Model run by stephane.hess using Apollo 0.3.6 on R 4.5.1 for Darwin. Please acknowledge the use of Apollo by citing Hess & Palma (2019) DOI 10.1016/j.jocm.2019.100170 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 : 2025-09-19 14:21:40.023033 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -71.381929 reciprocal of condition number : 2.04557e-07 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) : 00:01:58.99 pre-estimation : 00:00:7.19 estimation : 00:00:7.96 post-estimation : 00:01:43.83 Iterations : 12 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 -0.276720 0.03082 -8.979 0.03193 -8.666 b_brand_BestValue -0.580338 0.06615 -8.774 0.06430 -9.026 b_brand_Supermarket -0.266659 0.06726 -3.964 0.06621 -4.028 b_brand_PainAway -1.248705 0.06750 -18.498 0.06547 -19.072 b_country_CH 0.670170 0.03985 16.816 0.03879 17.278 b_country_DK 0.337703 0.03824 8.831 0.03755 8.994 b_country_USA 0.000000 NA NA NA NA b_country_IND -0.296331 0.05734 -5.168 0.05811 -5.100 b_country_RUS -0.893699 0.06171 -14.483 0.06112 -14.623 b_country_BRA -0.655568 0.06022 -10.887 0.06174 -10.618 b_char_standard 0.000000 NA NA NA NA b_char_fast 0.769958 0.02921 26.356 0.02888 26.660 b_char_double 1.212457 0.03777 32.102 0.03660 33.126 b_risk -0.001575 5.834e-05 -26.990 5.941e-05 -26.503 b_price -0.724325 0.01812 -39.966 0.01728 -41.908 lambda 0.659812 0.03260 20.238 0.03186 20.707 gamma_reg_user -0.741301 0.07947 -9.328 0.07969 -9.302 gamma_university -0.378846 0.07376 -5.137 0.07414 -5.110 gamma_age_50 0.673773 0.07593 8.873 0.07447 9.048 zeta_quality 0.534760 0.03940 13.572 0.03888 13.753 zeta_ingredient -0.503353 0.04020 -12.522 0.03964 -12.698 zeta_patent 0.606970 0.04097 14.815 0.03850 15.766 zeta_dominance -0.394495 0.03672 -10.743 0.03519 -11.212 sigma_qual 1.061358 0.02750 38.592 0.02701 39.294 sigma_ingr 1.108649 0.02786 39.793 0.02631 42.146 sigma_pate 1.084359 0.02913 37.230 0.02744 39.516 sigma_domi 1.045446 0.02530 41.318 0.02309 45.283 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_Novum 9.4984e-04 4.7298e-04 5.8289e-04 b_brand_BestValue 4.7298e-04 0.004375 0.003213 b_brand_Supermarket 5.8289e-04 0.003213 0.004524 b_brand_PainAway 5.0844e-04 0.002956 0.003024 b_country_CH -6.662e-05 7.5559e-04 7.4269e-04 b_country_DK -5.571e-05 6.7075e-04 7.0616e-04 b_country_IND -5.871e-05 -0.001544 -0.001619 b_country_RUS -7.186e-05 -0.001565 -0.001638 b_country_BRA -1.230e-05 -0.001428 -0.001713 b_char_fast 1.038e-05 -8.326e-06 9.027e-05 b_char_double 7.626e-05 4.0853e-04 4.8187e-04 b_risk 2.676e-09 -7.058e-07 -7.571e-07 b_price 3.702e-05 3.4404e-04 3.1566e-04 lambda -1.245e-05 -1.7879e-04 -1.5612e-04 gamma_reg_user 5.202e-06 4.1839e-04 4.3947e-04 gamma_university -6.183e-06 4.1410e-04 4.1831e-04 gamma_age_50 6.293e-07 3.6496e-04 3.5040e-04 zeta_quality -1.140e-06 9.687e-05 8.956e-05 zeta_ingredient -3.335e-06 -1.0160e-04 -1.0144e-04 zeta_patent 2.304e-06 1.0135e-04 1.1500e-04 zeta_dominance 6.312e-07 -6.584e-05 -7.289e-05 sigma_qual 9.188e-07 -3.267e-05 -2.588e-05 sigma_ingr -1.821e-06 -3.385e-05 -3.206e-05 sigma_pate -1.458e-06 -3.493e-05 -4.234e-05 sigma_domi 4.047e-07 -1.529e-05 -1.764e-05 b_brand_PainAway b_country_CH b_country_DK b_brand_Novum 5.0844e-04 -6.662e-05 -5.571e-05 b_brand_BestValue 0.002956 7.5559e-04 6.7075e-04 b_brand_Supermarket 0.003024 7.4269e-04 7.0616e-04 b_brand_PainAway 0.004557 5.9613e-04 5.8380e-04 b_country_CH 5.9613e-04 0.001588 7.5101e-04 b_country_DK 5.8380e-04 7.5101e-04 0.001462 b_country_IND -0.001414 1.669e-05 9.374e-05 b_country_RUS -0.001334 -7.883e-05 1.283e-05 b_country_BRA -0.001400 -7.943e-05 1.630e-06 b_char_fast -8.150e-05 8.913e-05 3.847e-05 b_char_double 3.0581e-04 1.3299e-04 3.007e-05 b_risk -2.166e-07 -1.506e-07 -6.191e-08 b_price 4.0708e-04 -8.769e-05 -3.300e-05 lambda -2.3923e-04 5.050e-05 1.576e-05 gamma_reg_user 4.0422e-04 2.001e-06 -8.958e-07 gamma_university 4.2858e-04 1.702e-06 -7.787e-06 gamma_age_50 3.7091e-04 -8.188e-06 3.464e-06 zeta_quality 9.623e-05 1.470e-06 -4.270e-06 zeta_ingredient -1.0874e-04 3.097e-06 -5.223e-07 zeta_patent 1.0278e-04 -1.272e-06 -5.567e-06 zeta_dominance -6.807e-05 6.111e-07 2.479e-06 sigma_qual -3.297e-05 -3.849e-07 2.368e-06 sigma_ingr -3.868e-05 2.316e-06 -6.695e-07 sigma_pate -3.689e-05 1.653e-06 3.510e-06 sigma_domi -1.678e-05 6.186e-07 9.794e-07 b_country_IND b_country_RUS b_country_BRA b_brand_Novum -5.871e-05 -7.186e-05 -1.230e-05 b_brand_BestValue -0.001544 -0.001565 -0.001428 b_brand_Supermarket -0.001619 -0.001638 -0.001713 b_brand_PainAway -0.001414 -0.001334 -0.001400 b_country_CH 1.669e-05 -7.883e-05 -7.943e-05 b_country_DK 9.374e-05 1.283e-05 1.630e-06 b_country_IND 0.003288 0.001564 0.001609 b_country_RUS 0.001564 0.003808 0.001576 b_country_BRA 0.001609 0.001576 0.003626 b_char_fast -9.388e-05 -1.1394e-04 -1.1995e-04 b_char_double -5.708e-05 -7.893e-05 -1.1556e-04 b_risk 1.745e-07 2.191e-07 1.117e-07 b_price 2.507e-05 5.033e-05 7.313e-05 lambda 3.644e-06 -8.944e-05 -5.075e-05 gamma_reg_user 7.625e-06 -1.257e-05 -7.001e-06 gamma_university 1.760e-05 -2.866e-06 3.987e-06 gamma_age_50 -2.346e-05 2.302e-05 9.505e-06 zeta_quality 1.305e-05 4.596e-06 1.214e-05 zeta_ingredient 2.006e-06 -1.955e-06 3.812e-06 zeta_patent 1.576e-05 -4.173e-06 -6.336e-06 zeta_dominance -3.658e-06 -3.195e-06 -7.860e-06 sigma_qual -6.800e-06 -4.683e-06 -8.495e-06 sigma_ingr 2.659e-06 -2.574e-06 1.780e-06 sigma_pate -9.265e-06 9.205e-07 3.912e-06 sigma_domi -8.317e-07 -2.492e-06 -4.157e-06 b_char_fast b_char_double b_risk b_brand_Novum 1.038e-05 7.626e-05 2.676e-09 b_brand_BestValue -8.326e-06 4.0853e-04 -7.058e-07 b_brand_Supermarket 9.027e-05 4.8187e-04 -7.571e-07 b_brand_PainAway -8.150e-05 3.0581e-04 -2.166e-07 b_country_CH 8.913e-05 1.3299e-04 -1.506e-07 b_country_DK 3.847e-05 3.007e-05 -6.191e-08 b_country_IND -9.388e-05 -5.708e-05 1.745e-07 b_country_RUS -1.1394e-04 -7.893e-05 2.191e-07 b_country_BRA -1.1995e-04 -1.1556e-04 1.117e-07 b_char_fast 8.5342e-04 5.0286e-04 -1.406e-07 b_char_double 5.0286e-04 0.001426 -1.123e-07 b_risk -1.406e-07 -1.123e-07 3.403e-09 b_price -7.472e-05 -1.1851e-04 1.254e-07 lambda 6.352e-05 8.476e-05 -1.037e-07 gamma_reg_user -7.246e-07 5.550e-06 1.430e-09 gamma_university 1.075e-07 -1.057e-06 9.669e-09 gamma_age_50 -4.160e-07 -1.102e-05 -6.449e-09 zeta_quality -2.877e-06 -2.637e-06 1.861e-08 zeta_ingredient 9.272e-06 7.065e-06 -1.158e-08 zeta_patent -9.088e-06 -5.545e-06 1.437e-08 zeta_dominance -6.229e-07 3.165e-06 -4.156e-09 sigma_qual 1.798e-06 2.479e-06 -1.148e-08 sigma_ingr 5.396e-06 4.805e-06 -6.242e-09 sigma_pate 6.500e-06 4.981e-06 -9.571e-09 sigma_domi -3.522e-07 1.967e-06 -1.653e-09 b_price lambda gamma_reg_user b_brand_Novum 3.702e-05 -1.245e-05 5.202e-06 b_brand_BestValue 3.4404e-04 -1.7879e-04 4.1839e-04 b_brand_Supermarket 3.1566e-04 -1.5612e-04 4.3947e-04 b_brand_PainAway 4.0708e-04 -2.3923e-04 4.0422e-04 b_country_CH -8.769e-05 5.050e-05 2.001e-06 b_country_DK -3.300e-05 1.576e-05 -8.958e-07 b_country_IND 2.507e-05 3.644e-06 7.625e-06 b_country_RUS 5.033e-05 -8.944e-05 -1.257e-05 b_country_BRA 7.313e-05 -5.075e-05 -7.001e-06 b_char_fast -7.472e-05 6.352e-05 -7.246e-07 b_char_double -1.1851e-04 8.476e-05 5.550e-06 b_risk 1.254e-07 -1.037e-07 1.430e-09 b_price 3.2846e-04 -4.001e-05 -9.209e-06 lambda -4.001e-05 0.001063 6.3063e-04 gamma_reg_user -9.209e-06 6.3063e-04 0.006316 gamma_university -4.085e-06 2.7349e-04 -7.5576e-04 gamma_age_50 1.239e-05 -5.7116e-04 -0.001720 zeta_quality -2.552e-06 2.1696e-04 6.3845e-04 zeta_ingredient -1.108e-06 -1.8496e-04 -5.5985e-04 zeta_patent -2.260e-06 2.3179e-04 6.5407e-04 zeta_dominance 1.044e-06 -1.5583e-04 -3.4106e-04 sigma_qual 4.903e-07 1.362e-05 -1.0546e-04 sigma_ingr -1.654e-06 2.292e-05 -6.521e-05 sigma_pate 1.551e-07 2.770e-05 -8.166e-05 sigma_domi -1.403e-07 9.599e-06 5.411e-06 gamma_university gamma_age_50 zeta_quality b_brand_Novum -6.183e-06 6.293e-07 -1.140e-06 b_brand_BestValue 4.1410e-04 3.6496e-04 9.687e-05 b_brand_Supermarket 4.1831e-04 3.5040e-04 8.956e-05 b_brand_PainAway 4.2858e-04 3.7091e-04 9.623e-05 b_country_CH 1.702e-06 -8.188e-06 1.470e-06 b_country_DK -7.787e-06 3.464e-06 -4.270e-06 b_country_IND 1.760e-05 -2.346e-05 1.305e-05 b_country_RUS -2.866e-06 2.302e-05 4.596e-06 b_country_BRA 3.987e-06 9.505e-06 1.214e-05 b_char_fast 1.075e-07 -4.160e-07 -2.877e-06 b_char_double -1.057e-06 -1.102e-05 -2.637e-06 b_risk 9.669e-09 -6.449e-09 1.861e-08 b_price -4.085e-06 1.239e-05 -2.552e-06 lambda 2.7349e-04 -5.7116e-04 2.1696e-04 gamma_reg_user -7.5576e-04 -0.001720 6.3845e-04 gamma_university 0.005440 -0.001699 3.2869e-04 gamma_age_50 -0.001699 0.005766 -4.6607e-04 zeta_quality 3.2869e-04 -4.6607e-04 0.001552 zeta_ingredient -3.3987e-04 4.6743e-04 -2.2298e-04 zeta_patent 3.4892e-04 -5.1801e-04 2.0298e-04 zeta_dominance -3.3008e-04 2.8909e-04 -1.3399e-04 sigma_qual -4.569e-05 4.583e-05 -3.0998e-04 sigma_ingr -5.674e-05 5.581e-05 -1.408e-05 sigma_pate -4.006e-05 4.980e-05 2.698e-05 sigma_domi -6.818e-05 -1.502e-06 1.081e-05 zeta_ingredient zeta_patent zeta_dominance b_brand_Novum -3.335e-06 2.304e-06 6.312e-07 b_brand_BestValue -1.0160e-04 1.0135e-04 -6.584e-05 b_brand_Supermarket -1.0144e-04 1.1500e-04 -7.289e-05 b_brand_PainAway -1.0874e-04 1.0278e-04 -6.807e-05 b_country_CH 3.097e-06 -1.272e-06 6.111e-07 b_country_DK -5.223e-07 -5.567e-06 2.479e-06 b_country_IND 2.006e-06 1.576e-05 -3.658e-06 b_country_RUS -1.955e-06 -4.173e-06 -3.195e-06 b_country_BRA 3.812e-06 -6.336e-06 -7.860e-06 b_char_fast 9.272e-06 -9.088e-06 -6.229e-07 b_char_double 7.065e-06 -5.545e-06 3.165e-06 b_risk -1.158e-08 1.437e-08 -4.156e-09 b_price -1.108e-06 -2.260e-06 1.044e-06 lambda -1.8496e-04 2.3179e-04 -1.5583e-04 gamma_reg_user -5.5985e-04 6.5407e-04 -3.4106e-04 gamma_university -3.3987e-04 3.4892e-04 -3.3008e-04 gamma_age_50 4.6743e-04 -5.1801e-04 2.8909e-04 zeta_quality -2.2298e-04 2.0298e-04 -1.3399e-04 zeta_ingredient 0.001616 -2.2522e-04 1.5381e-04 zeta_patent -2.2522e-04 0.001679 -1.3092e-04 zeta_dominance 1.5381e-04 -1.3092e-04 0.001348 sigma_qual 1.660e-05 1.820e-05 -9.742e-06 sigma_ingr 2.8516e-04 -4.713e-06 8.062e-06 sigma_pate 6.707e-07 -3.7178e-04 -2.767e-05 sigma_domi 3.933e-06 1.927e-05 1.9469e-04 sigma_qual sigma_ingr sigma_pate b_brand_Novum 9.188e-07 -1.821e-06 -1.458e-06 b_brand_BestValue -3.267e-05 -3.385e-05 -3.493e-05 b_brand_Supermarket -2.588e-05 -3.206e-05 -4.234e-05 b_brand_PainAway -3.297e-05 -3.868e-05 -3.689e-05 b_country_CH -3.849e-07 2.316e-06 1.653e-06 b_country_DK 2.368e-06 -6.695e-07 3.510e-06 b_country_IND -6.800e-06 2.659e-06 -9.265e-06 b_country_RUS -4.683e-06 -2.574e-06 9.205e-07 b_country_BRA -8.495e-06 1.780e-06 3.912e-06 b_char_fast 1.798e-06 5.396e-06 6.500e-06 b_char_double 2.479e-06 4.805e-06 4.981e-06 b_risk -1.148e-08 -6.242e-09 -9.571e-09 b_price 4.903e-07 -1.654e-06 1.551e-07 lambda 1.362e-05 2.292e-05 2.770e-05 gamma_reg_user -1.0546e-04 -6.521e-05 -8.166e-05 gamma_university -4.569e-05 -5.674e-05 -4.006e-05 gamma_age_50 4.583e-05 5.581e-05 4.980e-05 zeta_quality -3.0998e-04 -1.408e-05 2.698e-05 zeta_ingredient 1.660e-05 2.8516e-04 6.707e-07 zeta_patent 1.820e-05 -4.713e-06 -3.7178e-04 zeta_dominance -9.742e-06 8.062e-06 -2.767e-05 sigma_qual 7.5637e-04 1.533e-06 -2.550e-05 sigma_ingr 1.533e-06 7.7622e-04 -6.258e-06 sigma_pate -2.550e-05 -6.258e-06 8.4833e-04 sigma_domi -1.015e-05 -2.919e-07 -1.790e-05 sigma_domi b_brand_Novum 4.047e-07 b_brand_BestValue -1.529e-05 b_brand_Supermarket -1.764e-05 b_brand_PainAway -1.678e-05 b_country_CH 6.186e-07 b_country_DK 9.794e-07 b_country_IND -8.317e-07 b_country_RUS -2.492e-06 b_country_BRA -4.157e-06 b_char_fast -3.522e-07 b_char_double 1.967e-06 b_risk -1.653e-09 b_price -1.403e-07 lambda 9.599e-06 gamma_reg_user 5.411e-06 gamma_university -6.818e-05 gamma_age_50 -1.502e-06 zeta_quality 1.081e-05 zeta_ingredient 3.933e-06 zeta_patent 1.927e-05 zeta_dominance 1.9469e-04 sigma_qual -1.015e-05 sigma_ingr -2.919e-07 sigma_pate -1.790e-05 sigma_domi 6.4020e-04 Robust covariance matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_Novum 0.001020 4.2264e-04 5.0941e-04 b_brand_BestValue 4.2264e-04 0.004134 0.002918 b_brand_Supermarket 5.0941e-04 0.002918 0.004383 b_brand_PainAway 3.9755e-04 0.002710 0.002888 b_country_CH -1.2586e-04 5.5527e-04 6.2213e-04 b_country_DK -4.606e-05 4.7306e-04 6.0897e-04 b_country_IND -5.870e-05 -0.001649 -0.001679 b_country_RUS -5.226e-05 -0.001690 -0.001630 b_country_BRA 3.727e-05 -0.001579 -0.001920 b_char_fast -5.003e-05 -2.504e-05 1.1783e-04 b_char_double -1.508e-05 3.6973e-04 4.3174e-04 b_risk 1.350e-07 -4.536e-07 -5.492e-07 b_price 4.252e-05 3.0666e-04 2.7621e-04 lambda -4.938e-05 -1.9365e-04 -1.3061e-04 gamma_reg_user 1.662e-06 3.5810e-04 4.2994e-04 gamma_university -5.602e-05 2.8262e-04 1.3918e-04 gamma_age_50 -7.259e-05 5.3283e-04 5.4084e-04 zeta_quality -7.460e-07 9.907e-05 7.449e-05 zeta_ingredient -1.845e-05 -8.507e-05 -1.135e-06 zeta_patent 5.336e-05 1.5071e-04 1.7506e-04 zeta_dominance -3.288e-05 -7.158e-05 -6.979e-05 sigma_qual -1.233e-05 -6.090e-05 -1.991e-05 sigma_ingr -2.076e-05 1.063e-05 8.238e-05 sigma_pate 1.053e-05 -4.483e-05 -7.213e-05 sigma_domi -2.405e-05 -6.416e-05 -1.2318e-04 b_brand_PainAway b_country_CH b_country_DK b_brand_Novum 3.9755e-04 -1.2586e-04 -4.606e-05 b_brand_BestValue 0.002710 5.5527e-04 4.7306e-04 b_brand_Supermarket 0.002888 6.2213e-04 6.0897e-04 b_brand_PainAway 0.004287 4.7799e-04 4.9950e-04 b_country_CH 4.7799e-04 0.001505 6.8464e-04 b_country_DK 4.9950e-04 6.8464e-04 0.001410 b_country_IND -0.001431 -5.346e-05 5.439e-05 b_country_RUS -0.001447 -1.4726e-04 -1.493e-05 b_country_BRA -0.001468 -1.0893e-04 5.165e-06 b_char_fast -7.676e-05 1.1630e-04 7.380e-06 b_char_double 2.2116e-04 1.1362e-04 -2.146e-05 b_risk -1.885e-07 -1.356e-08 1.058e-07 b_price 3.5375e-04 -8.201e-05 -3.928e-05 lambda -1.9759e-04 1.0512e-04 4.093e-05 gamma_reg_user 4.5383e-04 4.400e-05 6.828e-05 gamma_university 2.4930e-04 -1.3003e-04 -4.244e-05 gamma_age_50 6.0359e-04 -2.445e-05 -3.680e-05 zeta_quality 1.2630e-04 -3.213e-06 -3.263e-05 zeta_ingredient 3.054e-05 3.584e-05 -1.011e-05 zeta_patent 1.7707e-04 -5.299e-05 -2.382e-05 zeta_dominance -6.497e-05 -3.550e-05 -2.303e-05 sigma_qual -7.264e-05 2.431e-05 1.030e-05 sigma_ingr 7.910e-05 4.374e-05 -2.144e-05 sigma_pate -7.322e-05 -2.378e-05 7.535e-07 sigma_domi -3.489e-05 -2.089e-05 -3.966e-06 b_country_IND b_country_RUS b_country_BRA b_brand_Novum -5.870e-05 -5.226e-05 3.727e-05 b_brand_BestValue -0.001649 -0.001690 -0.001579 b_brand_Supermarket -0.001679 -0.001630 -0.001920 b_brand_PainAway -0.001431 -0.001447 -0.001468 b_country_CH -5.346e-05 -1.4726e-04 -1.0893e-04 b_country_DK 5.439e-05 -1.493e-05 5.165e-06 b_country_IND 0.003377 0.001456 0.001846 b_country_RUS 0.001456 0.003735 0.001870 b_country_BRA 0.001846 0.001870 0.003812 b_char_fast -1.4473e-04 -1.5002e-04 -1.8631e-04 b_char_double -7.973e-05 -1.0553e-04 -1.3727e-04 b_risk 2.435e-07 2.617e-07 1.182e-07 b_price 5.564e-05 2.958e-05 5.811e-05 lambda 5.197e-05 -1.8085e-04 -6.084e-05 gamma_reg_user 1.4042e-04 -1.197e-05 1.4673e-04 gamma_university 1.1362e-04 5.139e-05 1.5985e-04 gamma_age_50 -1.6003e-04 -2.194e-05 -1.8478e-04 zeta_quality 1.0222e-04 -2.846e-05 3.391e-05 zeta_ingredient -5.676e-05 -6.432e-05 -2.844e-05 zeta_patent 2.983e-05 3.674e-05 4.074e-05 zeta_dominance -8.567e-06 -1.745e-05 4.936e-06 sigma_qual -1.409e-05 1.622e-05 2.758e-06 sigma_ingr -6.359e-07 -3.111e-05 -5.759e-05 sigma_pate 9.877e-05 2.072e-05 1.564e-05 sigma_domi 4.997e-05 1.828e-05 3.665e-05 b_char_fast b_char_double b_risk b_brand_Novum -5.003e-05 -1.508e-05 1.350e-07 b_brand_BestValue -2.504e-05 3.6973e-04 -4.536e-07 b_brand_Supermarket 1.1783e-04 4.3174e-04 -5.492e-07 b_brand_PainAway -7.676e-05 2.2116e-04 -1.885e-07 b_country_CH 1.1630e-04 1.1362e-04 -1.356e-08 b_country_DK 7.380e-06 -2.146e-05 1.058e-07 b_country_IND -1.4473e-04 -7.973e-05 2.435e-07 b_country_RUS -1.5002e-04 -1.0553e-04 2.617e-07 b_country_BRA -1.8631e-04 -1.3727e-04 1.182e-07 b_char_fast 8.3407e-04 4.6122e-04 -1.570e-07 b_char_double 4.6122e-04 0.001340 -2.116e-08 b_risk -1.570e-07 -2.116e-08 3.530e-09 b_price -7.462e-05 -1.1670e-04 1.254e-07 lambda 7.981e-05 6.588e-05 -1.074e-07 gamma_reg_user 3.224e-05 4.144e-05 2.088e-07 gamma_university -1.9404e-04 -1.892e-07 1.883e-07 gamma_age_50 1.5963e-04 7.901e-05 -3.412e-07 zeta_quality 1.274e-05 -6.576e-06 1.267e-07 zeta_ingredient 2.860e-05 7.522e-05 4.201e-08 zeta_patent -2.928e-05 4.141e-05 -4.075e-08 zeta_dominance 1.014e-05 -1.192e-05 -6.137e-09 sigma_qual 3.907e-06 4.752e-05 -5.602e-08 sigma_ingr 2.954e-05 4.201e-05 3.560e-08 sigma_pate 2.446e-05 2.602e-05 1.720e-08 sigma_domi -8.773e-06 4.340e-06 -2.708e-08 b_price lambda gamma_reg_user b_brand_Novum 4.252e-05 -4.938e-05 1.662e-06 b_brand_BestValue 3.0666e-04 -1.9365e-04 3.5810e-04 b_brand_Supermarket 2.7621e-04 -1.3061e-04 4.2994e-04 b_brand_PainAway 3.5375e-04 -1.9759e-04 4.5383e-04 b_country_CH -8.201e-05 1.0512e-04 4.400e-05 b_country_DK -3.928e-05 4.093e-05 6.828e-05 b_country_IND 5.564e-05 5.197e-05 1.4042e-04 b_country_RUS 2.958e-05 -1.8085e-04 -1.197e-05 b_country_BRA 5.811e-05 -6.084e-05 1.4673e-04 b_char_fast -7.462e-05 7.981e-05 3.224e-05 b_char_double -1.1670e-04 6.588e-05 4.144e-05 b_risk 1.254e-07 -1.074e-07 2.088e-07 b_price 2.9872e-04 -4.044e-05 -1.192e-05 lambda -4.044e-05 0.001015 5.7373e-04 gamma_reg_user -1.192e-05 5.7373e-04 0.006350 gamma_university -4.838e-05 1.9039e-04 -8.2123e-04 gamma_age_50 1.731e-05 -4.2142e-04 -0.001293 zeta_quality 9.423e-06 1.5967e-04 8.7071e-04 zeta_ingredient 1.411e-05 -1.7068e-04 -5.5072e-04 zeta_patent 2.803e-05 1.8079e-04 6.8980e-04 zeta_dominance 4.436e-05 -1.3107e-04 -2.2291e-04 sigma_qual 7.012e-06 2.907e-05 -1.5471e-04 sigma_ingr 3.030e-06 1.625e-05 6.200e-05 sigma_pate -4.810e-07 2.018e-05 7.458e-05 sigma_domi 2.913e-06 -1.769e-06 8.110e-05 gamma_university gamma_age_50 zeta_quality b_brand_Novum -5.602e-05 -7.259e-05 -7.460e-07 b_brand_BestValue 2.8262e-04 5.3283e-04 9.907e-05 b_brand_Supermarket 1.3918e-04 5.4084e-04 7.449e-05 b_brand_PainAway 2.4930e-04 6.0359e-04 1.2630e-04 b_country_CH -1.3003e-04 -2.445e-05 -3.213e-06 b_country_DK -4.244e-05 -3.680e-05 -3.263e-05 b_country_IND 1.1362e-04 -1.6003e-04 1.0222e-04 b_country_RUS 5.139e-05 -2.194e-05 -2.846e-05 b_country_BRA 1.5985e-04 -1.8478e-04 3.391e-05 b_char_fast -1.9404e-04 1.5963e-04 1.274e-05 b_char_double -1.892e-07 7.901e-05 -6.576e-06 b_risk 1.883e-07 -3.412e-07 1.267e-07 b_price -4.838e-05 1.731e-05 9.423e-06 lambda 1.9039e-04 -4.2142e-04 1.5967e-04 gamma_reg_user -8.2123e-04 -0.001293 8.7071e-04 gamma_university 0.005497 -0.001674 3.8893e-04 gamma_age_50 -0.001674 0.005545 -4.9936e-04 zeta_quality 3.8893e-04 -4.9936e-04 0.001512 zeta_ingredient -5.2459e-04 5.3673e-04 -3.6194e-04 zeta_patent 3.9770e-04 -5.1713e-04 2.2469e-04 zeta_dominance -6.2287e-04 2.9365e-04 -1.2003e-04 sigma_qual 1.022e-05 6.882e-05 -5.4587e-04 sigma_ingr -1.1687e-04 1.2105e-04 -5.907e-05 sigma_pate -1.952e-05 5.038e-05 2.278e-05 sigma_domi -1.2040e-04 -1.389e-07 2.387e-05 zeta_ingredient zeta_patent zeta_dominance b_brand_Novum -1.845e-05 5.336e-05 -3.288e-05 b_brand_BestValue -8.507e-05 1.5071e-04 -7.158e-05 b_brand_Supermarket -1.135e-06 1.7506e-04 -6.979e-05 b_brand_PainAway 3.054e-05 1.7707e-04 -6.497e-05 b_country_CH 3.584e-05 -5.299e-05 -3.550e-05 b_country_DK -1.011e-05 -2.382e-05 -2.303e-05 b_country_IND -5.676e-05 2.983e-05 -8.567e-06 b_country_RUS -6.432e-05 3.674e-05 -1.745e-05 b_country_BRA -2.844e-05 4.074e-05 4.936e-06 b_char_fast 2.860e-05 -2.928e-05 1.014e-05 b_char_double 7.522e-05 4.141e-05 -1.192e-05 b_risk 4.201e-08 -4.075e-08 -6.137e-09 b_price 1.411e-05 2.803e-05 4.436e-05 lambda -1.7068e-04 1.8079e-04 -1.3107e-04 gamma_reg_user -5.5072e-04 6.8980e-04 -2.2291e-04 gamma_university -5.2459e-04 3.9770e-04 -6.2287e-04 gamma_age_50 5.3673e-04 -5.1713e-04 2.9365e-04 zeta_quality -3.6194e-04 2.2469e-04 -1.2003e-04 zeta_ingredient 0.001571 -2.9013e-04 2.2886e-04 zeta_patent -2.9013e-04 0.001482 -1.2009e-04 zeta_dominance 2.2886e-04 -1.2009e-04 0.001238 sigma_qual 7.005e-05 -6.516e-06 -5.540e-07 sigma_ingr 5.3236e-04 -3.356e-06 6.884e-05 sigma_pate 1.267e-06 -5.5763e-04 1.800e-05 sigma_domi 5.236e-05 -1.982e-05 2.3586e-04 sigma_qual sigma_ingr sigma_pate b_brand_Novum -1.233e-05 -2.076e-05 1.053e-05 b_brand_BestValue -6.090e-05 1.063e-05 -4.483e-05 b_brand_Supermarket -1.991e-05 8.238e-05 -7.213e-05 b_brand_PainAway -7.264e-05 7.910e-05 -7.322e-05 b_country_CH 2.431e-05 4.374e-05 -2.378e-05 b_country_DK 1.030e-05 -2.144e-05 7.535e-07 b_country_IND -1.409e-05 -6.359e-07 9.877e-05 b_country_RUS 1.622e-05 -3.111e-05 2.072e-05 b_country_BRA 2.758e-06 -5.759e-05 1.564e-05 b_char_fast 3.907e-06 2.954e-05 2.446e-05 b_char_double 4.752e-05 4.201e-05 2.602e-05 b_risk -5.602e-08 3.560e-08 1.720e-08 b_price 7.012e-06 3.030e-06 -4.810e-07 lambda 2.907e-05 1.625e-05 2.018e-05 gamma_reg_user -1.5471e-04 6.200e-05 7.458e-05 gamma_university 1.022e-05 -1.1687e-04 -1.952e-05 gamma_age_50 6.882e-05 1.2105e-04 5.038e-05 zeta_quality -5.4587e-04 -5.907e-05 2.278e-05 zeta_ingredient 7.005e-05 5.3236e-04 1.267e-06 zeta_patent -6.516e-06 -3.356e-06 -5.5763e-04 zeta_dominance -5.540e-07 6.884e-05 1.800e-05 sigma_qual 7.2957e-04 5.784e-06 -1.667e-05 sigma_ingr 5.784e-06 6.9195e-04 -2.990e-05 sigma_pate -1.667e-05 -2.990e-05 7.5301e-04 sigma_domi -1.811e-06 -1.354e-05 2.638e-05 sigma_domi b_brand_Novum -2.405e-05 b_brand_BestValue -6.416e-05 b_brand_Supermarket -1.2318e-04 b_brand_PainAway -3.489e-05 b_country_CH -2.089e-05 b_country_DK -3.966e-06 b_country_IND 4.997e-05 b_country_RUS 1.828e-05 b_country_BRA 3.665e-05 b_char_fast -8.773e-06 b_char_double 4.340e-06 b_risk -2.708e-08 b_price 2.913e-06 lambda -1.769e-06 gamma_reg_user 8.110e-05 gamma_university -1.2040e-04 gamma_age_50 -1.389e-07 zeta_quality 2.387e-05 zeta_ingredient 5.236e-05 zeta_patent -1.982e-05 zeta_dominance 2.3586e-04 sigma_qual -1.811e-06 sigma_ingr -1.354e-05 sigma_pate 2.638e-05 sigma_domi 5.3302e-04 Classical correlation matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_Novum 1.000000 0.232011 0.28118 b_brand_BestValue 0.232011 1.000000 0.72206 b_brand_Supermarket 0.281182 0.722065 1.00000 b_brand_PainAway 0.244389 0.662076 0.66592 b_country_CH -0.054242 0.286633 0.27707 b_country_DK -0.047273 0.265168 0.27454 b_country_IND -0.033223 -0.407204 -0.41977 b_country_RUS -0.037786 -0.383332 -0.39469 b_country_BRA -0.006630 -0.358546 -0.42291 b_char_fast 0.011534 -0.004309 0.04594 b_char_double 0.065518 0.163527 0.18968 b_risk 0.001489 -0.182915 -0.19294 b_price 0.066276 0.286989 0.25895 lambda -0.012390 -0.082906 -0.07119 gamma_reg_user 0.002124 0.079591 0.08221 gamma_university -0.002720 0.084880 0.08432 gamma_age_50 2.6889e-04 0.072662 0.06860 zeta_quality -9.3920e-04 0.037170 0.03379 zeta_ingredient -0.002692 -0.038210 -0.03752 zeta_patent 0.001825 0.037397 0.04173 zeta_dominance 5.5775e-04 -0.027106 -0.02951 sigma_qual 0.001084 -0.017956 -0.01399 sigma_ingr -0.002120 -0.018366 -0.01711 sigma_pate -0.001624 -0.018132 -0.02161 sigma_domi 5.1893e-04 -0.009137 -0.01037 b_brand_PainAway b_country_CH b_country_DK b_brand_Novum 0.244389 -0.054242 -0.047273 b_brand_BestValue 0.662076 0.286633 0.265168 b_brand_Supermarket 0.665916 0.277066 0.274537 b_brand_PainAway 1.000000 0.221593 0.226151 b_country_CH 0.221593 1.000000 0.492786 b_country_DK 0.226151 0.492786 1.000000 b_country_IND -0.365407 0.007303 0.042754 b_country_RUS -0.320273 -0.032053 0.005437 b_country_BRA -0.344386 -0.033098 7.0787e-04 b_char_fast -0.041329 0.076559 0.034435 b_char_double 0.119945 0.088355 0.020818 b_risk -0.055013 -0.064793 -0.027751 b_price 0.332747 -0.121414 -0.047621 lambda -0.108703 0.038871 0.012642 gamma_reg_user 0.075350 6.3195e-04 -2.9476e-04 gamma_university 0.086081 5.7903e-04 -0.002761 gamma_age_50 0.072360 -0.002706 0.001193 zeta_quality 0.036179 9.3647e-04 -0.002834 zeta_ingredient -0.040075 0.001933 -3.3977e-04 zeta_patent 0.037163 -7.7901e-04 -0.003553 zeta_dominance -0.027459 4.1759e-04 0.001765 sigma_qual -0.017759 -3.5118e-04 0.002252 sigma_ingr -0.020566 0.002086 -6.2839e-04 sigma_pate -0.018764 0.001424 0.003152 sigma_domi -0.009827 6.1344e-04 0.001012 b_country_IND b_country_RUS b_country_BRA b_brand_Novum -0.033223 -0.037786 -0.006630 b_brand_BestValue -0.407204 -0.383332 -0.358546 b_brand_Supermarket -0.419773 -0.394693 -0.422906 b_brand_PainAway -0.365407 -0.320273 -0.344386 b_country_CH 0.007303 -0.032053 -0.033098 b_country_DK 0.042754 0.005437 7.0787e-04 b_country_IND 1.000000 0.442172 0.466124 b_country_RUS 0.442172 1.000000 0.424197 b_country_BRA 0.466124 0.424197 1.000000 b_char_fast -0.056045 -0.063203 -0.068184 b_char_double -0.026356 -0.033867 -0.050811 b_risk 0.052161 0.060871 0.031806 b_price 0.024130 0.045000 0.067009 lambda 0.001949 -0.044458 -0.025851 gamma_reg_user 0.001673 -0.002564 -0.001463 gamma_university 0.004162 -6.2974e-04 8.9759e-04 gamma_age_50 -0.005388 0.004912 0.002079 zeta_quality 0.005776 0.001890 0.005116 zeta_ingredient 8.7036e-04 -7.8799e-04 0.001575 zeta_patent 0.006709 -0.001650 -0.002568 zeta_dominance -0.001737 -0.001410 -0.003554 sigma_qual -0.004312 -0.002760 -0.005130 sigma_ingr 0.001664 -0.001497 0.001061 sigma_pate -0.005548 5.1216e-04 0.002230 sigma_domi -5.7326e-04 -0.001596 -0.002728 b_char_fast b_char_double b_risk b_brand_Novum 0.011534 0.065518 0.001489 b_brand_BestValue -0.004309 0.163527 -0.182915 b_brand_Supermarket 0.045938 0.189683 -0.192937 b_brand_PainAway -0.041329 0.119945 -0.055013 b_country_CH 0.076559 0.088355 -0.064793 b_country_DK 0.034435 0.020818 -0.027751 b_country_IND -0.056045 -0.026356 0.052161 b_country_RUS -0.063203 -0.033867 0.060871 b_country_BRA -0.068184 -0.050811 0.031806 b_char_fast 1.000000 0.455753 -0.082504 b_char_double 0.455753 1.000000 -0.050978 b_risk -0.082504 -0.050978 1.000000 b_price -0.141133 -0.173135 0.118638 lambda 0.066688 0.068833 -0.054513 gamma_reg_user -3.1212e-04 0.001849 3.0843e-04 gamma_university 4.991e-05 -3.7927e-04 0.002247 gamma_age_50 -1.8755e-04 -0.003841 -0.001456 zeta_quality -0.002500 -0.001772 0.008096 zeta_ingredient 0.007896 0.004653 -0.004940 zeta_patent -0.007593 -0.003583 0.006012 zeta_dominance -5.8066e-04 0.002282 -0.001940 sigma_qual 0.002238 0.002386 -0.007158 sigma_ingr 0.006630 0.004566 -0.003840 sigma_pate 0.007639 0.004528 -0.005633 sigma_domi -4.7647e-04 0.002059 -0.001120 b_price lambda gamma_reg_user b_brand_Novum 0.066276 -0.012390 0.002124 b_brand_BestValue 0.286989 -0.082906 0.079591 b_brand_Supermarket 0.258946 -0.071194 0.082214 b_brand_PainAway 0.332747 -0.108703 0.075350 b_country_CH -0.121414 0.038871 6.3195e-04 b_country_DK -0.047621 0.012642 -2.9476e-04 b_country_IND 0.024130 0.001949 0.001673 b_country_RUS 0.045000 -0.044458 -0.002564 b_country_BRA 0.067009 -0.025851 -0.001463 b_char_fast -0.141133 0.066688 -3.1212e-04 b_char_double -0.173135 0.068833 0.001849 b_risk 0.118638 -0.054513 3.0843e-04 b_price 1.000000 -0.067720 -0.006394 lambda -0.067720 1.000000 0.243397 gamma_reg_user -0.006394 0.243397 1.000000 gamma_university -0.003056 0.113737 -0.128938 gamma_age_50 0.009000 -0.230711 -0.284941 zeta_quality -0.003574 0.168903 0.203896 zeta_ingredient -0.001521 -0.141134 -0.175252 zeta_patent -0.003044 0.173534 0.200885 zeta_dominance 0.001569 -0.130158 -0.116870 sigma_qual 9.8363e-04 0.015193 -0.048252 sigma_ingr -0.003276 0.025229 -0.029452 sigma_pate 2.9374e-04 0.029169 -0.035280 sigma_domi -3.0596e-04 0.011636 0.002691 gamma_university gamma_age_50 zeta_quality b_brand_Novum -0.002720 2.6889e-04 -9.3920e-04 b_brand_BestValue 0.084880 0.072662 0.037170 b_brand_Supermarket 0.084321 0.068604 0.033795 b_brand_PainAway 0.086081 0.072360 0.036179 b_country_CH 5.7903e-04 -0.002706 9.3647e-04 b_country_DK -0.002761 0.001193 -0.002834 b_country_IND 0.004162 -0.005388 0.005776 b_country_RUS -6.2974e-04 0.004912 0.001890 b_country_BRA 8.9759e-04 0.002079 0.005116 b_char_fast 4.991e-05 -1.8755e-04 -0.002500 b_char_double -3.7927e-04 -0.003841 -0.001772 b_risk 0.002247 -0.001456 0.008096 b_price -0.003056 0.009000 -0.003574 lambda 0.113737 -0.230711 0.168903 gamma_reg_user -0.128938 -0.284941 0.203896 gamma_university 1.000000 -0.303330 0.113105 gamma_age_50 -0.303330 1.000000 -0.155777 zeta_quality 0.113105 -0.155777 1.000000 zeta_ingredient -0.114637 0.153136 -0.140786 zeta_patent 0.115469 -0.166508 0.125741 zeta_dominance -0.121870 0.103676 -0.092608 sigma_qual -0.022527 0.021945 -0.286059 sigma_ingr -0.027611 0.026382 -0.012825 sigma_pate -0.018648 0.022517 0.023512 sigma_domi -0.036536 -7.8158e-04 0.010842 zeta_ingredient zeta_patent zeta_dominance b_brand_Novum -0.002692 0.001825 5.5775e-04 b_brand_BestValue -0.038210 0.037397 -0.027106 b_brand_Supermarket -0.037517 0.041731 -0.029510 b_brand_PainAway -0.040075 0.037163 -0.027459 b_country_CH 0.001933 -7.7901e-04 4.1759e-04 b_country_DK -3.3977e-04 -0.003553 0.001765 b_country_IND 8.7036e-04 0.006709 -0.001737 b_country_RUS -7.8799e-04 -0.001650 -0.001410 b_country_BRA 0.001575 -0.002568 -0.003554 b_char_fast 0.007896 -0.007593 -5.8066e-04 b_char_double 0.004653 -0.003583 0.002282 b_risk -0.004940 0.006012 -0.001940 b_price -0.001521 -0.003044 0.001569 lambda -0.141134 0.173534 -0.130158 gamma_reg_user -0.175252 0.200885 -0.116870 gamma_university -0.114637 0.115469 -0.121870 gamma_age_50 0.153136 -0.166508 0.103676 zeta_quality -0.140786 0.125741 -0.092608 zeta_ingredient 1.000000 -0.136756 0.104196 zeta_patent -0.136756 1.000000 -0.087022 zeta_dominance 0.104196 -0.087022 1.000000 sigma_qual 0.015015 0.016148 -0.009646 sigma_ingr 0.254621 -0.004129 0.007880 sigma_pate 5.7290e-04 -0.311555 -0.025870 sigma_domi 0.003867 0.018593 0.209534 sigma_qual sigma_ingr sigma_pate b_brand_Novum 0.001084 -0.002120 -0.001624 b_brand_BestValue -0.017956 -0.018366 -0.018132 b_brand_Supermarket -0.013992 -0.017107 -0.021612 b_brand_PainAway -0.017759 -0.020566 -0.018764 b_country_CH -3.5118e-04 0.002086 0.001424 b_country_DK 0.002252 -6.2839e-04 0.003152 b_country_IND -0.004312 0.001664 -0.005548 b_country_RUS -0.002760 -0.001497 5.1216e-04 b_country_BRA -0.005130 0.001061 0.002230 b_char_fast 0.002238 0.006630 0.007639 b_char_double 0.002386 0.004566 0.004528 b_risk -0.007158 -0.003840 -0.005633 b_price 9.8363e-04 -0.003276 2.9374e-04 lambda 0.015193 0.025229 0.029169 gamma_reg_user -0.048252 -0.029452 -0.035280 gamma_university -0.022527 -0.027611 -0.018648 gamma_age_50 0.021945 0.026382 0.022517 zeta_quality -0.286059 -0.012825 0.023512 zeta_ingredient 0.015015 0.254621 5.7290e-04 zeta_patent 0.016148 -0.004129 -0.311555 zeta_dominance -0.009646 0.007880 -0.025870 sigma_qual 1.000000 0.002001 -0.031837 sigma_ingr 0.002001 1.000000 -0.007712 sigma_pate -0.031837 -0.007712 1.000000 sigma_domi -0.014590 -4.1412e-04 -0.024284 sigma_domi b_brand_Novum 5.1893e-04 b_brand_BestValue -0.009137 b_brand_Supermarket -0.010366 b_brand_PainAway -0.009827 b_country_CH 6.1344e-04 b_country_DK 0.001012 b_country_IND -5.7326e-04 b_country_RUS -0.001596 b_country_BRA -0.002728 b_char_fast -4.7647e-04 b_char_double 0.002059 b_risk -0.001120 b_price -3.0596e-04 lambda 0.011636 gamma_reg_user 0.002691 gamma_university -0.036536 gamma_age_50 -7.8158e-04 zeta_quality 0.010842 zeta_ingredient 0.003867 zeta_patent 0.018593 zeta_dominance 0.209534 sigma_qual -0.014590 sigma_ingr -4.1412e-04 sigma_pate -0.024284 sigma_domi 1.000000 Robust correlation matrix: b_brand_Novum b_brand_BestValue b_brand_Supermarket b_brand_Novum 1.00000 0.205847 0.24096 b_brand_BestValue 0.20585 1.000000 0.68541 b_brand_Supermarket 0.24096 0.685408 1.00000 b_brand_PainAway 0.19015 0.643757 0.66621 b_country_CH -0.10162 0.222643 0.24226 b_country_DK -0.03841 0.195949 0.24498 b_country_IND -0.03164 -0.441229 -0.43636 b_country_RUS -0.02678 -0.430048 -0.40278 b_country_BRA 0.01890 -0.397701 -0.46960 b_char_fast -0.05425 -0.013485 0.06163 b_char_double -0.01290 0.157107 0.17817 b_risk 0.07116 -0.118735 -0.13963 b_price 0.07704 0.275948 0.24138 lambda -0.04854 -0.094516 -0.06191 gamma_reg_user 6.5323e-04 0.069889 0.08149 gamma_university -0.02366 0.059282 0.02835 gamma_age_50 -0.03053 0.111285 0.10970 zeta_quality -6.0083e-04 0.039625 0.02893 zeta_ingredient -0.01458 -0.033377 -4.3252e-04 zeta_patent 0.04340 0.060883 0.06868 zeta_dominance -0.02926 -0.031641 -0.02996 sigma_qual -0.01430 -0.035065 -0.01113 sigma_ingr -0.02471 0.006282 0.04730 sigma_pate 0.01202 -0.025410 -0.03970 sigma_domi -0.03262 -0.043223 -0.08059 b_brand_PainAway b_country_CH b_country_DK b_brand_Novum 0.19015 -0.101617 -0.038413 b_brand_BestValue 0.64376 0.222643 0.195949 b_brand_Supermarket 0.66621 0.242263 0.244979 b_brand_PainAway 1.00000 0.188214 0.203187 b_country_CH 0.18821 1.000000 0.470101 b_country_DK 0.20319 0.470101 1.000000 b_country_IND -0.37614 -0.023719 0.024927 b_country_RUS -0.36168 -0.062118 -0.006507 b_country_BRA -0.36314 -0.045486 0.002228 b_char_fast -0.04059 0.103820 0.006805 b_char_double 0.09229 0.080032 -0.015615 b_risk -0.04847 -0.005886 0.047414 b_price 0.31260 -0.122333 -0.060525 lambda -0.09471 0.085055 0.034208 gamma_reg_user 0.08698 0.014234 0.022820 gamma_university 0.05135 -0.045211 -0.015244 gamma_age_50 0.12380 -0.008465 -0.013161 zeta_quality 0.04961 -0.002130 -0.022347 zeta_ingredient 0.01177 0.023308 -0.006791 zeta_patent 0.07025 -0.035484 -0.016477 zeta_dominance -0.02820 -0.026009 -0.017430 sigma_qual -0.04107 0.023203 0.010156 sigma_ingr 0.04593 0.042868 -0.021705 sigma_pate -0.04076 -0.022341 7.3130e-04 sigma_domi -0.02308 -0.023332 -0.004576 b_country_IND b_country_RUS b_country_BRA b_brand_Novum -0.031636 -0.026776 0.018902 b_brand_BestValue -0.441229 -0.430048 -0.397701 b_brand_Supermarket -0.436363 -0.402779 -0.469603 b_brand_PainAway -0.376138 -0.361678 -0.363145 b_country_CH -0.023719 -0.062118 -0.045486 b_country_DK 0.024927 -0.006507 0.002228 b_country_IND 1.000000 0.409905 0.514491 b_country_RUS 0.409905 1.000000 0.495657 b_country_BRA 0.514491 0.495657 1.000000 b_char_fast -0.086238 -0.084996 -0.104485 b_char_double -0.037487 -0.047178 -0.060746 b_risk 0.070525 0.072066 0.032224 b_price 0.055398 0.027999 0.054457 lambda 0.028066 -0.092867 -0.030923 gamma_reg_user 0.030324 -0.002457 0.029823 gamma_university 0.026372 0.011340 0.034919 gamma_age_50 -0.036982 -0.004821 -0.040191 zeta_quality 0.045238 -0.011978 0.014127 zeta_ingredient -0.024643 -0.026550 -0.011622 zeta_patent 0.013336 0.015615 0.017139 zeta_dominance -0.004190 -0.008114 0.002272 sigma_qual -0.008974 0.009824 0.001654 sigma_ingr -4.1602e-04 -0.019349 -0.035458 sigma_pate 0.061942 0.012354 0.009228 sigma_domi 0.037246 0.012956 0.025709 b_char_fast b_char_double b_risk b_brand_Novum -0.054248 -0.012900 0.071163 b_brand_BestValue -0.013485 0.157107 -0.118735 b_brand_Supermarket 0.061627 0.178168 -0.139630 b_brand_PainAway -0.040594 0.092286 -0.048471 b_country_CH 0.103820 0.080032 -0.005886 b_country_DK 0.006805 -0.015615 0.047414 b_country_IND -0.086238 -0.037487 0.070525 b_country_RUS -0.084996 -0.047178 0.072066 b_country_BRA -0.104485 -0.060746 0.032224 b_char_fast 1.000000 0.436331 -0.091496 b_char_double 0.436331 1.000000 -0.009729 b_risk -0.091496 -0.009729 1.000000 b_price -0.149499 -0.184486 0.122124 lambda 0.086723 0.056488 -0.056748 gamma_reg_user 0.014008 0.014207 0.044093 gamma_university -0.090619 -6.973e-05 0.042739 gamma_age_50 0.074227 0.028990 -0.077115 zeta_quality 0.011346 -0.004621 0.054858 zeta_ingredient 0.024981 0.051848 0.017837 zeta_patent -0.026335 0.029386 -0.017815 zeta_dominance 0.009978 -0.009254 -0.002936 sigma_qual 0.005008 0.048068 -0.034911 sigma_ingr 0.038890 0.043636 0.022777 sigma_pate 0.030864 0.025910 0.010551 sigma_domi -0.013157 0.005136 -0.019746 b_price lambda gamma_reg_user b_brand_Novum 0.077040 -0.048535 6.5323e-04 b_brand_BestValue 0.275948 -0.094516 0.069889 b_brand_Supermarket 0.241381 -0.061912 0.081492 b_brand_PainAway 0.312604 -0.094710 0.086982 b_country_CH -0.122333 0.085055 0.014234 b_country_DK -0.060525 0.034208 0.022820 b_country_IND 0.055398 0.028066 0.030324 b_country_RUS 0.027999 -0.092867 -0.002457 b_country_BRA 0.054457 -0.030923 0.029823 b_char_fast -0.149499 0.086723 0.014008 b_char_double -0.184486 0.056488 0.014207 b_risk 0.122124 -0.056748 0.044093 b_price 1.000000 -0.073423 -0.008654 lambda -0.073423 1.000000 0.225942 gamma_reg_user -0.008654 0.225942 1.000000 gamma_university -0.037753 0.080585 -0.138990 gamma_age_50 0.013451 -0.177602 -0.217918 zeta_quality 0.014021 0.128868 0.280997 zeta_ingredient 0.020599 -0.135133 -0.174343 zeta_patent 0.042125 0.147373 0.224844 zeta_dominance 0.072940 -0.116903 -0.079501 sigma_qual 0.015020 0.033772 -0.071874 sigma_ingr 0.006664 0.019382 0.029577 sigma_pate -0.001014 0.023078 0.034106 sigma_domi 0.007299 -0.002404 0.044083 gamma_university gamma_age_50 zeta_quality b_brand_Novum -0.023662 -0.030528 -6.0083e-04 b_brand_BestValue 0.059282 0.111285 0.039625 b_brand_Supermarket 0.028353 0.109702 0.028934 b_brand_PainAway 0.051354 0.123800 0.049610 b_country_CH -0.045211 -0.008465 -0.002130 b_country_DK -0.015244 -0.013161 -0.022347 b_country_IND 0.026372 -0.036982 0.045238 b_country_RUS 0.011340 -0.004821 -0.011978 b_country_BRA 0.034919 -0.040191 0.014127 b_char_fast -0.090619 0.074227 0.011346 b_char_double -6.973e-05 0.028990 -0.004621 b_risk 0.042739 -0.077115 0.054858 b_price -0.037753 0.013451 0.014021 lambda 0.080585 -0.177602 0.128868 gamma_reg_user -0.138990 -0.217918 0.280997 gamma_university 1.000000 -0.303243 0.134903 gamma_age_50 -0.303243 1.000000 -0.172460 zeta_quality 0.134903 -0.172460 1.000000 zeta_ingredient -0.178492 0.181837 -0.234822 zeta_patent 0.139327 -0.180387 0.150095 zeta_dominance -0.238754 0.112076 -0.087731 sigma_qual 0.005101 0.034216 -0.519742 sigma_ingr -0.059922 0.061799 -0.057754 sigma_pate -0.009594 0.024654 0.021349 sigma_domi -0.070333 -8.078e-05 0.026585 zeta_ingredient zeta_patent zeta_dominance b_brand_Novum -0.014578 0.043404 -0.029261 b_brand_BestValue -0.033377 0.060883 -0.031641 b_brand_Supermarket -4.3252e-04 0.068682 -0.029959 b_brand_PainAway 0.011767 0.070247 -0.028204 b_country_CH 0.023308 -0.035484 -0.026009 b_country_DK -0.006791 -0.016477 -0.017430 b_country_IND -0.024643 0.013336 -0.004190 b_country_RUS -0.026550 0.015615 -0.008114 b_country_BRA -0.011622 0.017139 0.002272 b_char_fast 0.024981 -0.026335 0.009978 b_char_double 0.051848 0.029386 -0.009254 b_risk 0.017837 -0.017815 -0.002936 b_price 0.020599 0.042125 0.072940 lambda -0.135133 0.147373 -0.116903 gamma_reg_user -0.174343 0.224844 -0.079501 gamma_university -0.178492 0.139327 -0.238754 gamma_age_50 0.181837 -0.180387 0.112076 zeta_quality -0.234822 0.150095 -0.087731 zeta_ingredient 1.000000 -0.190121 0.164086 zeta_patent -0.190121 1.000000 -0.088653 zeta_dominance 0.164086 -0.088653 1.000000 sigma_qual 0.065430 -0.006266 -5.8292e-04 sigma_ingr 0.510554 -0.003313 0.074381 sigma_pate 0.001165 -0.527844 0.018638 sigma_domi 0.057212 -0.022295 0.290346 sigma_qual sigma_ingr sigma_pate b_brand_Novum -0.014301 -0.024711 0.012016 b_brand_BestValue -0.035065 0.006282 -0.025410 b_brand_Supermarket -0.011132 0.047301 -0.039704 b_brand_PainAway -0.041074 0.045929 -0.040755 b_country_CH 0.023203 0.042868 -0.022341 b_country_DK 0.010156 -0.021705 7.3130e-04 b_country_IND -0.008974 -4.1602e-04 0.061942 b_country_RUS 0.009824 -0.019349 0.012354 b_country_BRA 0.001654 -0.035458 0.009228 b_char_fast 0.005008 0.038890 0.030864 b_char_double 0.048068 0.043636 0.025910 b_risk -0.034911 0.022777 0.010551 b_price 0.015020 0.006664 -0.001014 lambda 0.033772 0.019382 0.023078 gamma_reg_user -0.071874 0.029577 0.034106 gamma_university 0.005101 -0.059922 -0.009594 gamma_age_50 0.034216 0.061799 0.024654 zeta_quality -0.519742 -0.057754 0.021349 zeta_ingredient 0.065430 0.510554 0.001165 zeta_patent -0.006266 -0.003313 -0.527844 zeta_dominance -5.8292e-04 0.074381 0.018638 sigma_qual 1.000000 0.008140 -0.022493 sigma_ingr 0.008140 1.000000 -0.041422 sigma_pate -0.022493 -0.041422 1.000000 sigma_domi -0.002904 -0.022300 0.041639 sigma_domi b_brand_Novum -0.032618 b_brand_BestValue -0.043223 b_brand_Supermarket -0.080587 b_brand_PainAway -0.023081 b_country_CH -0.023332 b_country_DK -0.004576 b_country_IND 0.037246 b_country_RUS 0.012956 b_country_BRA 0.025709 b_char_fast -0.013157 b_char_double 0.005136 b_risk -0.019746 b_price 0.007299 lambda -0.002404 gamma_reg_user 0.044083 gamma_university -0.070333 gamma_age_50 -8.078e-05 zeta_quality 0.026585 zeta_ingredient 0.057212 zeta_patent -0.022295 zeta_dominance 0.290346 sigma_qual -0.002904 sigma_ingr -0.022300 sigma_pate 0.041639 sigma_domi 1.000000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 695 0.07321650 480 0.07708629 288 0.08368535 509 0.08492515 593 0.09011444 875 0.09015715 456 0.09198509 163 0.09329530 828 0.09702005 126 0.09764324 8 0.09819462 858 0.09864948 817 0.09892701 611 0.09967007 326 0.10026490 127 0.10064592 594 0.10074018 536 0.10273563 508 0.10291903 92 0.10374456 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Hybrid choice model on drug choice data, using continuous measurement model for indicators" indivID "ID" nCores "4" outputDirectory "output/" mixing "TRUE" debug "FALSE" modelName "Hybrid_with_continuous_measurement" workInLogs "FALSE" seed "13" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" analyticHessian "FALSE" memorySaver "FALSE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling used in computing Hessian --------------------------------- Value b_brand_Novum 0.276719696 b_brand_BestValue 0.580338032 b_brand_Supermarket 0.266658836 b_brand_PainAway 1.248705008 b_country_CH 0.670169885 b_country_DK 0.337703425 b_country_IND 0.296331492 b_country_RUS 0.893699059 b_country_BRA 0.655567751 b_char_fast 0.769958250 b_char_double 1.212456703 b_risk 0.001574531 b_price 0.724324798 lambda 0.659812284 gamma_reg_user 0.741300539 gamma_university 0.378845536 gamma_age_50 0.673772709 zeta_quality 0.534760169 zeta_ingredient 0.503352725 zeta_patent 0.606970158 zeta_dominance 0.394495084 sigma_qual 1.061357715 sigma_ingr 1.108648687 sigma_pate 1.084358717 sigma_domi 1.045446333 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)) normalDensity_settings2 = list(outcomeNormal = attitude_ingredients, xNormal = zeta_ingredient*LV, mu = 0, sigma = sigma_ingr, rows = (task==1)) normalDensity_settings3 = list(outcomeNormal = attitude_patent, xNormal = zeta_patent*LV, mu = 0, sigma = sigma_pate, rows = (task==1)) normalDensity_settings4 = list(outcomeNormal = attitude_dominance, xNormal = zeta_dominance*LV, mu = 0, sigma = sigma_domi, rows = (task==1)) P[["indic_quality"]] = apollo_normalDensity(normalDensity_settings1, functionality) P[["indic_quality"]] = apollo_panelProd(P[["indic_quality"]], apollo_inputs, functionality) P[["indic_ingredients"]] = apollo_normalDensity(normalDensity_settings2, functionality) P[["indic_ingredients"]] = apollo_panelProd(P[["indic_ingredients"]], apollo_inputs, functionality) P[["indic_patent"]] = apollo_normalDensity(normalDensity_settings3, functionality) P[["indic_patent"]] = apollo_panelProd(P[["indic_patent"]], apollo_inputs, functionality) P[["indic_dominance"]] = apollo_normalDensity(normalDensity_settings4, functionality) P[["indic_dominance"]] = apollo_panelProd(P[["indic_dominance"]], apollo_inputs, 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 ) ### Compute probabilities for MNL model component P[["choice"]] = apollo_mnl(mnl_settings, functionality) P[["choice"]] = apollo_panelProd(P[["choice"]] , apollo_inputs, functionality) ### Likelihood of the whole model P = apollo_combineModels(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) }