.150e-05 3.0581e-04 -2.166e-07 b_country_CH -7.943e-05 8.913e-05 1.3299e-04 -1.506e-07 b_country_DK 1.629e-06 3.847e-05 3.007e-05 -6.191e-08 b_country_IND 0.001609 -9.387e-05 -5.707e-05 1.745e-07 b_country_RUS 0.001576 -1.1393e-04 -7.893e-05 2.191e-07 b_country_BRA 0.003626 -1.1994e-04 -1.1556e-04 1.117e-07 b_char_fast -1.1994e-04 8.5341e-04 5.0285e-04 -1.406e-07 b_char_double -1.1556e-04 5.0285e-04 0.001426 -1.123e-07 b_risk 1.117e-07 -1.406e-07 -1.123e-07 3.403e-09 b_price 7.313e-05 -7.472e-05 -1.1851e-04 1.254e-07 lambda -5.075e-05 6.352e-05 8.476e-05 -1.037e-07 gamma_reg_user -6.999e-06 -7.261e-07 5.547e-06 1.431e-09 gamma_university 3.988e-06 1.076e-07 -1.057e-06 9.669e-09 gamma_age_50 9.501e-06 -4.145e-07 -1.101e-05 -6.450e-09 zeta_quality 1.214e-05 -2.877e-06 -2.636e-06 1.861e-08 zeta_ingredient 3.811e-06 9.272e-06 7.065e-06 -1.158e-08 zeta_patent -6.337e-06 -9.090e-06 -5.548e-06 1.437e-08 zeta_dominance -7.861e-06 -6.225e-07 3.166e-06 -4.157e-09 sigma_qual -8.495e-06 1.798e-06 2.479e-06 -1.148e-08 sigma_ingr 1.780e-06 5.396e-06 4.805e-06 -6.242e-09 sigma_pate 3.912e-06 6.501e-06 4.982e-06 -9.572e-09 sigma_domi -4.157e-06 -3.520e-07 1.968e-06 -1.653e-09 b_price lambda gamma_reg_user gamma_university b_brand_Novum 3.702e-05 -1.245e-05 5.202e-06 -6.183e-06 b_brand_BestValue 3.4404e-04 -1.7879e-04 4.1838e-04 4.1409e-04 b_brand_Supermarket 3.1566e-04 -1.5613e-04 4.3946e-04 4.1830e-04 b_brand_PainAway 4.0709e-04 -2.3924e-04 4.0422e-04 4.2857e-04 b_country_CH -8.769e-05 5.051e-05 1.999e-06 1.702e-06 b_country_DK -3.300e-05 1.576e-05 -8.959e-07 -7.787e-06 b_country_IND 2.507e-05 3.646e-06 7.622e-06 1.760e-05 b_country_RUS 5.033e-05 -8.944e-05 -1.257e-05 -2.865e-06 b_country_BRA 7.313e-05 -5.075e-05 -6.999e-06 3.988e-06 b_char_fast -7.472e-05 6.352e-05 -7.261e-07 1.076e-07 b_char_double -1.1851e-04 8.476e-05 5.547e-06 -1.057e-06 b_risk 1.254e-07 -1.037e-07 1.431e-09 9.669e-09 b_price 3.2846e-04 -4.001e-05 -9.207e-06 -4.084e-06 lambda -4.001e-05 0.001063 6.3054e-04 2.7348e-04 gamma_reg_user -9.207e-06 6.3054e-04 0.006315 -7.5582e-04 gamma_university -4.084e-06 2.7348e-04 -7.5582e-04 0.005440 gamma_age_50 1.238e-05 -5.7106e-04 -0.001719 -0.001699 zeta_quality -2.552e-06 2.1700e-04 6.3843e-04 3.2871e-04 zeta_ingredient -1.108e-06 -1.8496e-04 -5.5979e-04 -3.3986e-04 zeta_patent -2.259e-06 2.3171e-04 6.5390e-04 3.4886e-04 zeta_dominance 1.044e-06 -1.5584e-04 -3.4107e-04 -3.3010e-04 sigma_qual 4.903e-07 1.362e-05 -1.0545e-04 -4.569e-05 sigma_ingr -1.655e-06 2.292e-05 -6.519e-05 -5.673e-05 sigma_pate 1.545e-07 2.772e-05 -8.163e-05 -4.005e-05 sigma_domi -1.405e-07 9.600e-06 5.411e-06 -6.819e-05 gamma_age_50 zeta_quality zeta_ingredient zeta_patent b_brand_Novum 6.293e-07 -1.140e-06 -3.335e-06 2.305e-06 b_brand_BestValue 3.6495e-04 9.688e-05 -1.0160e-04 1.0136e-04 b_brand_Supermarket 3.5039e-04 8.957e-05 -1.0144e-04 1.1501e-04 b_brand_PainAway 3.7090e-04 9.623e-05 -1.0875e-04 1.0279e-04 b_country_CH -8.186e-06 1.470e-06 3.097e-06 -1.274e-06 b_country_DK 3.464e-06 -4.269e-06 -5.224e-07 -5.568e-06 b_country_IND -2.345e-05 1.305e-05 2.007e-06 1.576e-05 b_country_RUS 2.301e-05 4.595e-06 -1.955e-06 -4.170e-06 b_country_BRA 9.501e-06 1.214e-05 3.811e-06 -6.337e-06 b_char_fast -4.145e-07 -2.877e-06 9.272e-06 -9.090e-06 b_char_double -1.101e-05 -2.636e-06 7.065e-06 -5.548e-06 b_risk -6.450e-09 1.861e-08 -1.158e-08 1.437e-08 b_price 1.238e-05 -2.552e-06 -1.108e-06 -2.259e-06 lambda -5.7106e-04 2.1700e-04 -1.8496e-04 2.3171e-04 gamma_reg_user -0.001719 6.3843e-04 -5.5979e-04 6.5390e-04 gamma_university -0.001699 3.2871e-04 -3.3986e-04 3.4886e-04 gamma_age_50 0.005766 -4.6603e-04 4.6735e-04 -5.1784e-04 zeta_quality -4.6603e-04 0.001553 -2.2302e-04 2.0296e-04 zeta_ingredient 4.6735e-04 -2.2302e-04 0.001616 -2.2518e-04 zeta_patent -5.1784e-04 2.0296e-04 -2.2518e-04 0.001679 zeta_dominance 2.8908e-04 -1.3404e-04 1.5383e-04 -1.3089e-04 sigma_qual 4.581e-05 -3.0994e-04 1.660e-05 1.821e-05 sigma_ingr 5.579e-05 -1.408e-05 2.8515e-04 -4.704e-06 sigma_pate 4.976e-05 2.699e-05 6.587e-07 -3.7186e-04 sigma_domi -1.504e-06 1.081e-05 3.934e-06 1.928e-05 zeta_dominance sigma_qual sigma_ingr sigma_pate b_brand_Novum 6.312e-07 9.189e-07 -1.821e-06 -1.458e-06 b_brand_BestValue -6.585e-05 -3.267e-05 -3.385e-05 -3.494e-05 b_brand_Supermarket -7.290e-05 -2.588e-05 -3.206e-05 -4.234e-05 b_brand_PainAway -6.808e-05 -3.297e-05 -3.868e-05 -3.690e-05 b_country_CH 6.117e-07 -3.850e-07 2.316e-06 1.653e-06 b_country_DK 2.479e-06 2.368e-06 -6.696e-07 3.511e-06 b_country_IND -3.657e-06 -6.799e-06 2.659e-06 -9.265e-06 b_country_RUS -3.196e-06 -4.683e-06 -2.574e-06 9.197e-07 b_country_BRA -7.861e-06 -8.495e-06 1.780e-06 3.912e-06 b_char_fast -6.225e-07 1.798e-06 5.396e-06 6.501e-06 b_char_double 3.166e-06 2.479e-06 4.805e-06 4.982e-06 b_risk -4.157e-09 -1.148e-08 -6.242e-09 -9.572e-09 b_price 1.044e-06 4.903e-07 -1.655e-06 1.545e-07 lambda -1.5584e-04 1.362e-05 2.292e-05 2.772e-05 gamma_reg_user -3.4107e-04 -1.0545e-04 -6.519e-05 -8.163e-05 gamma_university -3.3010e-04 -4.569e-05 -5.673e-05 -4.005e-05 gamma_age_50 2.8908e-04 4.581e-05 5.579e-05 4.976e-05 zeta_quality -1.3404e-04 -3.0994e-04 -1.408e-05 2.699e-05 zeta_ingredient 1.5383e-04 1.660e-05 2.8515e-04 6.587e-07 zeta_patent -1.3089e-04 1.821e-05 -4.704e-06 -3.7186e-04 zeta_dominance 0.001349 -9.742e-06 8.060e-06 -2.769e-05 sigma_qual -9.742e-06 7.5654e-04 1.535e-06 -2.551e-05 sigma_ingr 8.060e-06 1.535e-06 7.7633e-04 -6.260e-06 sigma_pate -2.769e-05 -2.551e-05 -6.260e-06 8.4816e-04 sigma_domi 1.9468e-04 -1.015e-05 -2.924e-07 -1.790e-05 sigma_domi b_brand_Novum 4.046e-07 b_brand_BestValue -1.529e-05 b_brand_Supermarket -1.764e-05 b_brand_PainAway -1.679e-05 b_country_CH 6.188e-07 b_country_DK 9.794e-07 b_country_IND -8.314e-07 b_country_RUS -2.492e-06 b_country_BRA -4.157e-06 b_char_fast -3.520e-07 b_char_double 1.968e-06 b_risk -1.653e-09 b_price -1.405e-07 lambda 9.600e-06 gamma_reg_user 5.411e-06 gamma_university -6.819e-05 gamma_age_50 -1.504e-06 zeta_quality 1.081e-05 zeta_ingredient 3.934e-06 zeta_patent 1.928e-05 zeta_dominance 1.9468e-04 sigma_qual -1.015e-05 sigma_ingr -2.924e-07 sigma_pate -1.790e-05 sigma_domi 6.4019e-04 Robust covariance matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_PainAway b_brand_Novum 0.001021 4.2307e-04 5.0993e-04 3.9795e-04 b_brand_BestValue 4.2307e-04 0.004138 0.002921 0.002713 b_brand_Supermarket 5.0993e-04 0.002921 0.004388 0.002891 b_brand_PainAway 3.9795e-04 0.002713 0.002891 0.004291 b_country_CH -1.2599e-04 5.5583e-04 6.2274e-04 4.7846e-04 b_country_DK -4.610e-05 4.7353e-04 6.0958e-04 5.0000e-04 b_country_IND -5.877e-05 -0.001650 -0.001680 -0.001433 b_country_RUS -5.231e-05 -0.001692 -0.001631 -0.001449 b_country_BRA 3.730e-05 -0.001580 -0.001922 -0.001469 b_char_fast -5.008e-05 -2.507e-05 1.1794e-04 -7.684e-05 b_char_double -1.509e-05 3.7010e-04 4.3216e-04 2.2137e-04 b_risk 1.351e-07 -4.540e-07 -5.497e-07 -1.887e-07 b_price 4.256e-05 3.0697e-04 2.7649e-04 3.5411e-04 lambda -4.944e-05 -1.9384e-04 -1.3075e-04 -1.9780e-04 gamma_reg_user 1.658e-06 3.5845e-04 4.3035e-04 4.5425e-04 gamma_university -5.608e-05 2.8291e-04 1.3933e-04 2.4955e-04 gamma_age_50 -7.266e-05 5.3335e-04 5.4136e-04 6.0417e-04 zeta_quality -7.508e-07 9.917e-05 7.456e-05 1.2643e-04 zeta_ingredient -1.847e-05 -8.515e-05 -1.135e-06 3.057e-05 zeta_patent 5.341e-05 1.5089e-04 1.7526e-04 1.7727e-04 zeta_dominance -3.291e-05 -7.167e-05 -6.987e-05 -6.505e-05 sigma_qual -1.235e-05 -6.096e-05 -1.993e-05 -7.272e-05 sigma_ingr -2.078e-05 1.064e-05 8.247e-05 7.919e-05 sigma_pate 1.054e-05 -4.489e-05 -7.221e-05 -7.330e-05 sigma_domi -2.407e-05 -6.423e-05 -1.2330e-04 -3.493e-05 b_country_CH b_country_DK b_country_IND b_country_RUS b_brand_Novum -1.2599e-04 -4.610e-05 -5.877e-05 -5.231e-05 b_brand_BestValue 5.5583e-04 4.7353e-04 -0.001650 -0.001692 b_brand_Supermarket 6.2274e-04 6.0958e-04 -0.001680 -0.001631 b_brand_PainAway 4.7846e-04 5.0000e-04 -0.001433 -0.001449 b_country_CH 0.001506 6.8532e-04 -5.351e-05 -1.4740e-04 b_country_DK 6.8532e-04 0.001411 5.444e-05 -1.494e-05 b_country_IND -5.351e-05 5.444e-05 0.003380 0.001457 b_country_RUS -1.4740e-04 -1.494e-05 0.001457 0.003739 b_country_BRA -1.0903e-04 5.170e-06 0.001848 0.001872 b_char_fast 1.1641e-04 7.386e-06 -1.4486e-04 -1.5017e-04 b_char_double 1.1373e-04 -2.148e-05 -7.980e-05 -1.0564e-04 b_risk -1.357e-08 1.059e-07 2.437e-07 2.619e-07 b_price -8.209e-05 -3.932e-05 5.569e-05 2.961e-05 lambda 1.0523e-04 4.096e-05 5.202e-05 -1.8104e-04 gamma_reg_user 4.403e-05 6.834e-05 1.4054e-04 -1.197e-05 gamma_university -1.3014e-04 -4.247e-05 1.1373e-04 5.145e-05 gamma_age_50 -2.448e-05 -3.683e-05 -1.6016e-04 -2.197e-05 zeta_quality -3.212e-06 -3.265e-05 1.0231e-04 -2.849e-05 zeta_ingredient 3.588e-05 -1.011e-05 -5.682e-05 -6.438e-05 zeta_patent -5.304e-05 -2.385e-05 2.984e-05 3.678e-05 zeta_dominance -3.553e-05 -2.305e-05 -8.576e-06 -1.747e-05 sigma_qual 2.433e-05 1.031e-05 -1.409e-05 1.623e-05 sigma_ingr 4.379e-05 -2.146e-05 -6.355e-07 -3.114e-05 sigma_pate -2.380e-05 7.578e-07 9.886e-05 2.073e-05 sigma_domi -2.092e-05 -3.971e-06 5.002e-05 1.830e-05 b_country_BRA b_char_fast b_char_double b_risk b_brand_Novum 3.730e-05 -5.008e-05 -1.509e-05 1.351e-07 b_brand_BestValue -0.001580 -2.507e-05 3.7010e-04 -4.540e-07 b_brand_Supermarket -0.001922 1.1794e-04 4.3216e-04 -5.497e-07 b_brand_PainAway -0.001469 -7.684e-05 2.2137e-04 -1.887e-07 b_country_CH -1.0903e-04 1.1641e-04 1.1373e-04 -1.357e-08 b_country_DK 5.170e-06 7.386e-06 -2.148e-05 1.059e-07 b_country_IND 0.001848 -1.4486e-04 -7.980e-05 2.437e-07 b_country_RUS 0.001872 -1.5017e-04 -1.0564e-04 2.619e-07 b_country_BRA 0.003816 -1.8648e-04 -1.3740e-04 1.183e-07 b_char_fast -1.8648e-04 8.3490e-04 4.6168e-04 -1.571e-07 b_char_double -1.3740e-04 4.6168e-04 0.001341 -2.118e-08 b_risk 1.183e-07 -1.571e-07 -2.118e-08 3.533e-09 b_price 5.817e-05 -7.470e-05 -1.1682e-04 1.255e-07 lambda -6.090e-05 7.989e-05 6.595e-05 -1.075e-07 gamma_reg_user 1.4688e-04 3.227e-05 4.148e-05 2.090e-07 gamma_university 1.6000e-04 -1.9423e-04 -1.873e-07 1.885e-07 gamma_age_50 -1.8496e-04 1.5978e-04 7.909e-05 -3.415e-07 zeta_quality 3.395e-05 1.275e-05 -6.578e-06 1.268e-07 zeta_ingredient -2.847e-05 2.862e-05 7.530e-05 4.205e-08 zeta_patent 4.077e-05 -2.931e-05 4.145e-05 -4.081e-08 zeta_dominance 4.942e-06 1.015e-05 -1.193e-05 -6.149e-09 sigma_qual 2.764e-06 3.911e-06 4.757e-05 -5.608e-08 sigma_ingr -5.765e-05 2.958e-05 4.206e-05 3.563e-08 sigma_pate 1.565e-05 2.448e-05 2.605e-05 1.722e-08 sigma_domi 3.668e-05 -8.781e-06 4.344e-06 -2.711e-08 b_price lambda gamma_reg_user gamma_university b_brand_Novum 4.256e-05 -4.944e-05 1.658e-06 -5.608e-05 b_brand_BestValue 3.0697e-04 -1.9384e-04 3.5845e-04 2.8291e-04 b_brand_Supermarket 2.7649e-04 -1.3075e-04 4.3035e-04 1.3933e-04 b_brand_PainAway 3.5411e-04 -1.9780e-04 4.5425e-04 2.4955e-04 b_country_CH -8.209e-05 1.0523e-04 4.403e-05 -1.3014e-04 b_country_DK -3.932e-05 4.096e-05 6.834e-05 -4.247e-05 b_country_IND 5.569e-05 5.202e-05 1.4054e-04 1.1373e-04 b_country_RUS 2.961e-05 -1.8104e-04 -1.197e-05 5.145e-05 b_country_BRA 5.817e-05 -6.090e-05 1.4688e-04 1.6000e-04 b_char_fast -7.470e-05 7.989e-05 3.227e-05 -1.9423e-04 b_char_double -1.1682e-04 6.595e-05 4.148e-05 -1.873e-07 b_risk 1.255e-07 -1.075e-07 2.090e-07 1.885e-07 b_price 2.9902e-04 -4.048e-05 -1.193e-05 -4.843e-05 lambda -4.048e-05 0.001016 5.7411e-04 1.9055e-04 gamma_reg_user -1.193e-05 5.7411e-04 0.006356 -8.2207e-04 gamma_university -4.843e-05 1.9055e-04 -8.2207e-04 0.005503 gamma_age_50 1.733e-05 -4.2163e-04 -0.001294 -0.001676 zeta_quality 9.432e-06 1.5983e-04 8.7147e-04 3.8936e-04 zeta_ingredient 1.413e-05 -1.7083e-04 -5.5112e-04 -5.2508e-04 zeta_patent 2.806e-05 1.8085e-04 6.9012e-04 3.9798e-04 zeta_dominance 4.441e-05 -1.3119e-04 -2.2313e-04 -6.2354e-04 sigma_qual 7.020e-06 2.909e-05 -1.5483e-04 1.023e-05 sigma_ingr 3.034e-06 1.627e-05 6.209e-05 -1.1697e-04 sigma_pate -4.838e-07 2.024e-05 7.472e-05 -1.951e-05 sigma_domi 2.917e-06 -1.769e-06 8.117e-05 -1.2052e-04 gamma_age_50 zeta_quality zeta_ingredient zeta_patent b_brand_Novum -7.266e-05 -7.508e-07 -1.847e-05 5.341e-05 b_brand_BestValue 5.3335e-04 9.917e-05 -8.515e-05 1.5089e-04 b_brand_Supermarket 5.4136e-04 7.456e-05 -1.135e-06 1.7526e-04 b_brand_PainAway 6.0417e-04 1.2643e-04 3.057e-05 1.7727e-04 b_country_CH -2.448e-05 -3.212e-06 3.588e-05 -5.304e-05 b_country_DK -3.683e-05 -3.265e-05 -1.011e-05 -2.385e-05 b_country_IND -1.6016e-04 1.0231e-04 -5.682e-05 2.984e-05 b_country_RUS -2.197e-05 -2.849e-05 -6.438e-05 3.678e-05 b_country_BRA -1.8496e-04 3.395e-05 -2.847e-05 4.077e-05 b_char_fast 1.5978e-04 1.275e-05 2.862e-05 -2.931e-05 b_char_double 7.909e-05 -6.578e-06 7.530e-05 4.145e-05 b_risk -3.415e-07 1.268e-07 4.205e-08 -4.081e-08 b_price 1.733e-05 9.432e-06 1.413e-05 2.806e-05 lambda -4.2163e-04 1.5983e-04 -1.7083e-04 1.8085e-04 gamma_reg_user -0.001294 8.7147e-04 -5.5112e-04 6.9012e-04 gamma_university -0.001676 3.8936e-04 -5.2508e-04 3.9798e-04 gamma_age_50 0.005550 -4.9974e-04 5.3707e-04 -5.1729e-04 zeta_quality -4.9974e-04 0.001513 -3.6230e-04 2.2485e-04 zeta_ingredient 5.3707e-04 -3.6230e-04 0.001573 -2.9035e-04 zeta_patent -5.1729e-04 2.2485e-04 -2.9035e-04 0.001484 zeta_dominance 2.9388e-04 -1.2018e-04 2.2908e-04 -1.2015e-04 sigma_qual 6.886e-05 -5.4634e-04 7.013e-05 -6.509e-06 sigma_ingr 1.2113e-04 -5.913e-05 5.3286e-04 -3.344e-06 sigma_pate 5.035e-05 2.282e-05 1.256e-06 -5.5833e-04 sigma_domi -1.398e-07 2.389e-05 5.241e-05 -1.983e-05 zeta_dominance sigma_qual sigma_ingr sigma_pate b_brand_Novum -3.291e-05 -1.235e-05 -2.078e-05 1.054e-05 b_brand_BestValue -7.167e-05 -6.096e-05 1.064e-05 -4.489e-05 b_brand_Supermarket -6.987e-05 -1.993e-05 8.247e-05 -7.221e-05 b_brand_PainAway -6.505e-05 -7.272e-05 7.919e-05 -7.330e-05 b_country_CH -3.553e-05 2.433e-05 4.379e-05 -2.380e-05 b_country_DK -2.305e-05 1.031e-05 -2.146e-05 7.578e-07 b_country_IND -8.576e-06 -1.409e-05 -6.355e-07 9.886e-05 b_country_RUS -1.747e-05 1.623e-05 -3.114e-05 2.073e-05 b_country_BRA 4.942e-06 2.764e-06 -5.765e-05 1.565e-05 b_char_fast 1.015e-05 3.911e-06 2.958e-05 2.448e-05 b_char_double -1.193e-05 4.757e-05 4.206e-05 2.605e-05 b_risk -6.149e-09 -5.608e-08 3.563e-08 1.722e-08 b_price 4.441e-05 7.020e-06 3.034e-06 -4.838e-07 lambda -1.3119e-04 2.909e-05 1.627e-05 2.024e-05 gamma_reg_user -2.2313e-04 -1.5483e-04 6.209e-05 7.472e-05 gamma_university -6.2354e-04 1.023e-05 -1.1697e-04 -1.951e-05 gamma_age_50 2.9388e-04 6.886e-05 1.2113e-04 5.035e-05 zeta_quality -1.2018e-04 -5.4634e-04 -5.913e-05 2.282e-05 zeta_ingredient 2.2908e-04 7.013e-05 5.3286e-04 1.256e-06 zeta_patent -1.2015e-04 -6.509e-06 -3.344e-06 -5.5833e-04 zeta_dominance 0.001239 -5.527e-07 6.891e-05 1.798e-05 sigma_qual -5.527e-07 7.3039e-04 5.791e-06 -1.669e-05 sigma_ingr 6.891e-05 5.791e-06 6.9270e-04 -2.993e-05 sigma_pate 1.798e-05 -1.669e-05 -2.993e-05 7.5370e-04 sigma_domi 2.3610e-04 -1.812e-06 -1.356e-05 2.640e-05 sigma_domi b_brand_Novum -2.407e-05 b_brand_BestValue -6.423e-05 b_brand_Supermarket -1.2330e-04 b_brand_PainAway -3.493e-05 b_country_CH -2.092e-05 b_country_DK -3.971e-06 b_country_IND 5.002e-05 b_country_RUS 1.830e-05 b_country_BRA 3.668e-05 b_char_fast -8.781e-06 b_char_double 4.344e-06 b_risk -2.711e-08 b_price 2.917e-06 lambda -1.769e-06 gamma_reg_user 8.117e-05 gamma_university -1.2052e-04 gamma_age_50 -1.398e-07 zeta_quality 2.389e-05 zeta_ingredient 5.241e-05 zeta_patent -1.983e-05 zeta_dominance 2.3610e-04 sigma_qual -1.812e-06 sigma_ingr -1.356e-05 sigma_pate 2.640e-05 sigma_domi 5.3354e-04 Classical correlation matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_PainAway b_brand_Novum 1.000000 0.232012 0.28118 0.244389 b_brand_BestValue 0.232012 1.000000 0.72207 0.662076 b_brand_Supermarket 0.281182 0.722068 1.00000 0.665914 b_brand_PainAway 0.244389 0.662076 0.66591 1.000000 b_country_CH -0.054243 0.286633 0.27706 0.221591 b_country_DK -0.047274 0.265168 0.27454 0.226149 b_country_IND -0.033224 -0.407206 -0.41977 -0.365406 b_country_RUS -0.037787 -0.383334 -0.39469 -0.320270 b_country_BRA -0.006631 -0.358551 -0.42291 -0.344387 b_char_fast 0.011534 -0.004309 0.04594 -0.041330 b_char_double 0.065517 0.163527 0.18968 0.119945 b_risk 0.001490 -0.182917 -0.19294 -0.055011 b_price 0.066278 0.286989 0.25895 0.332748 lambda -0.012391 -0.082908 -0.07120 -0.108706 gamma_reg_user 0.002124 0.079591 0.08221 0.075350 gamma_university -0.002720 0.084880 0.08432 0.086080 gamma_age_50 2.6890e-04 0.072662 0.06860 0.072360 zeta_quality -9.3915e-04 0.037171 0.03380 0.036180 zeta_ingredient -0.002692 -0.038210 -0.03752 -0.040076 zeta_patent 0.001825 0.037401 0.04174 0.037168 zeta_dominance 5.5772e-04 -0.027110 -0.02951 -0.027463 sigma_qual 0.001084 -0.017955 -0.01399 -0.017758 sigma_ingr -0.002120 -0.018366 -0.01711 -0.020566 sigma_pate -0.001624 -0.018136 -0.02162 -0.018768 sigma_domi 5.1891e-04 -0.009138 -0.01037 -0.009829 b_country_CH b_country_DK b_country_IND b_country_RUS b_brand_Novum -0.054243 -0.047274 -0.033224 -0.037787 b_brand_BestValue 0.286633 0.265168 -0.407206 -0.383334 b_brand_Supermarket 0.277063 0.274536 -0.419774 -0.394692 b_brand_PainAway 0.221591 0.226149 -0.365406 -0.320270 b_country_CH 1.000000 0.492786 0.007304 -0.032053 b_country_DK 0.492786 1.000000 0.042753 0.005438 b_country_IND 0.007304 0.042753 1.000000 0.442171 b_country_RUS -0.032053 0.005438 0.442171 1.000000 b_country_BRA -0.033098 7.0735e-04 0.466126 0.424198 b_char_fast 0.076558 0.034435 -0.056042 -0.063202 b_char_double 0.088354 0.020817 -0.026354 -0.033867 b_risk -0.064793 -0.027752 0.052162 0.060871 b_price -0.121414 -0.047621 0.024129 0.045001 lambda 0.038871 0.012642 0.001950 -0.044457 gamma_reg_user 6.3130e-04 -2.9479e-04 0.001673 -0.002563 gamma_university 5.7898e-04 -0.002761 0.004161 -6.2942e-04 gamma_age_50 -0.002705 0.001193 -0.005387 0.004911 zeta_quality 9.3639e-04 -0.002833 0.005775 0.001890 zeta_ingredient 0.001933 -3.3985e-04 8.7078e-04 -7.8830e-04 zeta_patent -7.8006e-04 -0.003554 0.006710 -0.001649 zeta_dominance 4.1800e-04 0.001765 -0.001737 -0.001411 sigma_qual -3.5127e-04 0.002251 -0.004311 -0.002759 sigma_ingr 0.002086 -6.2845e-04 0.001664 -0.001497 sigma_pate 0.001425 0.003152 -0.005548 5.1177e-04 sigma_domi 6.1366e-04 0.001012 -5.7309e-04 -0.001596 b_country_BRA b_char_fast b_char_double b_risk b_brand_Novum -0.006631 0.011534 0.065517 0.001490 b_brand_BestValue -0.358551 -0.004309 0.163527 -0.182917 b_brand_Supermarket -0.422908 0.045936 0.189681 -0.192935 b_brand_PainAway -0.344387 -0.041330 0.119945 -0.055011 b_country_CH -0.033098 0.076558 0.088354 -0.064793 b_country_DK 7.0735e-04 0.034435 0.020817 -0.027752 b_country_IND 0.466126 -0.056042 -0.026354 0.052162 b_country_RUS 0.424198 -0.063202 -0.033867 0.060871 b_country_BRA 1.000000 -0.068180 -0.050810 0.031803 b_char_fast -0.068180 1.000000 0.455751 -0.082503 b_char_double -0.050810 0.455751 1.000000 -0.050978 b_risk 0.031803 -0.082503 -0.050978 1.000000 b_price 0.067008 -0.141131 -0.173132 0.118640 lambda -0.025848 0.066689 0.068833 -0.054514 gamma_reg_user -0.001463 -3.1277e-04 0.001848 3.0874e-04 gamma_university 8.9790e-04 4.992e-05 -3.7944e-04 0.002247 gamma_age_50 0.002078 -1.8685e-04 -0.003840 -0.001456 zeta_quality 0.005115 -0.002499 -0.001772 0.008095 zeta_ingredient 0.001574 0.007896 0.004653 -0.004939 zeta_patent -0.002569 -0.007595 -0.003586 0.006013 zeta_dominance -0.003555 -5.8024e-04 0.002283 -0.001940 sigma_qual -0.005129 0.002238 0.002386 -0.007157 sigma_ingr 0.001061 0.006630 0.004566 -0.003840 sigma_pate 0.002231 0.007641 0.004529 -0.005634 sigma_domi -0.002729 -4.7627e-04 0.002059 -0.001120 b_price lambda gamma_reg_user gamma_university b_brand_Novum 0.066278 -0.012391 0.002124 -0.002720 b_brand_BestValue 0.286989 -0.082908 0.079591 0.084880 b_brand_Supermarket 0.258947 -0.071198 0.082214 0.084320 b_brand_PainAway 0.332748 -0.108706 0.075350 0.086080 b_country_CH -0.121414 0.038871 6.3130e-04 5.7898e-04 b_country_DK -0.047621 0.012642 -2.9479e-04 -0.002761 b_country_IND 0.024129 0.001950 0.001673 0.004161 b_country_RUS 0.045001 -0.044457 -0.002563 -6.2942e-04 b_country_BRA 0.067008 -0.025848 -0.001463 8.9790e-04 b_char_fast -0.141131 0.066689 -3.1277e-04 4.992e-05 b_char_double -0.173132 0.068833 0.001848 -3.7944e-04 b_risk 0.118640 -0.054514 3.0874e-04 0.002247 b_price 1.000000 -0.067720 -0.006393 -0.003056 lambda -0.067720 1.000000 0.243366 0.113730 gamma_reg_user -0.006393 0.243366 1.000000 -0.128952 gamma_university -0.003056 0.113730 -0.128952 1.000000 gamma_age_50 0.008999 -0.230675 -0.284919 -0.303323 zeta_quality -0.003574 0.168919 0.203883 0.113108 zeta_ingredient -0.001521 -0.141129 -0.175230 -0.114631 zeta_patent -0.003042 0.173473 0.200839 0.115452 zeta_dominance 0.001568 -0.130165 -0.116870 -0.121877 sigma_qual 9.8349e-04 0.015191 -0.048242 -0.022525 sigma_ingr -0.003276 0.025232 -0.029442 -0.027607 sigma_pate 2.9279e-04 0.029195 -0.035269 -0.018645 sigma_domi -3.0635e-04 0.011638 0.002691 -0.036539 gamma_age_50 zeta_quality zeta_ingredient zeta_patent b_brand_Novum 2.6890e-04 -9.3915e-04 -0.002692 0.001825 b_brand_BestValue 0.072662 0.037171 -0.038210 0.037401 b_brand_Supermarket 0.068604 0.033796 -0.037517 0.041735 b_brand_PainAway 0.072360 0.036180 -0.040076 0.037168 b_country_CH -0.002705 9.3639e-04 0.001933 -7.8006e-04 b_country_DK 0.001193 -0.002833 -3.3985e-04 -0.003554 b_country_IND -0.005387 0.005775 8.7078e-04 0.006710 b_country_RUS 0.004911 0.001890 -7.8830e-04 -0.001649 b_country_BRA 0.002078 0.005115 0.001574 -0.002569 b_char_fast -1.8685e-04 -0.002499 0.007896 -0.007595 b_char_double -0.003840 -0.001772 0.004653 -0.003586 b_risk -0.001456 0.008095 -0.004939 0.006013 b_price 0.008999 -0.003574 -0.001521 -0.003042 lambda -0.230675 0.168919 -0.141129 0.173473 gamma_reg_user -0.284919 0.203883 -0.175230 0.200839 gamma_university -0.303323 0.113108 -0.114631 0.115452 gamma_age_50 1.000000 -0.155761 0.153108 -0.166456 zeta_quality -0.155761 1.000000 -0.140797 0.125720 zeta_ingredient 0.153108 -0.140797 1.000000 -0.136725 zeta_patent -0.166456 0.125720 -0.136725 1.000000 zeta_dominance 0.103670 -0.092630 0.104204 -0.086999 sigma_qual 0.021935 -0.285981 0.015017 0.016158 sigma_ingr 0.026370 -0.012825 0.254588 -0.004121 sigma_pate 0.022501 0.023522 5.6262e-04 -0.311655 sigma_domi -7.8282e-04 0.010839 0.003868 0.018602 zeta_dominance sigma_qual sigma_ingr sigma_pate b_brand_Novum 5.5772e-04 0.001084 -0.002120 -0.001624 b_brand_BestValue -0.027110 -0.017955 -0.018366 -0.018136 b_brand_Supermarket -0.029513 -0.013991 -0.017107 -0.021616 b_brand_PainAway -0.027463 -0.017758 -0.020566 -0.018768 b_country_CH 4.1800e-04 -3.5127e-04 0.002086 0.001425 b_country_DK 0.001765 0.002251 -6.2845e-04 0.003152 b_country_IND -0.001737 -0.004311 0.001664 -0.005548 b_country_RUS -0.001411 -0.002759 -0.001497 5.1177e-04 b_country_BRA -0.003555 -0.005129 0.001061 0.002231 b_char_fast -5.8024e-04 0.002238 0.006630 0.007641 b_char_double 0.002283 0.002386 0.004566 0.004529 b_risk -0.001940 -0.007157 -0.003840 -0.005634 b_price 0.001568 9.8349e-04 -0.003276 2.9279e-04 lambda -0.130165 0.015191 0.025232 0.029195 gamma_reg_user -0.116870 -0.048242 -0.029442 -0.035269 gamma_university -0.121877 -0.022525 -0.027607 -0.018645 gamma_age_50 0.103670 0.021935 0.026370 0.022501 zeta_quality -0.092630 -0.285981 -0.012825 0.023522 zeta_ingredient 0.104204 0.015017 0.254588 5.6262e-04 zeta_patent -0.086999 0.016158 -0.004121 -0.311655 zeta_dominance 1.000000 -0.009645 0.007877 -0.025887 sigma_qual -0.009645 1.000000 0.002003 -0.031841 sigma_ingr 0.007877 0.002003 1.000000 -0.007714 sigma_pate -0.025887 -0.031841 -0.007714 1.000000 sigma_domi 0.209526 -0.014589 -4.1480e-04 -0.024292 sigma_domi b_brand_Novum 5.1891e-04 b_brand_BestValue -0.009138 b_brand_Supermarket -0.010368 b_brand_PainAway -0.009829 b_country_CH 6.1366e-04 b_country_DK 0.001012 b_country_IND -5.7309e-04 b_country_RUS -0.001596 b_country_BRA -0.002729 b_char_fast -4.7627e-04 b_char_double 0.002059 b_risk -0.001120 b_price -3.0635e-04 lambda 0.011638 gamma_reg_user 0.002691 gamma_university -0.036539 gamma_age_50 -7.8282e-04 zeta_quality 0.010839 zeta_ingredient 0.003868 zeta_patent 0.018602 zeta_dominance 0.209526 sigma_qual -0.014589 sigma_ingr -4.1480e-04 sigma_pate -0.024292 sigma_domi 1.000000 Robust correlation matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_PainAway b_brand_Novum 1.00000 0.205849 0.24096 0.19015 b_brand_BestValue 0.20585 1.000000 0.68541 0.64376 b_brand_Supermarket 0.24096 0.685414 1.00000 0.66620 b_brand_PainAway 0.19015 0.643757 0.66620 1.00000 b_country_CH -0.10162 0.222643 0.24226 0.18821 b_country_DK -0.03841 0.195951 0.24498 0.20318 b_country_IND -0.03164 -0.441235 -0.43637 -0.37614 b_country_RUS -0.02678 -0.430052 -0.40278 -0.36167 b_country_BRA 0.01890 -0.397713 -0.46961 -0.36315 b_char_fast -0.05425 -0.013485 0.06162 -0.04060 b_char_double -0.01290 0.157107 0.17816 0.09228 b_risk 0.07116 -0.118740 -0.13963 -0.04847 b_price 0.07704 0.275947 0.24138 0.31261 lambda -0.04854 -0.094517 -0.06192 -0.09471 gamma_reg_user 6.5076e-04 0.069892 0.08149 0.08698 gamma_university -0.02367 0.059284 0.02836 0.05135 gamma_age_50 -0.03053 0.111291 0.10970 0.12380 zeta_quality -6.0414e-04 0.039628 0.02894 0.04961 zeta_ingredient -0.01458 -0.033377 -4.3196e-04 0.01177 zeta_patent 0.04340 0.060891 0.06869 0.07025 zeta_dominance -0.02926 -0.031646 -0.02996 -0.02821 sigma_qual -0.01430 -0.035066 -0.01113 -0.04107 sigma_ingr -0.02471 0.006285 0.04730 0.04593 sigma_pate 0.01201 -0.025416 -0.03971 -0.04076 sigma_domi -0.03262 -0.043225 -0.08059 -0.02308 b_country_CH b_country_DK b_country_IND b_country_RUS b_brand_Novum -0.101618 -0.038415 -0.031639 -0.026778 b_brand_BestValue 0.222643 0.195951 -0.441235 -0.430052 b_brand_Supermarket 0.242258 0.244977 -0.436366 -0.402777 b_brand_PainAway 0.188208 0.203183 -0.376136 -0.361671 b_country_CH 1.000000 0.470100 -0.023717 -0.062118 b_country_DK 0.470100 1.000000 0.024926 -0.006506 b_country_IND -0.023717 0.024926 1.000000 0.409904 b_country_RUS -0.062118 -0.006506 0.409904 1.000000 b_country_BRA -0.045484 0.002228 0.514494 0.495659 b_char_fast 0.103819 0.006805 -0.086232 -0.084994 b_char_double 0.080029 -0.015615 -0.037484 -0.047177 b_risk -0.005885 0.047415 0.070525 0.072066 b_price -0.122333 -0.060525 0.055397 0.028001 lambda 0.085055 0.034205 0.028067 -0.092869 gamma_reg_user 0.014233 0.022821 0.030322 -0.002456 gamma_university -0.045209 -0.015241 0.026371 0.011343 gamma_age_50 -0.008467 -0.013160 -0.036979 -0.004822 zeta_quality -0.002128 -0.022342 0.045236 -0.011977 zeta_ingredient 0.023310 -0.006789 -0.024643 -0.026550 zeta_patent -0.035484 -0.016481 0.013325 0.015616 zeta_dominance -0.026009 -0.017432 -0.004190 -0.008114 sigma_qual 0.023203 0.010151 -0.008970 0.009824 sigma_ingr 0.042870 -0.021704 -4.1535e-04 -0.019349 sigma_pate -0.022336 7.3483e-04 0.061939 0.012350 sigma_domi -0.023334 -0.004577 0.037246 0.012957 b_country_BRA b_char_fast b_char_double b_risk b_brand_Novum 0.018898 -0.054249 -0.012902 0.071165 b_brand_BestValue -0.397713 -0.013485 0.157107 -0.118740 b_brand_Supermarket -0.469608 0.061622 0.178165 -0.139625 b_brand_PainAway -0.363147 -0.040596 0.092283 -0.048470 b_country_CH -0.045484 0.103819 0.080029 -0.005885 b_country_DK 0.002228 0.006805 -0.015615 0.047415 b_country_IND 0.514494 -0.086232 -0.037484 0.070525 b_country_RUS 0.495659 -0.084994 -0.047177 0.072066 b_country_BRA 1.000000 -0.104479 -0.060744 0.032220 b_char_fast -0.104479 1.000000 0.436328 -0.091493 b_char_double -0.060744 0.436328 1.000000 -0.009729 b_risk 0.032220 -0.091493 -0.009729 1.000000 b_price 0.054454 -0.149495 -0.184482 0.122127 lambda -0.030923 0.086730 0.056488 -0.056751 gamma_reg_user 0.029825 0.014009 0.014208 0.044095 gamma_university 0.034917 -0.090617 -6.895e-05 0.042743 gamma_age_50 -0.040193 0.074228 0.028991 -0.077115 zeta_quality 0.014127 0.011347 -0.004618 0.054858 zeta_ingredient -0.011621 0.024980 0.051849 0.017839 zeta_patent 0.017134 -0.026334 0.029383 -0.017823 zeta_dominance 0.002272 0.009978 -0.009256 -0.002938 sigma_qual 0.001656 0.005009 0.048069 -0.034909 sigma_ingr -0.035458 0.038890 0.043635 0.022779 sigma_pate 0.009228 0.030866 0.025908 0.010554 sigma_domi 0.025710 -0.013156 0.005135 -0.019747 b_price lambda gamma_reg_user gamma_university b_brand_Novum 0.077044 -0.048541 6.5076e-04 -0.023665 b_brand_BestValue 0.275947 -0.094517 0.069892 0.059284 b_brand_Supermarket 0.241383 -0.061917 0.081492 0.028355 b_brand_PainAway 0.312605 -0.094715 0.086980 0.051355 b_country_CH -0.122333 0.085055 0.014233 -0.045209 b_country_DK -0.060525 0.034205 0.022821 -0.015241 b_country_IND 0.055397 0.028067 0.030322 0.026371 b_country_RUS 0.028001 -0.092869 -0.002456 0.011343 b_country_BRA 0.054454 -0.030923 0.029825 0.034917 b_char_fast -0.149495 0.086730 0.014009 -0.090617 b_char_double -0.184482 0.056488 0.014208 -6.895e-05 b_risk 0.122127 -0.056751 0.044095 0.042743 b_price 1.000000 -0.073426 -0.008655 -0.037753 lambda -0.073426 1.000000 0.225884 0.080575 gamma_reg_user -0.008655 0.225884 1.000000 -0.139006 gamma_university -0.037753 0.080575 -0.139006 1.000000 gamma_age_50 0.013451 -0.177525 -0.217869 -0.303234 zeta_quality 0.014021 0.128875 0.280994 0.134926 zeta_ingredient 0.020604 -0.135116 -0.174310 -0.178488 zeta_patent 0.042129 0.147266 0.224725 0.139280 zeta_dominance 0.072944 -0.116889 -0.079500 -0.238770 sigma_qual 0.015021 0.033769 -0.071861 0.005103 sigma_ingr 0.006667 0.019385 0.029593 -0.059915 sigma_pate -0.001019 0.023122 0.034138 -0.009582 sigma_domi 0.007302 -0.002402 0.044080 -0.070341 gamma_age_50 zeta_quality zeta_ingredient zeta_patent b_brand_Novum -0.030527 -6.0414e-04 -0.014576 0.043401 b_brand_BestValue 0.111291 0.039628 -0.033377 0.060891 b_brand_Supermarket 0.109705 0.028936 -4.3196e-04 0.068689 b_brand_PainAway 0.123802 0.049613 0.011767 0.070252 b_country_CH -0.008467 -0.002128 0.023310 -0.035484 b_country_DK -0.013160 -0.022342 -0.006789 -0.016481 b_country_IND -0.036979 0.045236 -0.024643 0.013325 b_country_RUS -0.004822 -0.011977 -0.026550 0.015616 b_country_BRA -0.040193 0.014127 -0.011621 0.017134 b_char_fast 0.074228 0.011347 0.024980 -0.026334 b_char_double 0.028991 -0.004618 0.051849 0.029383 b_risk -0.077115 0.054858 0.017839 -0.017823 b_price 0.013451 0.014021 0.020604 0.042129 lambda -0.177525 0.128875 -0.135116 0.147266 gamma_reg_user -0.217869 0.280994 -0.174310 0.224725 gamma_university -0.303234 0.134926 -0.178488 0.139280 gamma_age_50 1.000000 -0.172440 0.181785 -0.180262 zeta_quality -0.172440 1.000000 -0.234839 0.150047 zeta_ingredient 0.181785 -0.234839 1.000000 -0.190067 zeta_patent -0.180262 0.150047 -0.190067 1.000000 zeta_dominance 0.112057 -0.087752 0.164084 -0.088599 sigma_qual 0.034203 -0.519655 0.065431 -0.006253 sigma_ingr 0.061781 -0.057756 0.510517 -0.003298 sigma_pate 0.024617 0.021367 0.001154 -0.527959 sigma_domi -8.125e-05 0.026582 0.057213 -0.022288 zeta_dominance sigma_qual sigma_ingr sigma_pate b_brand_Novum -0.029258 -0.014301 -0.024711 0.012013 b_brand_BestValue -0.031646 -0.035066 0.006285 -0.025416 b_brand_Supermarket -0.029963 -0.011133 0.047303 -0.039708 b_brand_PainAway -0.028207 -0.041075 0.045929 -0.040759 b_country_CH -0.026009 0.023203 0.042870 -0.022336 b_country_DK -0.017432 0.010151 -0.021704 7.3483e-04 b_country_IND -0.004190 -0.008970 -4.1535e-04 0.061939 b_country_RUS -0.008114 0.009824 -0.019349 0.012350 b_country_BRA 0.002272 0.001656 -0.035458 0.009228 b_char_fast 0.009978 0.005009 0.038890 0.030866 b_char_double -0.009256 0.048069 0.043635 0.025908 b_risk -0.002938 -0.034909 0.022779 0.010554 b_price 0.072944 0.015021 0.006667 -0.001019 lambda -0.116889 0.033769 0.019385 0.023122 gamma_reg_user -0.079500 -0.071861 0.029593 0.034138 gamma_university -0.238770 0.005103 -0.059915 -0.009582 gamma_age_50 0.112057 0.034203 0.061781 0.024617 zeta_quality -0.087752 -0.519655 -0.057756 0.021367 zeta_ingredient 0.164084 0.065431 0.510517 0.001154 zeta_patent -0.088599 -0.006253 -0.003298 -0.527959 zeta_dominance 1.000000 -5.8095e-04 0.074376 0.018602 sigma_qual -5.8095e-04 1.000000 0.008141 -0.022496 sigma_ingr 0.074376 0.008141 1.000000 -0.041425 sigma_pate 0.018602 -0.022496 -0.041425 1.000000 sigma_domi 0.290342 -0.002902 -0.022303 0.041626 sigma_domi b_brand_Novum -0.032618 b_brand_BestValue -0.043225 b_brand_Supermarket -0.080589 b_brand_PainAway -0.023082 b_country_CH -0.023334 b_country_DK -0.004577 b_country_IND 0.037246 b_country_RUS 0.012957 b_country_BRA 0.025710 b_char_fast -0.013156 b_char_double 0.005135 b_risk -0.019747 b_price 0.007302 lambda -0.002402 gamma_reg_user 0.044080 gamma_university -0.070341 gamma_age_50 -8.125e-05 zeta_quality 0.026582 zeta_ingredient 0.057213 zeta_patent -0.022288 zeta_dominance 0.290342 sigma_qual -0.002902 sigma_ingr -0.022303 sigma_pate 0.041626 sigma_domi 1.000000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 695 0.07321535 480 0.07708906 288 0.08368666 509 0.08492901 593 0.09011650 875 0.09015646 456 0.09198220 163 0.09329483 828 0.09702056 126 0.09764443 8 0.09819337 858 0.09865115 817 0.09892613 611 0.09967040 326 0.10026817 127 0.10064678 594 0.10073878 536 0.10273925 508 0.10291851 92 0.10374656 Changes in parameter estimates from starting values: Initial Estimate Difference b_brand_Artemis 0.000 0.000000 0.000000 b_brand_Novum 0.000 -0.276728 -0.276728 b_brand_BestValue 0.000 -0.580333 -0.580333 b_brand_Supermarket 0.000 -0.266708 -0.266708 b_brand_PainAway 0.000 -1.248770 -1.248770 b_country_CH 0.000 0.670161 0.670161 b_country_DK 0.000 0.337698 0.337698 b_country_USA 0.000 0.000000 0.000000 b_country_IND 0.000 -0.296318 -0.296318 b_country_RUS 0.000 -0.893694 -0.893694 b_country_BRA 0.000 -0.655527 -0.655527 b_char_standard 0.000 0.000000 0.000000 b_char_fast 0.000 0.769947 0.769947 b_char_double 0.000 1.212442 1.212442 b_risk 0.000 -0.001575 -0.001575 b_price 0.000 -0.724328 -0.724328 lambda 0.000 0.659834 0.659834 gamma_reg_user 0.000 -0.741191 -0.741191 gamma_university 0.000 -0.378841 -0.378841 gamma_age_50 0.000 0.673645 0.673645 zeta_quality 1.000 0.534809 -0.465191 zeta_ingredient 1.000 -0.503374 -1.503374 zeta_patent 1.000 0.606945 -0.393055 zeta_dominance 1.000 -0.394531 -1.394531 sigma_qual 1.000 1.061415 0.061415 sigma_ingr 1.000 1.108686 0.108686 sigma_pate 1.000 1.084298 0.084298 sigma_domi 1.000 1.045437 0.045437 Settings and functions used in model definition: apollo_control -------------- Value modelName "Apollo_example_25" modelDescr "ICLV model on drug choice data, using continuous measurement model for indicators" indivID "ID" mixing "TRUE" nCores "5" debug "FALSE" workInLogs "FALSE" seed "13" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" panelData "TRUE" analyticGrad "TRUE" Hessian routines attempted -------------- numerical jacobian of LL analytical gradient Scaling used in computing Hessian -------------- Value b_brand_Novum 0.276727744 b_brand_BestValue 0.580333087 b_brand_Supermarket 0.266708046 b_brand_PainAway 1.248770024 b_country_CH 0.670160921 b_country_DK 0.337698371 b_country_IND 0.296317616 b_country_RUS 0.893694143 b_country_BRA 0.655526538 b_char_fast 0.769947304 b_char_double 1.212441562 b_risk 0.001574511 b_price 0.724327696 lambda 0.659833868 gamma_reg_user 0.741191136 gamma_university 0.378840587 gamma_age_50 0.673645091 zeta_quality 0.534808737 zeta_ingredient 0.503373595 zeta_patent 0.606944658 zeta_dominance 0.394530691 sigma_qual 1.061415118 sigma_ingr 1.108686496 sigma_pate 1.084298404 sigma_domi 1.045436566 apollo_randCoeff ---------------- function(apollo_beta, apollo_inputs){ randcoeff = list() randcoeff[["LV"]] = gamma_reg_user*regular_user + gamma_university*university_educated + gamma_age_50*over_50 + eta 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)) ### Create list of probabilities P P = list() ### Likelihood of indicators normalDensity_settings1 = list(outcomeNormal = attitude_quality, xNormal = zeta_quality*LV, mu = 0, sigma = sigma_qual, rows = (task==1), componentName = "indic_quality") normalDensity_settings2 = list(outcomeNormal = attitude_ingredients, xNormal = zeta_ingredient*LV, mu = 0, sigma = sigma_ingr, rows = (task==1), componentName = "indic_ingredients") normalDensity_settings3 = list(outcomeNormal = attitude_patent, xNormal = zeta_patent*LV, mu = 0, sigma = sigma_pate, rows = (task==1), componentName = "indic_patent") normalDensity_settings4 = list(outcomeNormal = attitude_dominance, xNormal = zeta_dominance*LV, mu = 0, sigma = sigma_domi, rows = (task==1), componentName = "indic_dominance") P[["indic_quality"]] = apollo_normalDensity(normalDensity_settings1, functionality) P[["indic_ingredients"]] = apollo_normalDensity(normalDensity_settings2, functionality) P[["indic_patent"]] = apollo_normalDensity(normalDensity_settings3, functionality) P[["indic_dominance"]] = apollo_normalDensity(normalDensity_settings4, functionality) ### Likelihood of choices ### List of utilities: these must use the same names as in mnl_settings, order is irrelevant V = list() V[['alt1']] = ( b_brand_Artemis*(brand_1=="Artemis") + b_brand_Novum*(brand_1=="Novum") + b_country_CH*(country_1=="Switzerland") + b_country_DK*(country_1=="Denmark") + b_country_USA*(country_1=="USA") + b_char_standard*(char_1=="standard") + b_char_fast*(char_1=="fast acting") + b_char_double*(char_1=="double strength") + b_risk*side_effects_1 + b_price*price_1 + lambda*LV ) V[['alt2']] = ( b_brand_Artemis*(brand_2=="Artemis") + b_brand_Novum*(brand_2=="Novum") + b_country_CH*(country_2=="Switzerland") + b_country_DK*(country_2=="Denmark") + b_country_USA*(country_2=="USA") + b_char_standard*(char_2=="standard") + b_char_fast*(char_2=="fast acting") + b_char_double*(char_2=="double strength") + b_risk*side_effects_2 + b_price*price_2 + lambda*LV ) V[['alt3']] = ( b_brand_BestValue*(brand_3=="BestValue") + b_brand_Supermarket*(brand_3=="Supermarket") + b_brand_PainAway*(brand_3=="PainAway") + b_country_USA*(country_3=="USA") + b_country_IND*(country_3=="India") + b_country_RUS*(country_3=="Russia") + b_country_BRA*(country_3=="Brazil") + b_char_standard*(char_3=="standard") + b_char_fast*(char_3=="fast acting") + b_risk*side_effects_3 + b_price*price_3 ) V[['alt4']] = ( b_brand_BestValue*(brand_4=="BestValue") + b_brand_Supermarket*(brand_4=="Supermarket") + b_brand_PainAway*(brand_4=="PainAway") + b_country_USA*(country_4=="USA") + b_country_IND*(country_4=="India") + b_country_RUS*(country_4=="Russia") + b_country_BRA*(country_4=="Brazil") + b_char_standard*(char_4=="standard") + b_char_fast*(char_4=="fast acting") + b_risk*side_effects_4 + b_price*price_4 ) ### Define settings for MNL model component mnl_settings = list( alternatives = c(alt1=1, alt2=2, alt3=3, alt4=4), avail = list(alt1=1, alt2=1, alt3=1, alt4=1), choiceVar = best, V = V, componentName = "choice" ) ### Compute probabilities for MNL model component P[["choice"]] = apollo_mnl(mnl_settings, functionality) ### Likelihood of the whole model P = apollo_combineModels(P, apollo_inputs, 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)