Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : Hybrid_with_continuous_measurement Model description : Hybrid choice model on drug choice data, using continuous measurement model for indicators Model run at : 2023-05-11 21:40:43 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -71.381623 Number of individuals : 1000 Number of rows in database : 10000 Number of modelled outcomes : 14000 indic_quality : 1000 indic_ingredients : 1000 indic_patent : 1000 indic_dominance : 1000 choice : 10000 Number of cores used : 4 Number of inter-individual draws : 100 (halton) LL(start) : -20881.08 LL (whole model) at equal shares, LL(0) : NA LL (whole model) at observed shares, LL(C) : NA LL(final, whole model) : -17073.4 Rho-squared vs equal shares : Not applicable Adj.Rho-squared vs equal shares : Not applicable Rho-squared vs observed shares : Not applicable Adj.Rho-squared vs observed shares : Not applicable AIC : 34196.81 BIC : 34319.5 LL(0,indic_quality) : Not applicable LL(final,indic_quality) : -1597.3 LL(0,indic_ingredients) : Not applicable LL(final,indic_ingredients) : -1620.26 LL(0,indic_patent) : Not applicable LL(final,indic_patent) : -1636.34 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) : 00:06:32.6 pre-estimation : 00:00:37.6 estimation : 00:01:25.17 initial estimation : 00:01:20.1 estimation after rescaling : 00:00:5.07 post-estimation : 00:04:29.83 Iterations : 40 initial estimation : 39 estimation after rescaling : 1 Unconstrained optimisation. 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 -0.580336 0.06615 -8.774 0.06433 -9.021 b_brand_Supermarket -0.266708 0.06726 -3.965 0.06624 -4.026 b_brand_PainAway -1.248761 0.06750 -18.499 0.06551 -19.063 b_country_CH 0.670162 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 -0.655528 0.06022 -10.886 0.06177 -10.612 b_char_standard 0.000000 NA NA NA NA b_char_fast 0.769948 0.02921 26.356 0.02889 26.647 b_char_double 1.212447 0.03777 32.102 0.03662 33.110 b_risk -0.001575 5.834e-05 -26.990 5.944e-05 -26.489 b_price -0.724323 0.01812 -39.966 0.01729 -41.887 lambda 0.659833 0.03260 20.239 0.03188 20.697 gamma_reg_user -0.741193 0.07947 -9.327 0.07972 -9.297 gamma_university -0.378840 0.07375 -5.137 0.07418 -5.107 gamma_age_50 0.673648 0.07593 8.872 0.07450 9.043 zeta_quality 0.534805 0.03940 13.573 0.03890 13.747 zeta_ingredient -0.503372 0.04020 -12.522 0.03966 -12.692 zeta_patent 0.606951 0.04097 14.814 0.03852 15.757 zeta_dominance -0.394530 0.03672 -10.743 0.03520 -11.207 sigma_qual 1.061380 0.02750 38.590 0.02702 39.274 sigma_ingr 1.108661 0.02786 39.792 0.02632 42.125 sigma_pate 1.084333 0.02912 37.231 0.02745 39.496 sigma_domi 1.045440 0.02530 41.318 0.02310 45.260 Summary statistics for 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 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 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 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_country_CH b_brand_Novum 9.4984e-04 4.7298e-04 5.8289e-04 5.0844e-04 -6.662e-05 b_brand_BestValue 4.7298e-04 0.004375 0.003213 0.002956 7.5558e-04 b_brand_Supermarket 5.8289e-04 0.003213 0.004524 0.003024 7.4268e-04 b_brand_PainAway 5.0844e-04 0.002956 0.003024 0.004557 5.9612e-04 b_country_CH -6.662e-05 7.5558e-04 7.4268e-04 5.9612e-04 0.001588 b_country_DK -5.572e-05 6.7075e-04 7.0616e-04 5.8379e-04 7.5101e-04 b_country_IND -5.871e-05 -0.001544 -0.001619 -0.001414 1.669e-05 b_country_RUS -7.186e-05 -0.001565 -0.001638 -0.001334 -7.883e-05 b_country_BRA -1.231e-05 -0.001428 -0.001713 -0.001400 -7.943e-05 b_char_fast 1.038e-05 -8.327e-06 9.026e-05 -8.150e-05 8.913e-05 b_char_double 7.626e-05 4.0853e-04 4.8187e-04 3.0581e-04 1.3299e-04 b_risk 2.678e-09 -7.058e-07 -7.571e-07 -2.166e-07 -1.506e-07 b_price 3.702e-05 3.4404e-04 3.1566e-04 4.0709e-04 -8.769e-05 lambda -1.245e-05 -1.7880e-04 -1.5614e-04 -2.3925e-04 5.050e-05 gamma_reg_user 5.202e-06 4.1838e-04 4.3946e-04 4.0422e-04 1.999e-06 gamma_university -6.183e-06 4.1409e-04 4.1830e-04 4.2857e-04 1.701e-06 gamma_age_50 6.293e-07 3.6496e-04 3.5039e-04 3.7090e-04 -8.186e-06 zeta_quality -1.140e-06 9.689e-05 8.958e-05 9.624e-05 1.470e-06 zeta_ingredient -3.335e-06 -1.0161e-04 -1.0145e-04 -1.0876e-04 3.098e-06 zeta_patent 2.304e-06 1.0135e-04 1.1501e-04 1.0279e-04 -1.273e-06 zeta_dominance 6.311e-07 -6.585e-05 -7.290e-05 -6.808e-05 6.118e-07 sigma_qual 9.188e-07 -3.267e-05 -2.589e-05 -3.298e-05 -3.847e-07 sigma_ingr -1.821e-06 -3.385e-05 -3.206e-05 -3.868e-05 2.316e-06 sigma_pate -1.458e-06 -3.493e-05 -4.234e-05 -3.689e-05 1.653e-06 sigma_domi 4.046e-07 -1.529e-05 -1.764e-05 -1.679e-05 6.188e-07 b_country_DK b_country_IND b_country_RUS b_country_BRA b_char_fast b_brand_Novum -5.572e-05 -5.871e-05 -7.186e-05 -1.231e-05 1.038e-05 b_brand_BestValue 6.7075e-04 -0.001544 -0.001565 -0.001428 -8.327e-06 b_brand_Supermarket 7.0616e-04 -0.001619 -0.001638 -0.001713 9.026e-05 b_brand_PainAway 5.8379e-04 -0.001414 -0.001334 -0.001400 -8.150e-05 b_country_CH 7.5101e-04 1.669e-05 -7.883e-05 -7.943e-05 8.913e-05 b_country_DK 0.001462 9.374e-05 1.283e-05 1.630e-06 3.847e-05 b_country_IND 9.374e-05 0.003288 0.001564 0.001609 -9.387e-05 b_country_RUS 1.283e-05 0.001564 0.003808 0.001576 -1.1393e-04 b_country_BRA 1.630e-06 0.001609 0.001576 0.003626 -1.1994e-04 b_char_fast 3.847e-05 -9.387e-05 -1.1393e-04 -1.1994e-04 8.5341e-04 b_char_double 3.007e-05 -5.707e-05 -7.893e-05 -1.1556e-04 5.0286e-04 b_risk -6.191e-08 1.745e-07 2.191e-07 1.117e-07 -1.406e-07 b_price -3.300e-05 2.507e-05 5.033e-05 7.313e-05 -7.472e-05 lambda 1.576e-05 3.645e-06 -8.944e-05 -5.075e-05 6.352e-05 gamma_reg_user -8.961e-07 7.622e-06 -1.257e-05 -6.998e-06 -7.269e-07 gamma_university -7.787e-06 1.760e-05 -2.864e-06 3.988e-06 1.069e-07 gamma_age_50 3.464e-06 -2.345e-05 2.301e-05 9.501e-06 -4.147e-07 zeta_quality -4.270e-06 1.305e-05 4.597e-06 1.214e-05 -2.878e-06 zeta_ingredient -5.223e-07 2.007e-06 -1.956e-06 3.811e-06 9.273e-06 zeta_patent -5.568e-06 1.576e-05 -4.171e-06 -6.337e-06 -9.089e-06 zeta_dominance 2.479e-06 -3.657e-06 -3.196e-06 -7.861e-06 -6.223e-07 sigma_qual 2.368e-06 -6.799e-06 -4.684e-06 -8.495e-06 1.799e-06 sigma_ingr -6.695e-07 2.659e-06 -2.575e-06 1.780e-06 5.396e-06 sigma_pate 3.510e-06 -9.265e-06 9.203e-07 3.912e-06 6.500e-06 sigma_domi 9.794e-07 -8.314e-07 -2.492e-06 -4.157e-06 -3.520e-07 b_char_double b_risk b_price lambda gamma_reg_user b_brand_Novum 7.626e-05 2.678e-09 3.702e-05 -1.245e-05 5.202e-06 b_brand_BestValue 4.0853e-04 -7.058e-07 3.4404e-04 -1.7880e-04 4.1838e-04 b_brand_Supermarket 4.8187e-04 -7.571e-07 3.1566e-04 -1.5614e-04 4.3946e-04 b_brand_PainAway 3.0581e-04 -2.166e-07 4.0709e-04 -2.3925e-04 4.0422e-04 b_country_CH 1.3299e-04 -1.506e-07 -8.769e-05 5.050e-05 1.999e-06 b_country_DK 3.007e-05 -6.191e-08 -3.300e-05 1.576e-05 -8.961e-07 b_country_IND -5.707e-05 1.745e-07 2.507e-05 3.645e-06 7.622e-06 b_country_RUS -7.893e-05 2.191e-07 5.033e-05 -8.944e-05 -1.257e-05 b_country_BRA -1.1556e-04 1.117e-07 7.313e-05 -5.075e-05 -6.998e-06 b_char_fast 5.0286e-04 -1.406e-07 -7.472e-05 6.352e-05 -7.269e-07 b_char_double 0.001426 -1.123e-07 -1.1851e-04 8.476e-05 5.546e-06 b_risk -1.123e-07 3.403e-09 1.254e-07 -1.037e-07 1.433e-09 b_price -1.1851e-04 1.254e-07 3.2846e-04 -4.001e-05 -9.207e-06 lambda 8.476e-05 -1.037e-07 -4.001e-05 0.001063 6.3053e-04 gamma_reg_user 5.546e-06 1.433e-09 -9.207e-06 6.3053e-04 0.006315 gamma_university -1.058e-06 9.670e-09 -4.084e-06 2.7347e-04 -7.5582e-04 gamma_age_50 -1.101e-05 -6.450e-09 1.238e-05 -5.7106e-04 -0.001719 zeta_quality -2.638e-06 1.861e-08 -2.552e-06 2.1698e-04 6.3843e-04 zeta_ingredient 7.066e-06 -1.158e-08 -1.109e-06 -1.8495e-04 -5.5978e-04 zeta_patent -5.547e-06 1.437e-08 -2.259e-06 2.3173e-04 6.5391e-04 zeta_dominance 3.166e-06 -4.157e-09 1.043e-06 -1.5584e-04 -3.4107e-04 sigma_qual 2.479e-06 -1.149e-08 4.901e-07 1.363e-05 -1.0545e-04 sigma_ingr 4.806e-06 -6.242e-09 -1.655e-06 2.292e-05 -6.519e-05 sigma_pate 4.981e-06 -9.570e-09 1.548e-07 2.771e-05 -8.162e-05 sigma_domi 1.968e-06 -1.653e-09 -1.405e-07 9.601e-06 5.411e-06 gamma_university gamma_age_50 zeta_quality zeta_ingredient zeta_patent b_brand_Novum -6.183e-06 6.293e-07 -1.140e-06 -3.335e-06 2.304e-06 b_brand_BestValue 4.1409e-04 3.6496e-04 9.689e-05 -1.0161e-04 1.0135e-04 b_brand_Supermarket 4.1830e-04 3.5039e-04 8.958e-05 -1.0145e-04 1.1501e-04 b_brand_PainAway 4.2857e-04 3.7090e-04 9.624e-05 -1.0876e-04 1.0279e-04 b_country_CH 1.701e-06 -8.186e-06 1.470e-06 3.098e-06 -1.273e-06 b_country_DK -7.787e-06 3.464e-06 -4.270e-06 -5.223e-07 -5.568e-06 b_country_IND 1.760e-05 -2.345e-05 1.305e-05 2.007e-06 1.576e-05 b_country_RUS -2.864e-06 2.301e-05 4.597e-06 -1.956e-06 -4.171e-06 b_country_BRA 3.988e-06 9.501e-06 1.214e-05 3.811e-06 -6.337e-06 b_char_fast 1.069e-07 -4.147e-07 -2.878e-06 9.273e-06 -9.089e-06 b_char_double -1.058e-06 -1.101e-05 -2.638e-06 7.066e-06 -5.547e-06 b_risk 9.670e-09 -6.450e-09 1.861e-08 -1.158e-08 1.437e-08 b_price -4.084e-06 1.238e-05 -2.552e-06 -1.109e-06 -2.259e-06 lambda 2.7347e-04 -5.7106e-04 2.1698e-04 -1.8495e-04 2.3173e-04 gamma_reg_user -7.5582e-04 -0.001719 6.3843e-04 -5.5978e-04 6.5391e-04 gamma_university 0.005440 -0.001699 3.2871e-04 -3.3987e-04 3.4887e-04 gamma_age_50 -0.001699 0.005766 -4.6602e-04 4.6734e-04 -5.1784e-04 zeta_quality 3.2871e-04 -4.6602e-04 0.001553 -2.2300e-04 2.0296e-04 zeta_ingredient -3.3987e-04 4.6734e-04 -2.2300e-04 0.001616 -2.2519e-04 zeta_patent 3.4887e-04 -5.1784e-04 2.0296e-04 -2.2519e-04 0.001679 zeta_dominance -3.3010e-04 2.8907e-04 -1.3402e-04 1.5382e-04 -1.3091e-04 sigma_qual -4.570e-05 4.581e-05 -3.0996e-04 1.660e-05 1.821e-05 sigma_ingr -5.673e-05 5.579e-05 -1.408e-05 2.8516e-04 -4.707e-06 sigma_pate -4.005e-05 4.975e-05 2.699e-05 6.605e-07 -3.7183e-04 sigma_domi -6.819e-05 -1.505e-06 1.081e-05 3.933e-06 1.928e-05 zeta_dominance sigma_qual sigma_ingr sigma_pate sigma_domi b_brand_Novum 6.311e-07 9.188e-07 -1.821e-06 -1.458e-06 4.046e-07 b_brand_BestValue -6.585e-05 -3.267e-05 -3.385e-05 -3.493e-05 -1.529e-05 b_brand_Supermarket -7.290e-05 -2.589e-05 -3.206e-05 -4.234e-05 -1.764e-05 b_brand_PainAway -6.808e-05 -3.298e-05 -3.868e-05 -3.689e-05 -1.679e-05 b_country_CH 6.118e-07 -3.847e-07 2.316e-06 1.653e-06 6.188e-07 b_country_DK 2.479e-06 2.368e-06 -6.695e-07 3.510e-06 9.794e-07 b_country_IND -3.657e-06 -6.799e-06 2.659e-06 -9.265e-06 -8.314e-07 b_country_RUS -3.196e-06 -4.684e-06 -2.575e-06 9.203e-07 -2.492e-06 b_country_BRA -7.861e-06 -8.495e-06 1.780e-06 3.912e-06 -4.157e-06 b_char_fast -6.223e-07 1.799e-06 5.396e-06 6.500e-06 -3.520e-07 b_char_double 3.166e-06 2.479e-06 4.806e-06 4.981e-06 1.968e-06 b_risk -4.157e-09 -1.149e-08 -6.242e-09 -9.570e-09 -1.653e-09 b_price 1.043e-06 4.901e-07 -1.655e-06 1.548e-07 -1.405e-07 lambda -1.5584e-04 1.363e-05 2.292e-05 2.771e-05 9.601e-06 gamma_reg_user -3.4107e-04 -1.0545e-04 -6.519e-05 -8.162e-05 5.411e-06 gamma_university -3.3010e-04 -4.570e-05 -5.673e-05 -4.005e-05 -6.819e-05 gamma_age_50 2.8907e-04 4.581e-05 5.579e-05 4.975e-05 -1.505e-06 zeta_quality -1.3402e-04 -3.0996e-04 -1.408e-05 2.699e-05 1.081e-05 zeta_ingredient 1.5382e-04 1.660e-05 2.8516e-04 6.605e-07 3.933e-06 zeta_patent -1.3091e-04 1.821e-05 -4.707e-06 -3.7183e-04 1.928e-05 zeta_dominance 0.001349 -9.744e-06 8.059e-06 -2.768e-05 1.9468e-04 sigma_qual -9.744e-06 7.5645e-04 1.532e-06 -2.551e-05 -1.015e-05 sigma_ingr 8.059e-06 1.532e-06 7.7626e-04 -6.259e-06 -2.929e-07 sigma_pate -2.768e-05 -2.551e-05 -6.259e-06 8.4824e-04 -1.790e-05 sigma_domi 1.9468e-04 -1.015e-05 -2.929e-07 -1.790e-05 6.4019e-04 Robust covariance matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_PainAway b_country_CH b_brand_Novum 0.001021 4.2306e-04 5.0993e-04 3.9795e-04 -1.2599e-04 b_brand_BestValue 4.2306e-04 0.004138 0.002921 0.002713 5.5582e-04 b_brand_Supermarket 5.0993e-04 0.002921 0.004388 0.002891 6.2274e-04 b_brand_PainAway 3.9795e-04 0.002713 0.002891 0.004291 4.7846e-04 b_country_CH -1.2599e-04 5.5582e-04 6.2274e-04 4.7846e-04 0.001506 b_country_DK -4.610e-05 4.7353e-04 6.0957e-04 4.9999e-04 6.8532e-04 b_country_IND -5.877e-05 -0.001650 -0.001680 -0.001433 -5.351e-05 b_country_RUS -5.231e-05 -0.001692 -0.001631 -0.001449 -1.4740e-04 b_country_BRA 3.730e-05 -0.001580 -0.001922 -0.001469 -1.0903e-04 b_char_fast -5.008e-05 -2.507e-05 1.1794e-04 -7.684e-05 1.1642e-04 b_char_double -1.509e-05 3.7010e-04 4.3216e-04 2.2137e-04 1.1373e-04 b_risk 1.351e-07 -4.540e-07 -5.497e-07 -1.887e-07 -1.357e-08 b_price 4.256e-05 3.0697e-04 2.7649e-04 3.5411e-04 -8.209e-05 lambda -4.944e-05 -1.9386e-04 -1.3076e-04 -1.9782e-04 1.0523e-04 gamma_reg_user 1.660e-06 3.5845e-04 4.3035e-04 4.5426e-04 4.403e-05 gamma_university -5.608e-05 2.8292e-04 1.3933e-04 2.4956e-04 -1.3014e-04 gamma_age_50 -7.266e-05 5.3336e-04 5.4136e-04 6.0418e-04 -2.447e-05 zeta_quality -7.488e-07 9.919e-05 7.458e-05 1.2645e-04 -3.215e-06 zeta_ingredient -1.847e-05 -8.516e-05 -1.138e-06 3.056e-05 3.588e-05 zeta_patent 5.341e-05 1.5088e-04 1.7525e-04 1.7726e-04 -5.304e-05 zeta_dominance -3.291e-05 -7.167e-05 -6.987e-05 -6.505e-05 -3.553e-05 sigma_qual -1.235e-05 -6.097e-05 -1.994e-05 -7.272e-05 2.433e-05 sigma_ingr -2.078e-05 1.064e-05 8.246e-05 7.918e-05 4.379e-05 sigma_pate 1.054e-05 -4.488e-05 -7.221e-05 -7.330e-05 -2.380e-05 sigma_domi -2.407e-05 -6.423e-05 -1.2330e-04 -3.493e-05 -2.092e-05 b_country_DK b_country_IND b_country_RUS b_country_BRA b_char_fast b_brand_Novum -4.610e-05 -5.877e-05 -5.231e-05 3.730e-05 -5.008e-05 b_brand_BestValue 4.7353e-04 -0.001650 -0.001692 -0.001580 -2.507e-05 b_brand_Supermarket 6.0957e-04 -0.001680 -0.001631 -0.001922 1.1794e-04 b_brand_PainAway 4.9999e-04 -0.001433 -0.001449 -0.001469 -7.684e-05 b_country_CH 6.8532e-04 -5.351e-05 -1.4740e-04 -1.0903e-04 1.1642e-04 b_country_DK 0.001411 5.444e-05 -1.494e-05 5.172e-06 7.387e-06 b_country_IND 5.444e-05 0.003380 0.001457 0.001848 -1.4486e-04 b_country_RUS -1.494e-05 0.001457 0.003739 0.001872 -1.5017e-04 b_country_BRA 5.172e-06 0.001848 0.001872 0.003816 -1.8648e-04 b_char_fast 7.387e-06 -1.4486e-04 -1.5017e-04 -1.8648e-04 8.3490e-04 b_char_double -2.148e-05 -7.980e-05 -1.0564e-04 -1.3740e-04 4.6168e-04 b_risk 1.059e-07 2.437e-07 2.619e-07 1.183e-07 -1.571e-07 b_price -3.932e-05 5.569e-05 2.960e-05 5.817e-05 -7.470e-05 lambda 4.097e-05 5.202e-05 -1.8104e-04 -6.090e-05 7.989e-05 gamma_reg_user 6.834e-05 1.4054e-04 -1.197e-05 1.4688e-04 3.227e-05 gamma_university -4.247e-05 1.1373e-04 5.145e-05 1.6000e-04 -1.9423e-04 gamma_age_50 -3.683e-05 -1.6016e-04 -2.196e-05 -1.8496e-04 1.5978e-04 zeta_quality -3.265e-05 1.0231e-04 -2.849e-05 3.395e-05 1.275e-05 zeta_ingredient -1.011e-05 -5.682e-05 -6.439e-05 -2.847e-05 2.863e-05 zeta_patent -2.385e-05 2.985e-05 3.678e-05 4.077e-05 -2.931e-05 zeta_dominance -2.305e-05 -8.576e-06 -1.747e-05 4.942e-06 1.015e-05 sigma_qual 1.031e-05 -1.410e-05 1.623e-05 2.764e-06 3.912e-06 sigma_ingr -2.146e-05 -6.372e-07 -3.114e-05 -5.765e-05 2.958e-05 sigma_pate 7.568e-07 9.887e-05 2.073e-05 1.565e-05 2.448e-05 sigma_domi -3.971e-06 5.002e-05 1.830e-05 3.669e-05 -8.781e-06 b_char_double b_risk b_price lambda gamma_reg_user b_brand_Novum -1.509e-05 1.351e-07 4.256e-05 -4.944e-05 1.660e-06 b_brand_BestValue 3.7010e-04 -4.540e-07 3.0697e-04 -1.9386e-04 3.5845e-04 b_brand_Supermarket 4.3216e-04 -5.497e-07 2.7649e-04 -1.3076e-04 4.3035e-04 b_brand_PainAway 2.2137e-04 -1.887e-07 3.5411e-04 -1.9782e-04 4.5426e-04 b_country_CH 1.1373e-04 -1.357e-08 -8.209e-05 1.0523e-04 4.403e-05 b_country_DK -2.148e-05 1.059e-07 -3.932e-05 4.097e-05 6.834e-05 b_country_IND -7.980e-05 2.437e-07 5.569e-05 5.202e-05 1.4054e-04 b_country_RUS -1.0564e-04 2.619e-07 2.960e-05 -1.8104e-04 -1.197e-05 b_country_BRA -1.3740e-04 1.183e-07 5.817e-05 -6.090e-05 1.4688e-04 b_char_fast 4.6168e-04 -1.571e-07 -7.470e-05 7.989e-05 3.227e-05 b_char_double 0.001341 -2.118e-08 -1.1682e-04 6.595e-05 4.147e-05 b_risk -2.118e-08 3.533e-09 1.255e-07 -1.075e-07 2.090e-07 b_price -1.1682e-04 1.255e-07 2.9902e-04 -4.048e-05 -1.193e-05 lambda 6.595e-05 -1.075e-07 -4.048e-05 0.001016 5.7409e-04 gamma_reg_user 4.147e-05 2.090e-07 -1.193e-05 5.7409e-04 0.006356 gamma_university -1.918e-07 1.885e-07 -4.843e-05 1.9052e-04 -8.2208e-04 gamma_age_50 7.909e-05 -3.415e-07 1.733e-05 -4.2163e-04 -0.001294 zeta_quality -6.582e-06 1.269e-07 9.433e-06 1.5980e-04 8.7149e-04 zeta_ingredient 7.530e-05 4.205e-08 1.413e-05 -1.7081e-04 -5.5112e-04 zeta_patent 4.145e-05 -4.081e-08 2.806e-05 1.8087e-04 6.9015e-04 zeta_dominance -1.193e-05 -6.147e-09 4.441e-05 -1.3118e-04 -2.2312e-04 sigma_qual 4.757e-05 -5.608e-08 7.019e-06 2.911e-05 -1.5485e-04 sigma_ingr 4.206e-05 3.563e-08 3.034e-06 1.627e-05 6.208e-05 sigma_pate 2.605e-05 1.722e-08 -4.822e-07 2.022e-05 7.473e-05 sigma_domi 4.344e-06 -2.711e-08 2.917e-06 -1.768e-06 8.118e-05 gamma_university gamma_age_50 zeta_quality zeta_ingredient zeta_patent b_brand_Novum -5.608e-05 -7.266e-05 -7.488e-07 -1.847e-05 5.341e-05 b_brand_BestValue 2.8292e-04 5.3336e-04 9.919e-05 -8.516e-05 1.5088e-04 b_brand_Supermarket 1.3933e-04 5.4136e-04 7.458e-05 -1.138e-06 1.7525e-04 b_brand_PainAway 2.4956e-04 6.0418e-04 1.2645e-04 3.056e-05 1.7726e-04 b_country_CH -1.3014e-04 -2.447e-05 -3.215e-06 3.588e-05 -5.304e-05 b_country_DK -4.247e-05 -3.683e-05 -3.265e-05 -1.011e-05 -2.385e-05 b_country_IND 1.1373e-04 -1.6016e-04 1.0231e-04 -5.682e-05 2.985e-05 b_country_RUS 5.145e-05 -2.196e-05 -2.849e-05 -6.439e-05 3.678e-05 b_country_BRA 1.6000e-04 -1.8496e-04 3.395e-05 -2.847e-05 4.077e-05 b_char_fast -1.9423e-04 1.5978e-04 1.275e-05 2.863e-05 -2.931e-05 b_char_double -1.918e-07 7.909e-05 -6.582e-06 7.530e-05 4.145e-05 b_risk 1.885e-07 -3.415e-07 1.269e-07 4.205e-08 -4.081e-08 b_price -4.843e-05 1.733e-05 9.433e-06 1.413e-05 2.806e-05 lambda 1.9052e-04 -4.2163e-04 1.5980e-04 -1.7081e-04 1.8087e-04 gamma_reg_user -8.2208e-04 -0.001294 8.7149e-04 -5.5112e-04 6.9015e-04 gamma_university 0.005503 -0.001676 3.8936e-04 -5.2509e-04 3.9799e-04 gamma_age_50 -0.001676 0.005550 -4.9973e-04 5.3707e-04 -5.1730e-04 zeta_quality 3.8936e-04 -4.9973e-04 0.001513 -3.6229e-04 2.2485e-04 zeta_ingredient -5.2509e-04 5.3707e-04 -3.6229e-04 0.001573 -2.9036e-04 zeta_patent 3.9799e-04 -5.1730e-04 2.2485e-04 -2.9036e-04 0.001484 zeta_dominance -6.2354e-04 2.9388e-04 -1.2016e-04 2.2908e-04 -1.2017e-04 sigma_qual 1.022e-05 6.886e-05 -5.4638e-04 7.012e-05 -6.511e-06 sigma_ingr -1.1698e-04 1.2114e-04 -5.913e-05 5.3289e-04 -3.349e-06 sigma_pate -1.951e-05 5.034e-05 2.282e-05 1.256e-06 -5.5826e-04 sigma_domi -1.2052e-04 -1.414e-07 2.389e-05 5.241e-05 -1.984e-05 zeta_dominance sigma_qual sigma_ingr sigma_pate sigma_domi b_brand_Novum -3.291e-05 -1.235e-05 -2.078e-05 1.054e-05 -2.407e-05 b_brand_BestValue -7.167e-05 -6.097e-05 1.064e-05 -4.488e-05 -6.423e-05 b_brand_Supermarket -6.987e-05 -1.994e-05 8.246e-05 -7.221e-05 -1.2330e-04 b_brand_PainAway -6.505e-05 -7.272e-05 7.918e-05 -7.330e-05 -3.493e-05 b_country_CH -3.553e-05 2.433e-05 4.379e-05 -2.380e-05 -2.092e-05 b_country_DK -2.305e-05 1.031e-05 -2.146e-05 7.568e-07 -3.971e-06 b_country_IND -8.576e-06 -1.410e-05 -6.372e-07 9.887e-05 5.002e-05 b_country_RUS -1.747e-05 1.623e-05 -3.114e-05 2.073e-05 1.830e-05 b_country_BRA 4.942e-06 2.764e-06 -5.765e-05 1.565e-05 3.669e-05 b_char_fast 1.015e-05 3.912e-06 2.958e-05 2.448e-05 -8.781e-06 b_char_double -1.193e-05 4.757e-05 4.206e-05 2.605e-05 4.344e-06 b_risk -6.147e-09 -5.608e-08 3.563e-08 1.722e-08 -2.711e-08 b_price 4.441e-05 7.019e-06 3.034e-06 -4.822e-07 2.917e-06 lambda -1.3118e-04 2.911e-05 1.627e-05 2.022e-05 -1.768e-06 gamma_reg_user -2.2312e-04 -1.5485e-04 6.208e-05 7.473e-05 8.118e-05 gamma_university -6.2354e-04 1.022e-05 -1.1698e-04 -1.951e-05 -1.2052e-04 gamma_age_50 2.9388e-04 6.886e-05 1.2114e-04 5.034e-05 -1.414e-07 zeta_quality -1.2016e-04 -5.4638e-04 -5.913e-05 2.282e-05 2.389e-05 zeta_ingredient 2.2908e-04 7.012e-05 5.3289e-04 1.256e-06 5.241e-05 zeta_patent -1.2017e-04 -6.511e-06 -3.349e-06 -5.5826e-04 -1.984e-05 zeta_dominance 0.001239 -5.584e-07 6.891e-05 1.799e-05 2.3609e-04 sigma_qual -5.584e-07 7.3035e-04 5.788e-06 -1.669e-05 -1.815e-06 sigma_ingr 6.891e-05 5.788e-06 6.9267e-04 -2.993e-05 -1.356e-05 sigma_pate 1.799e-05 -1.669e-05 -2.993e-05 7.5373e-04 2.640e-05 sigma_domi 2.3609e-04 -1.815e-06 -1.356e-05 2.640e-05 5.3355e-04 Classical correlation matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_PainAway b_country_CH b_brand_Novum 1.000000 0.232011 0.28118 0.244389 -0.054243 b_brand_BestValue 0.232011 1.000000 0.72207 0.662076 0.286632 b_brand_Supermarket 0.281182 0.722067 1.00000 0.665915 0.277063 b_brand_PainAway 0.244389 0.662076 0.66591 1.000000 0.221590 b_country_CH -0.054243 0.286632 0.27706 0.221590 1.000000 b_country_DK -0.047273 0.265168 0.27454 0.226149 0.492786 b_country_IND -0.033224 -0.407206 -0.41977 -0.365407 0.007304 b_country_RUS -0.037786 -0.383333 -0.39469 -0.320270 -0.032053 b_country_BRA -0.006631 -0.358550 -0.42291 -0.344387 -0.033098 b_char_fast 0.011534 -0.004309 0.04594 -0.041330 0.076558 b_char_double 0.065517 0.163527 0.18968 0.119944 0.088355 b_risk 0.001489 -0.182916 -0.19293 -0.055012 -0.064793 b_price 0.066278 0.286989 0.25895 0.332748 -0.121415 lambda -0.012391 -0.082913 -0.07120 -0.108711 0.038871 gamma_reg_user 0.002124 0.079591 0.08221 0.075350 6.3113e-04 gamma_university -0.002720 0.084879 0.08432 0.086080 5.7878e-04 gamma_age_50 2.6892e-04 0.072662 0.06860 0.072360 -0.002705 zeta_quality -9.3909e-04 0.037174 0.03380 0.036183 9.3601e-04 zeta_ingredient -0.002692 -0.038212 -0.03752 -0.040078 0.001934 zeta_patent 0.001825 0.037400 0.04173 0.037166 -7.7970e-04 zeta_dominance 5.5766e-04 -0.027110 -0.02951 -0.027463 4.1806e-04 sigma_qual 0.001084 -0.017958 -0.01399 -0.017761 -3.5099e-04 sigma_ingr -0.002120 -0.018368 -0.01711 -0.020568 0.002086 sigma_pate -0.001624 -0.018134 -0.02161 -0.018766 0.001424 sigma_domi 5.1888e-04 -0.009139 -0.01037 -0.009829 6.1366e-04 b_country_DK b_country_IND b_country_RUS b_country_BRA b_char_fast b_brand_Novum -0.047273 -0.033224 -0.037786 -0.006631 0.011534 b_brand_BestValue 0.265168 -0.407206 -0.383333 -0.358550 -0.004309 b_brand_Supermarket 0.274535 -0.419774 -0.394692 -0.422908 0.045936 b_brand_PainAway 0.226149 -0.365407 -0.320270 -0.344387 -0.041330 b_country_CH 0.492786 0.007304 -0.032053 -0.033098 0.076558 b_country_DK 1.000000 0.042753 0.005438 7.0766e-04 0.034435 b_country_IND 0.042753 1.000000 0.442172 0.466126 -0.056042 b_country_RUS 0.005438 0.442172 1.000000 0.424198 -0.063202 b_country_BRA 7.0766e-04 0.466126 0.424198 1.000000 -0.068180 b_char_fast 0.034435 -0.056042 -0.063202 -0.068180 1.000000 b_char_double 0.020818 -0.026354 -0.033867 -0.050810 0.455752 b_risk -0.027752 0.052162 0.060871 0.031804 -0.082503 b_price -0.047621 0.024129 0.045000 0.067007 -0.141131 lambda 0.012642 0.001950 -0.044457 -0.025848 0.066689 gamma_reg_user -2.9485e-04 0.001673 -0.002563 -0.001462 -3.1310e-04 gamma_university -0.002761 0.004161 -6.2923e-04 8.9801e-04 4.961e-05 gamma_age_50 0.001193 -0.005387 0.004911 0.002078 -1.8693e-04 zeta_quality -0.002834 0.005775 0.001891 0.005116 -0.002500 zeta_ingredient -3.3979e-04 8.7088e-04 -7.8861e-04 0.001574 0.007896 zeta_patent -0.003554 0.006709 -0.001650 -0.002569 -0.007594 zeta_dominance 0.001765 -0.001737 -0.001411 -0.003555 -5.8008e-04 sigma_qual 0.002252 -0.004312 -0.002760 -0.005129 0.002239 sigma_ingr -6.2841e-04 0.001665 -0.001497 0.001061 0.006630 sigma_pate 0.003152 -0.005548 5.1209e-04 0.002231 0.007640 sigma_domi 0.001012 -5.7311e-04 -0.001596 -0.002729 -4.7622e-04 b_char_double b_risk b_price lambda gamma_reg_user b_brand_Novum 0.065517 0.001489 0.066278 -0.012391 0.002124 b_brand_BestValue 0.163527 -0.182916 0.286989 -0.082913 0.079591 b_brand_Supermarket 0.189681 -0.192935 0.258947 -0.071203 0.082214 b_brand_PainAway 0.119944 -0.055012 0.332748 -0.108711 0.075350 b_country_CH 0.088355 -0.064793 -0.121415 0.038871 6.3113e-04 b_country_DK 0.020818 -0.027752 -0.047621 0.012642 -2.9485e-04 b_country_IND -0.026354 0.052162 0.024129 0.001950 0.001673 b_country_RUS -0.033867 0.060871 0.045000 -0.044457 -0.002563 b_country_BRA -0.050810 0.031804 0.067007 -0.025848 -0.001462 b_char_fast 0.455752 -0.082503 -0.141131 0.066689 -3.1310e-04 b_char_double 1.000000 -0.050978 -0.173133 0.068833 0.001848 b_risk -0.050978 1.000000 0.118639 -0.054514 3.0908e-04 b_price -0.173133 0.118639 1.000000 -0.067720 -0.006392 lambda 0.068833 -0.054514 -0.067720 1.000000 0.243362 gamma_reg_user 0.001848 3.0908e-04 -0.006392 0.243362 1.000000 gamma_university -3.7975e-04 0.002247 -0.003055 0.113727 -0.128952 gamma_age_50 -0.003840 -0.001456 0.008999 -0.230676 -0.284919 zeta_quality -0.001772 0.008096 -0.003573 0.168906 0.203886 zeta_ingredient 0.004654 -0.004940 -0.001522 -0.141122 -0.175232 zeta_patent -0.003585 0.006012 -0.003042 0.173486 0.200840 zeta_dominance 0.002283 -0.001940 0.001568 -0.130163 -0.116870 sigma_qual 0.002386 -0.007158 9.8314e-04 0.015198 -0.048247 sigma_ingr 0.004567 -0.003841 -0.003277 0.025236 -0.029445 sigma_pate 0.004528 -0.005633 2.9329e-04 0.029186 -0.035265 sigma_domi 0.002059 -0.001120 -3.0633e-04 0.011638 0.002691 gamma_university gamma_age_50 zeta_quality zeta_ingredient zeta_patent b_brand_Novum -0.002720 2.6892e-04 -9.3909e-04 -0.002692 0.001825 b_brand_BestValue 0.084879 0.072662 0.037174 -0.038212 0.037400 b_brand_Supermarket 0.084320 0.068605 0.033798 -0.037519 0.041734 b_brand_PainAway 0.086080 0.072360 0.036183 -0.040078 0.037166 b_country_CH 5.7878e-04 -0.002705 9.3601e-04 0.001934 -7.7970e-04 b_country_DK -0.002761 0.001193 -0.002834 -3.3979e-04 -0.003554 b_country_IND 0.004161 -0.005387 0.005775 8.7088e-04 0.006709 b_country_RUS -6.2923e-04 0.004911 0.001891 -7.8861e-04 -0.001650 b_country_BRA 8.9801e-04 0.002078 0.005116 0.001574 -0.002569 b_char_fast 4.961e-05 -1.8693e-04 -0.002500 0.007896 -0.007594 b_char_double -3.7975e-04 -0.003840 -0.001772 0.004654 -0.003585 b_risk 0.002247 -0.001456 0.008096 -0.004940 0.006012 b_price -0.003055 0.008999 -0.003573 -0.001522 -0.003042 lambda 0.113727 -0.230676 0.168906 -0.141122 0.173486 gamma_reg_user -0.128952 -0.284919 0.203886 -0.175232 0.200840 gamma_university 1.000000 -0.303323 0.113110 -0.114634 0.115453 gamma_age_50 -0.303323 1.000000 -0.155760 0.153108 -0.166456 zeta_quality 0.113110 -0.155760 1.000000 -0.140791 0.125723 zeta_ingredient -0.114634 0.153108 -0.140791 1.000000 -0.136730 zeta_patent 0.115453 -0.166456 0.125723 -0.136730 1.000000 zeta_dominance -0.121876 0.103669 -0.092625 0.104202 -0.087009 sigma_qual -0.022528 0.021937 -0.286018 0.015013 0.016156 sigma_ingr -0.027609 0.026372 -0.012822 0.254610 -0.004123 sigma_pate -0.018643 0.022498 0.023522 5.6414e-04 -0.311609 sigma_domi -0.036539 -7.8327e-04 0.010842 0.003867 0.018597 zeta_dominance sigma_qual sigma_ingr sigma_pate sigma_domi b_brand_Novum 5.5766e-04 0.001084 -0.002120 -0.001624 5.1888e-04 b_brand_BestValue -0.027110 -0.017958 -0.018368 -0.018134 -0.009139 b_brand_Supermarket -0.029514 -0.013994 -0.017108 -0.021614 -0.010368 b_brand_PainAway -0.027463 -0.017761 -0.020568 -0.018766 -0.009829 b_country_CH 4.1806e-04 -3.5099e-04 0.002086 0.001424 6.1366e-04 b_country_DK 0.001765 0.002252 -6.2841e-04 0.003152 0.001012 b_country_IND -0.001737 -0.004312 0.001665 -0.005548 -5.7311e-04 b_country_RUS -0.001411 -0.002760 -0.001497 5.1209e-04 -0.001596 b_country_BRA -0.003555 -0.005129 0.001061 0.002231 -0.002729 b_char_fast -5.8008e-04 0.002239 0.006630 0.007640 -4.7622e-04 b_char_double 0.002283 0.002386 0.004567 0.004528 0.002059 b_risk -0.001940 -0.007158 -0.003841 -0.005633 -0.001120 b_price 0.001568 9.8314e-04 -0.003277 2.9329e-04 -3.0633e-04 lambda -0.130163 0.015198 0.025236 0.029186 0.011638 gamma_reg_user -0.116870 -0.048247 -0.029445 -0.035265 0.002691 gamma_university -0.121876 -0.022528 -0.027609 -0.018643 -0.036539 gamma_age_50 0.103669 0.021937 0.026372 0.022498 -7.8327e-04 zeta_quality -0.092625 -0.286018 -0.012822 0.023522 0.010842 zeta_ingredient 0.104202 0.015013 0.254610 5.6414e-04 0.003867 zeta_patent -0.087009 0.016156 -0.004123 -0.311609 0.018597 zeta_dominance 1.000000 -0.009648 0.007877 -0.025880 0.209522 sigma_qual -0.009648 1.000000 0.002000 -0.031841 -0.014592 sigma_ingr 0.007877 0.002000 1.000000 -0.007713 -4.1547e-04 sigma_pate -0.025880 -0.031841 -0.007713 1.000000 -0.024288 sigma_domi 0.209522 -0.014592 -4.1547e-04 -0.024288 1.000000 Robust correlation matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_PainAway b_country_CH b_brand_Novum 1.00000 0.205847 0.24096 0.19015 -0.101618 b_brand_BestValue 0.20585 1.000000 0.68541 0.64376 0.222642 b_brand_Supermarket 0.24096 0.685413 1.00000 0.66620 0.242257 b_brand_PainAway 0.19015 0.643757 0.66620 1.00000 0.188208 b_country_CH -0.10162 0.222642 0.24226 0.18821 1.000000 b_country_DK -0.03841 0.195949 0.24498 0.20318 0.470100 b_country_IND -0.03164 -0.441234 -0.43637 -0.37614 -0.023718 b_country_RUS -0.02678 -0.430051 -0.40278 -0.36167 -0.062118 b_country_BRA 0.01890 -0.397711 -0.46961 -0.36315 -0.045483 b_char_fast -0.05425 -0.013485 0.06162 -0.04060 0.103819 b_char_double -0.01290 0.157105 0.17816 0.09228 0.080031 b_risk 0.07116 -0.118739 -0.13963 -0.04847 -0.005885 b_price 0.07704 0.275947 0.24138 0.31260 -0.122334 lambda -0.04854 -0.094524 -0.06192 -0.09472 0.085055 gamma_reg_user 6.5183e-04 0.069892 0.08149 0.08698 0.014232 gamma_university -0.02366 0.059286 0.02836 0.05136 -0.045209 gamma_age_50 -0.03053 0.111291 0.10971 0.12380 -0.008466 zeta_quality -6.0246e-04 0.039633 0.02894 0.04962 -0.002130 zeta_ingredient -0.01458 -0.033379 -4.3312e-04 0.01176 0.023312 zeta_patent 0.04340 0.060890 0.06869 0.07025 -0.035485 zeta_dominance -0.02926 -0.031646 -0.02996 -0.02821 -0.026009 sigma_qual -0.01430 -0.035070 -0.01114 -0.04108 0.023203 sigma_ingr -0.02471 0.006284 0.04730 0.04593 0.042871 sigma_pate 0.01202 -0.025413 -0.03971 -0.04076 -0.022339 sigma_domi -0.03262 -0.043224 -0.08059 -0.02308 -0.023334 b_country_DK b_country_IND b_country_RUS b_country_BRA b_char_fast b_brand_Novum -0.038414 -0.031638 -0.026778 0.018898 -0.054248 b_brand_BestValue 0.195949 -0.441234 -0.430051 -0.397711 -0.013485 b_brand_Supermarket 0.244976 -0.436366 -0.402776 -0.469607 0.061622 b_brand_PainAway 0.203182 -0.376137 -0.361672 -0.363147 -0.040596 b_country_CH 0.470100 -0.023718 -0.062118 -0.045483 0.103819 b_country_DK 1.000000 0.024926 -0.006506 0.002229 0.006805 b_country_IND 0.024926 1.000000 0.409904 0.514494 -0.086233 b_country_RUS -0.006506 0.409904 1.000000 0.495659 -0.084994 b_country_BRA 0.002229 0.514494 0.495659 1.000000 -0.104479 b_char_fast 0.006805 -0.086233 -0.084994 -0.104479 1.000000 b_char_double -0.015615 -0.037484 -0.047177 -0.060743 0.436329 b_risk 0.047414 0.070525 0.072066 0.032221 -0.091492 b_price -0.060525 0.055396 0.027999 0.054453 -0.149495 lambda 0.034206 0.028066 -0.092869 -0.030923 0.086729 gamma_reg_user 0.022820 0.030322 -0.002455 0.029826 0.014008 gamma_university -0.015241 0.026371 0.011344 0.034918 -0.090617 gamma_age_50 -0.013162 -0.036979 -0.004822 -0.040192 0.074228 zeta_quality -0.022343 0.045236 -0.011976 0.014127 0.011345 zeta_ingredient -0.006789 -0.024643 -0.026552 -0.011622 0.024982 zeta_patent -0.016481 0.013327 0.015616 0.017136 -0.026333 zeta_dominance -0.017432 -0.004190 -0.008115 0.002272 0.009979 sigma_qual 0.010152 -0.008972 0.009823 0.001655 0.005010 sigma_ingr -0.021704 -4.1641e-04 -0.019350 -0.035458 0.038891 sigma_pate 7.3385e-04 0.061941 0.012351 0.009228 0.030864 sigma_domi -0.004577 0.037247 0.012957 0.025711 -0.013156 b_char_double b_risk b_price lambda gamma_reg_user b_brand_Novum -0.012902 0.071164 0.077043 -0.048538 6.5183e-04 b_brand_BestValue 0.157105 -0.118739 0.275947 -0.094524 0.069892 b_brand_Supermarket 0.178164 -0.139625 0.241383 -0.061923 0.081492 b_brand_PainAway 0.092283 -0.048470 0.312604 -0.094720 0.086982 b_country_CH 0.080031 -0.005885 -0.122334 0.085055 0.014232 b_country_DK -0.015615 0.047414 -0.060525 0.034206 0.022820 b_country_IND -0.037484 0.070525 0.055396 0.028066 0.030322 b_country_RUS -0.047177 0.072066 0.027999 -0.092869 -0.002455 b_country_BRA -0.060743 0.032221 0.054453 -0.030923 0.029826 b_char_fast 0.436329 -0.091492 -0.149495 0.086729 0.014008 b_char_double 1.000000 -0.009729 -0.184482 0.056489 0.014207 b_risk -0.009729 1.000000 0.122126 -0.056753 0.044095 b_price -0.184482 0.122126 1.000000 -0.073423 -0.008654 lambda 0.056489 -0.056753 -0.073423 1.000000 0.225873 gamma_reg_user 0.014207 0.044095 -0.008654 0.225873 1.000000 gamma_university -7.061e-05 0.042743 -0.037753 0.080563 -0.139008 gamma_age_50 0.028992 -0.077115 0.013450 -0.177528 -0.217872 zeta_quality -0.004620 0.054860 0.014022 0.128845 0.280992 zeta_ingredient 0.051851 0.017839 0.020602 -0.135097 -0.174307 zeta_patent 0.029385 -0.017823 0.042128 0.147292 0.224740 zeta_dominance -0.009255 -0.002938 0.072944 -0.116886 -0.079499 sigma_qual 0.048069 -0.034913 0.015019 0.033784 -0.071871 sigma_ingr 0.043637 0.022778 0.006666 0.019393 0.029589 sigma_pate 0.025909 0.010554 -0.001016 0.023104 0.034141 sigma_domi 0.005136 -0.019747 0.007302 -0.002401 0.044082 gamma_university gamma_age_50 zeta_quality zeta_ingredient zeta_patent b_brand_Novum -0.023665 -0.030528 -6.0246e-04 -0.014577 0.043401 b_brand_BestValue 0.059286 0.111291 0.039633 -0.033379 0.060890 b_brand_Supermarket 0.028356 0.109705 0.028940 -4.3312e-04 0.068686 b_brand_PainAway 0.051356 0.123802 0.049618 0.011765 0.070251 b_country_CH -0.045209 -0.008466 -0.002130 0.023312 -0.035485 b_country_DK -0.015241 -0.013162 -0.022343 -0.006789 -0.016481 b_country_IND 0.026371 -0.036979 0.045236 -0.024643 0.013327 b_country_RUS 0.011344 -0.004822 -0.011976 -0.026552 0.015616 b_country_BRA 0.034918 -0.040192 0.014127 -0.011622 0.017136 b_char_fast -0.090617 0.074228 0.011345 0.024982 -0.026333 b_char_double -7.061e-05 0.028992 -0.004620 0.051851 0.029385 b_risk 0.042743 -0.077115 0.054860 0.017839 -0.017823 b_price -0.037753 0.013450 0.014022 0.020602 0.042128 lambda 0.080563 -0.177528 0.128845 -0.135097 0.147292 gamma_reg_user -0.139008 -0.217872 0.280992 -0.174307 0.224740 gamma_university 1.000000 -0.303230 0.134923 -0.178488 0.139289 gamma_age_50 -0.303230 1.000000 -0.172431 0.181782 -0.180273 zeta_quality 0.134923 -0.172431 1.000000 -0.234820 0.150051 zeta_ingredient -0.178488 0.181782 -0.234820 1.000000 -0.190075 zeta_patent 0.139289 -0.180273 0.150051 -0.190075 1.000000 zeta_dominance -0.238771 0.112056 -0.087739 0.164078 -0.088620 sigma_qual 0.005098 0.034205 -0.519699 0.065428 -0.006255 sigma_ingr -0.059919 0.061783 -0.057750 0.510542 -0.003304 sigma_pate -0.009582 0.024613 0.021369 0.001153 -0.527909 sigma_domi -0.070340 -8.214e-05 0.026587 0.057210 -0.022294 zeta_dominance sigma_qual sigma_ingr sigma_pate sigma_domi b_brand_Novum -0.029258 -0.014301 -0.024711 0.012016 -0.032618 b_brand_BestValue -0.031646 -0.035070 0.006284 -0.025413 -0.043224 b_brand_Supermarket -0.029964 -0.011137 0.047302 -0.039705 -0.080589 b_brand_PainAway -0.028209 -0.041079 0.045928 -0.040757 -0.023083 b_country_CH -0.026009 0.023203 0.042871 -0.022339 -0.023334 b_country_DK -0.017432 0.010152 -0.021704 7.3385e-04 -0.004577 b_country_IND -0.004190 -0.008972 -4.1641e-04 0.061941 0.037247 b_country_RUS -0.008115 0.009823 -0.019350 0.012351 0.012957 b_country_BRA 0.002272 0.001655 -0.035458 0.009228 0.025711 b_char_fast 0.009979 0.005010 0.038891 0.030864 -0.013156 b_char_double -0.009255 0.048069 0.043637 0.025909 0.005136 b_risk -0.002938 -0.034913 0.022778 0.010554 -0.019747 b_price 0.072944 0.015019 0.006666 -0.001016 0.007302 lambda -0.116886 0.033784 0.019393 0.023104 -0.002401 gamma_reg_user -0.079499 -0.071871 0.029589 0.034141 0.044082 gamma_university -0.238771 0.005098 -0.059919 -0.009582 -0.070340 gamma_age_50 0.112056 0.034205 0.061783 0.024613 -8.214e-05 zeta_quality -0.087739 -0.519699 -0.057750 0.021369 0.026587 zeta_ingredient 0.164078 0.065428 0.510542 0.001153 0.057210 zeta_patent -0.088620 -0.006255 -0.003304 -0.527909 -0.022294 zeta_dominance 1.000000 -5.8696e-04 0.074374 0.018615 0.290337 sigma_qual -5.8696e-04 1.000000 0.008137 -0.022498 -0.002908 sigma_ingr 0.074374 0.008137 1.000000 -0.041423 -0.022304 sigma_pate 0.018615 -0.022498 -0.041423 1.000000 0.041634 sigma_domi 0.290337 -0.002908 -0.022304 0.041634 1.000000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 695 0.07321660 480 0.07708895 288 0.08368613 509 0.08492651 593 0.09011578 875 0.09015651 456 0.09198315 163 0.09329469 828 0.09702089 126 0.09764450 8 0.09819353 858 0.09865033 817 0.09892745 611 0.09967049 326 0.10026760 127 0.10064458 594 0.10073910 536 0.10273746 508 0.10291950 92 0.10374541 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 -0.580336 -0.580336 b_brand_Supermarket 0.000 -0.266708 -0.266708 b_brand_PainAway 0.000 -1.248761 -1.248761 b_country_CH 0.000 0.670162 0.670162 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 -0.655528 -0.655528 b_char_standard 0.000 0.000000 0.000000 b_char_fast 0.000 0.769948 0.769948 b_char_double 0.000 1.212447 1.212447 b_risk 0.000 -0.001575 -0.001575 b_price 0.000 -0.724323 -0.724323 lambda 0.000 0.659833 0.659833 gamma_reg_user 0.000 -0.741193 -0.741193 gamma_university 0.000 -0.378840 -0.378840 gamma_age_50 0.000 0.673648 0.673648 zeta_quality 1.000 0.534805 -0.465195 zeta_ingredient 1.000 -0.503372 -1.503372 zeta_patent 1.000 0.606951 -0.393049 zeta_dominance 1.000 -0.394530 -1.394530 sigma_qual 1.000 1.061380 0.061380 sigma_ingr 1.000 1.108661 0.108661 sigma_pate 1.000 1.084333 0.084333 sigma_domi 1.000 1.045440 0.045440 Settings and functions used in model definition: apollo_control -------------- Value modelName "Hybrid_with_continuous_measurement" modelDescr "Hybrid choice model on drug choice data, using continuous measurement model for indicators" indivID "ID" nCores "4" outputDirectory "output/" mixing "TRUE" debug "FALSE" workInLogs "FALSE" seed "13" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling in estimation --------------------- 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 Scaling used in computing Hessian --------------------------------- Value b_brand_Novum 0.276727529 b_brand_BestValue 0.580336446 b_brand_Supermarket 0.266707867 b_brand_PainAway 1.248760923 b_country_CH 0.670161905 b_country_DK 0.337698469 b_country_IND 0.296317665 b_country_RUS 0.893693546 b_country_BRA 0.655528274 b_char_fast 0.769948316 b_char_double 1.212446517 b_risk 0.001574518 b_price 0.724323076 lambda 0.659833327 gamma_reg_user 0.741192803 gamma_university 0.378840336 gamma_age_50 0.673647864 zeta_quality 0.534804528 zeta_ingredient 0.503372042 zeta_patent 0.606951207 zeta_dominance 0.394529914 sigma_qual 1.061379585 sigma_ingr 1.108660920 sigma_pate 1.084333352 sigma_domi 1.045440249 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, utilities = 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) }