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 : BW_joint_model_diff_params Model description : Best-worst model on drug choice data, using different parameters for best and worst choices Model run at : 2025-09-19 11:48:13.01209 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -70.384499 reciprocal of condition number : 6.15994e-08 Number of individuals : 1000 Number of rows in database : 10000 Number of modelled outcomes : 20000 choice_best : 10000 choice_worst : 10000 Number of cores used : 1 Model without mixing LL(start) : -24849.07 LL (whole model) at equal shares, LL(0) : -24849.07 LL (whole model) at observed shares, LL(C) : -26184.18 LL(final, whole model) : -20780.24 Rho-squared vs equal shares : 0.1637 Adj.Rho-squared vs equal shares : 0.1627 Rho-squared vs observed shares : 0.2064 Adj.Rho-squared vs observed shares : 0.2056 AIC : 41612.47 BIC : 41799.94 LL(0,choice_best) : -13862.94 LL(final,choice_best) : -11088.61 LL(0,choice_worst) : -10986.12 LL(final,choice_worst) : -9691.63 Estimated parameters : 26 Time taken (hh:mm:ss) : 00:00:7.07 pre-estimation : 00:00:1.02 estimation : 00:00:0.66 post-estimation : 00:00:5.39 Iterations : 8 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) b_brand_Artemis_best 0.000000 NA NA NA NA b_brand_Artemis_worst 0.000000 NA NA NA NA b_brand_Novum_best -0.269840 0.03034 -8.894 0.03123 -8.642 b_brand_Novum_worst -0.285961 0.04287 -6.670 0.04158 -6.877 b_brand_BestValue_best -0.461959 0.06098 -7.576 0.06298 -7.335 b_brand_worstValue_worst -0.586512 0.06595 -8.893 0.06897 -8.504 b_brand_Supermarket_best -0.154960 0.06200 -2.499 0.06607 -2.345 b_brand_Supermarket_worst -0.418166 0.06735 -6.209 0.07295 -5.732 b_brand_PainAway_best -1.099518 0.06221 -17.673 0.06410 -17.152 b_brand_PainAway_worst -0.977448 0.06616 -14.775 0.07095 -13.776 b_country_CH_best 0.642623 0.03914 16.420 0.03803 16.896 b_country_CH_worst 0.319067 0.05339 5.976 0.05426 5.880 b_country_DK_best 0.330874 0.03767 8.783 0.03670 9.016 b_country_DK_worst 0.098948 0.05096 1.942 0.05221 1.895 b_country_USA_best 0.000000 NA NA NA NA b_country_USA_worst 0.000000 NA NA NA NA b_country_IND_best -0.305615 0.05553 -5.504 0.05635 -5.424 b_country_IND_worst -0.091536 0.04803 -1.906 0.04920 -1.860 b_country_RUS_best -0.849571 0.06022 -14.107 0.05891 -14.423 b_country_RUS_worst -0.540563 0.04536 -11.918 0.04481 -12.063 b_country_BRA_best -0.632877 0.05819 -10.876 0.05964 -10.611 b_country_BRA_worst -0.342121 0.04730 -7.233 0.04854 -7.048 b_char_standard_best 0.000000 NA NA NA NA b_char_standard_worst 0.000000 NA NA NA NA b_char_fast_best 0.739517 0.02845 25.990 0.02786 26.548 b_char_fast_worst 0.462363 0.02860 16.168 0.02846 16.247 b_char_double_best 1.171770 0.03685 31.799 0.03570 32.824 b_char_double_worst 0.715425 0.05205 13.744 0.05170 13.838 b_risk_best -0.001528 5.701e-05 -26.805 5.748e-05 -26.585 b_risk_worst -0.001038 3.594e-05 -28.872 3.557e-05 -29.169 b_price_best -0.704463 0.01773 -39.728 0.01697 -41.512 b_price_worst -0.512148 0.01954 -26.205 0.01928 -26.562 Overview of choices for MNL model component choice_best: 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 Overview of choices for MNL model component choice_worst: alt1 alt2 alt3 alt4 Times available 6597.00 6454.00 8483.00 8466.00 Times chosen 1531.00 1545.00 3482.00 3442.00 Percentage chosen overall 15.31 15.45 34.82 34.42 Percentage chosen when available 23.21 23.94 41.05 40.66 Classical covariance matrix: b_brand_Novum_best b_brand_Novum_worst b_brand_Novum_best 9.2055e-04 -6.327e-15 b_brand_Novum_worst -6.327e-15 0.001838 b_brand_BestValue_best 4.5082e-04 6.060e-15 b_brand_worstValue_worst -8.198e-15 0.001129 b_brand_Supermarket_best 5.5920e-04 -1.843e-16 b_brand_Supermarket_worst -1.104e-14 0.001160 b_brand_PainAway_best 4.8531e-04 2.420e-15 b_brand_PainAway_worst -8.725e-15 0.001139 b_country_CH_best -6.381e-05 1.259e-15 b_country_CH_worst -7.818e-15 -1.7207e-04 b_country_DK_best -5.339e-05 5.820e-16 b_country_DK_worst -2.554e-15 -1.3917e-04 b_country_IND_best -5.128e-05 -1.319e-14 b_country_IND_worst -1.028e-14 -4.938e-05 b_country_RUS_best -6.791e-05 -4.025e-15 b_country_RUS_worst -2.691e-16 3.606e-05 b_country_BRA_best -6.784e-06 -9.607e-15 b_country_BRA_worst 4.557e-16 3.116e-05 b_char_fast_best 1.300e-05 2.459e-16 b_char_fast_worst 6.841e-16 -4.256e-05 b_char_double_best 7.274e-05 3.560e-15 b_char_double_worst -3.063e-15 1.5515e-04 b_risk_best 1.965e-09 6.303e-20 b_risk_worst 3.977e-18 5.078e-08 b_price_best 3.442e-05 -2.914e-15 b_price_worst 7.184e-16 1.2194e-04 b_brand_BestValue_best b_brand_worstValue_worst b_brand_Novum_best 4.5082e-04 -8.198e-15 b_brand_Novum_worst 6.060e-15 0.001129 b_brand_BestValue_best 0.003719 -3.577e-14 b_brand_worstValue_worst -3.577e-14 0.004349 b_brand_Supermarket_best 0.002624 -6.550e-14 b_brand_Supermarket_worst -3.582e-14 0.003623 b_brand_PainAway_best 0.002352 -3.310e-14 b_brand_PainAway_worst -2.753e-14 0.003598 b_country_CH_best 7.4305e-04 -1.557e-14 b_country_CH_worst -4.929e-14 0.001086 b_country_DK_best 6.5831e-04 -1.219e-14 b_country_DK_worst -7.199e-14 0.001232 b_country_IND_best -0.001447 2.979e-14 b_country_IND_worst -4.843e-14 -0.001185 b_country_RUS_best -0.001508 3.857e-14 b_country_RUS_worst -1.695e-14 -0.001077 b_country_BRA_best -0.001337 3.304e-14 b_country_BRA_worst -9.773e-15 -0.001076 b_char_fast_best 1.164e-06 1.360e-14 b_char_fast_worst -6.445e-15 1.992e-05 b_char_double_best 4.0128e-04 2.026e-15 b_char_double_worst -5.599e-15 5.7001e-04 b_risk_best -6.878e-07 7.201e-18 b_risk_worst 1.291e-17 -3.255e-07 b_price_best 3.2726e-04 -3.577e-15 b_price_worst -1.451e-15 4.8866e-04 b_brand_Supermarket_best b_brand_Supermarket_worst b_brand_Novum_best 5.5920e-04 -1.104e-14 b_brand_Novum_worst -1.843e-16 0.001160 b_brand_BestValue_best 0.002624 -3.582e-14 b_brand_worstValue_worst -6.550e-14 0.003623 b_brand_Supermarket_best 0.003844 -6.797e-14 b_brand_Supermarket_worst -6.797e-14 0.004536 b_brand_PainAway_best 0.002432 -3.366e-14 b_brand_PainAway_worst -5.826e-14 0.003642 b_country_CH_best 7.3672e-04 -1.580e-14 b_country_CH_worst -6.395e-14 0.001128 b_country_DK_best 6.9918e-04 -1.514e-14 b_country_DK_worst -9.057e-14 0.001239 b_country_IND_best -0.001509 2.545e-14 b_country_IND_worst -3.271e-14 -0.001157 b_country_RUS_best -0.001558 3.332e-14 b_country_RUS_worst -8.576e-15 -0.001067 b_country_BRA_best -0.001593 3.160e-14 b_country_BRA_worst 2.065e-15 -0.001137 b_char_fast_best 1.0879e-04 1.214e-14 b_char_fast_worst -5.328e-15 1.575e-05 b_char_double_best 4.8315e-04 3.513e-16 b_char_double_worst -1.122e-14 6.3895e-04 b_risk_best -7.317e-07 7.106e-18 b_risk_worst 1.195e-17 -4.096e-07 b_price_best 2.9919e-04 -3.693e-15 b_price_worst -2.928e-15 4.7512e-04 b_brand_PainAway_best b_brand_PainAway_worst b_brand_Novum_best 4.8531e-04 -8.725e-15 b_brand_Novum_worst 2.420e-15 0.001139 b_brand_BestValue_best 0.002352 -2.753e-14 b_brand_worstValue_worst -3.310e-14 0.003598 b_brand_Supermarket_best 0.002432 -5.826e-14 b_brand_Supermarket_worst -3.366e-14 0.003642 b_brand_PainAway_best 0.003871 -2.622e-14 b_brand_PainAway_worst -2.622e-14 0.004377 b_country_CH_best 5.9704e-04 -1.112e-14 b_country_CH_worst -3.506e-14 0.001144 b_country_DK_best 5.7575e-04 -8.153e-15 b_country_DK_worst -4.546e-14 0.001301 b_country_IND_best -0.001312 2.779e-14 b_country_IND_worst -1.504e-14 -0.001209 b_country_RUS_best -0.001297 3.448e-14 b_country_RUS_worst 6.573e-16 -0.001091 b_country_BRA_best -0.001313 3.020e-14 b_country_BRA_worst 8.564e-15 -0.001129 b_char_fast_best -5.616e-05 1.304e-14 b_char_fast_worst -6.248e-15 -1.1180e-04 b_char_double_best 3.1340e-04 2.677e-15 b_char_double_worst -4.701e-15 5.4450e-04 b_risk_best -2.471e-07 5.620e-18 b_risk_worst 7.619e-18 -1.974e-07 b_price_best 3.8506e-04 -2.790e-15 b_price_worst 1.398e-15 4.8893e-04 b_country_CH_best b_country_CH_worst b_brand_Novum_best -6.381e-05 -7.818e-15 b_brand_Novum_worst 1.259e-15 -1.7207e-04 b_brand_BestValue_best 7.4305e-04 -4.929e-14 b_brand_worstValue_worst -1.557e-14 0.001086 b_brand_Supermarket_best 7.3672e-04 -6.395e-14 b_brand_Supermarket_worst -1.580e-14 0.001128 b_brand_PainAway_best 5.9704e-04 -3.506e-14 b_brand_PainAway_worst -1.112e-14 0.001144 b_country_CH_best 0.001532 2.860e-16 b_country_CH_worst 2.860e-16 0.002851 b_country_DK_best 7.3241e-04 3.393e-15 b_country_DK_worst -9.604e-15 0.001289 b_country_IND_best 8.996e-06 5.470e-14 b_country_IND_worst 2.716e-16 -2.0949e-04 b_country_RUS_best -6.669e-05 5.459e-14 b_country_RUS_worst 3.739e-15 -1.6850e-04 b_country_BRA_best -8.328e-05 4.830e-14 b_country_BRA_worst 5.635e-15 -2.4176e-04 b_char_fast_best 7.601e-05 7.391e-15 b_char_fast_worst -5.769e-16 2.1594e-04 b_char_double_best 1.2045e-04 -6.810e-15 b_char_double_worst -2.678e-15 8.705e-05 b_risk_best -1.367e-07 1.050e-17 b_risk_worst 4.432e-18 -6.450e-08 b_price_best -7.871e-05 -1.404e-15 b_price_worst -2.453e-15 -1.7711e-04 b_country_DK_best b_country_DK_worst b_brand_Novum_best -5.339e-05 -2.554e-15 b_brand_Novum_worst 5.820e-16 -1.3917e-04 b_brand_BestValue_best 6.5831e-04 -7.199e-14 b_brand_worstValue_worst -1.219e-14 0.001232 b_brand_Supermarket_best 6.9918e-04 -9.057e-14 b_brand_Supermarket_worst -1.514e-14 0.001239 b_brand_PainAway_best 5.7575e-04 -4.546e-14 b_brand_PainAway_worst -8.153e-15 0.001301 b_country_CH_best 7.3241e-04 -9.604e-15 b_country_CH_worst 3.393e-15 0.001289 b_country_DK_best 0.001419 -3.254e-15 b_country_DK_worst -3.254e-15 0.002597 b_country_IND_best 9.072e-05 8.058e-14 b_country_IND_worst 1.950e-15 -5.405e-05 b_country_RUS_best 1.083e-05 8.640e-14 b_country_RUS_worst 4.093e-15 -7.780e-05 b_country_BRA_best 4.093e-06 6.942e-14 b_country_BRA_worst 6.807e-15 -2.0976e-04 b_char_fast_best 3.244e-05 8.067e-15 b_char_fast_worst -7.694e-16 1.7559e-04 b_char_double_best 2.974e-05 -1.539e-14 b_char_double_worst -3.690e-15 2.054e-05 b_risk_best -5.300e-08 1.887e-17 b_risk_worst 5.732e-18 -4.484e-08 b_price_best -2.947e-05 3.068e-15 b_price_worst -1.518e-15 -1.116e-05 b_country_IND_best b_country_IND_worst b_brand_Novum_best -5.128e-05 -1.028e-14 b_brand_Novum_worst -1.319e-14 -4.938e-05 b_brand_BestValue_best -0.001447 -4.843e-14 b_brand_worstValue_worst 2.979e-14 -0.001185 b_brand_Supermarket_best -0.001509 -3.271e-14 b_brand_Supermarket_worst 2.545e-14 -0.001157 b_brand_PainAway_best -0.001312 -1.504e-14 b_brand_PainAway_worst 2.779e-14 -0.001209 b_country_CH_best 8.996e-06 2.716e-16 b_country_CH_worst 5.470e-14 -2.0949e-04 b_country_DK_best 9.072e-05 1.950e-15 b_country_DK_worst 8.058e-14 -5.405e-05 b_country_IND_best 0.003084 2.077e-14 b_country_IND_worst 2.077e-14 0.002307 b_country_RUS_best 0.001490 2.936e-14 b_country_RUS_worst 6.570e-15 0.001159 b_country_BRA_best 0.001507 1.734e-14 b_country_BRA_worst 1.069e-15 0.001235 b_char_fast_best -9.933e-05 -1.765e-14 b_char_fast_worst 7.272e-15 -7.246e-05 b_char_double_best -6.575e-05 -2.648e-14 b_char_double_worst 2.675e-15 -3.261e-05 b_risk_best 1.661e-07 1.656e-17 b_risk_worst -1.663e-18 -5.460e-08 b_price_best 3.306e-05 3.068e-15 b_price_worst -2.088e-15 6.014e-05 b_country_RUS_best b_country_RUS_worst b_brand_Novum_best -6.791e-05 -2.691e-16 b_brand_Novum_worst -4.025e-15 3.606e-05 b_brand_BestValue_best -0.001508 -1.695e-14 b_brand_worstValue_worst 3.857e-14 -0.001077 b_brand_Supermarket_best -0.001558 -8.576e-15 b_brand_Supermarket_worst 3.332e-14 -0.001067 b_brand_PainAway_best -0.001297 6.573e-16 b_brand_PainAway_worst 3.448e-14 -0.001091 b_country_CH_best -6.669e-05 3.739e-15 b_country_CH_worst 5.459e-14 -1.6850e-04 b_country_DK_best 1.083e-05 4.093e-15 b_country_DK_worst 8.640e-14 -7.780e-05 b_country_IND_best 0.001490 6.570e-15 b_country_IND_worst 2.936e-14 0.001159 b_country_RUS_best 0.003627 1.855e-14 b_country_RUS_worst 1.855e-14 0.002057 b_country_BRA_best 0.001472 7.550e-15 b_country_BRA_worst 1.086e-14 0.001195 b_char_fast_best -1.0730e-04 -9.626e-15 b_char_fast_worst 4.311e-15 -1.4121e-04 b_char_double_best -6.242e-05 -1.253e-14 b_char_double_worst 2.338e-16 -7.515e-05 b_risk_best 1.745e-07 8.562e-18 b_risk_worst -3.241e-18 1.399e-07 b_price_best 4.211e-05 2.691e-15 b_price_worst 1.467e-15 1.1422e-04 b_country_BRA_best b_country_BRA_worst b_brand_Novum_best -6.784e-06 4.557e-16 b_brand_Novum_worst -9.607e-15 3.116e-05 b_brand_BestValue_best -0.001337 -9.773e-15 b_brand_worstValue_worst 3.304e-14 -0.001076 b_brand_Supermarket_best -0.001593 2.065e-15 b_brand_Supermarket_worst 3.160e-14 -0.001137 b_brand_PainAway_best -0.001313 8.564e-15 b_brand_PainAway_worst 3.020e-14 -0.001129 b_country_CH_best -8.328e-05 5.635e-15 b_country_CH_worst 4.830e-14 -2.4176e-04 b_country_DK_best 4.093e-06 6.807e-15 b_country_DK_worst 6.942e-14 -2.0976e-04 b_country_IND_best 0.001507 1.069e-15 b_country_IND_worst 1.734e-14 0.001235 b_country_RUS_best 0.001472 1.086e-14 b_country_RUS_worst 7.550e-15 0.001195 b_country_BRA_best 0.003386 2.814e-15 b_country_BRA_worst 2.814e-15 0.002237 b_char_fast_best -1.1997e-04 -9.601e-15 b_char_fast_worst 6.987e-15 -9.320e-05 b_char_double_best -9.636e-05 -1.045e-14 b_char_double_worst 4.131e-15 -1.1070e-04 b_risk_best 9.617e-08 4.734e-18 b_risk_worst -3.476e-18 4.997e-09 b_price_best 7.203e-05 2.365e-15 b_price_worst 3.188e-16 1.3300e-04 b_char_fast_best b_char_fast_worst b_brand_Novum_best 1.300e-05 6.841e-16 b_brand_Novum_worst 2.459e-16 -4.256e-05 b_brand_BestValue_best 1.164e-06 -6.445e-15 b_brand_worstValue_worst 1.360e-14 1.992e-05 b_brand_Supermarket_best 1.0879e-04 -5.328e-15 b_brand_Supermarket_worst 1.214e-14 1.575e-05 b_brand_PainAway_best -5.616e-05 -6.248e-15 b_brand_PainAway_worst 1.304e-14 -1.1180e-04 b_country_CH_best 7.601e-05 -5.769e-16 b_country_CH_worst 7.391e-15 2.1594e-04 b_country_DK_best 3.244e-05 -7.694e-16 b_country_DK_worst 8.067e-15 1.7559e-04 b_country_IND_best -9.933e-05 7.272e-15 b_country_IND_worst -1.765e-14 -7.246e-05 b_country_RUS_best -1.0730e-04 4.311e-15 b_country_RUS_worst -9.626e-15 -1.4121e-04 b_country_BRA_best -1.1997e-04 6.987e-15 b_country_BRA_worst -9.601e-15 -9.320e-05 b_char_fast_best 8.0964e-04 3.023e-15 b_char_fast_worst 3.023e-15 8.1785e-04 b_char_double_best 4.7482e-04 2.407e-15 b_char_double_worst 1.583e-15 3.6276e-04 b_risk_best -1.217e-07 8.674e-19 b_risk_worst 8.863e-19 -8.794e-08 b_price_best -6.687e-05 -6.984e-16 b_price_worst -5.942e-16 -1.1796e-04 b_char_double_best b_char_double_worst b_brand_Novum_best 7.274e-05 -3.063e-15 b_brand_Novum_worst 3.560e-15 1.5515e-04 b_brand_BestValue_best 4.0128e-04 -5.599e-15 b_brand_worstValue_worst 2.026e-15 5.7001e-04 b_brand_Supermarket_best 4.8315e-04 -1.122e-14 b_brand_Supermarket_worst 3.513e-16 6.3895e-04 b_brand_PainAway_best 3.1340e-04 -4.701e-15 b_brand_PainAway_worst 2.677e-15 5.4450e-04 b_country_CH_best 1.2045e-04 -2.678e-15 b_country_CH_worst -6.810e-15 8.705e-05 b_country_DK_best 2.974e-05 -3.690e-15 b_country_DK_worst -1.539e-14 2.054e-05 b_country_IND_best -6.575e-05 2.675e-15 b_country_IND_worst -2.648e-14 -3.261e-05 b_country_RUS_best -6.242e-05 2.338e-16 b_country_RUS_worst -1.253e-14 -7.515e-05 b_country_BRA_best -9.636e-05 4.131e-15 b_country_BRA_worst -1.045e-14 -1.1070e-04 b_char_fast_best 4.7482e-04 1.583e-15 b_char_fast_worst 2.407e-15 3.6276e-04 b_char_double_best 0.001358 -4.038e-16 b_char_double_worst -4.038e-16 0.002710 b_risk_best -9.387e-08 -2.050e-18 b_risk_worst 3.018e-18 -6.690e-08 b_price_best -1.0604e-04 -6.005e-16 b_price_worst -1.203e-15 -1.1134e-04 b_risk_best b_risk_worst b_brand_Novum_best 1.965e-09 3.977e-18 b_brand_Novum_worst 6.303e-20 5.078e-08 b_brand_BestValue_best -6.878e-07 1.291e-17 b_brand_worstValue_worst 7.201e-18 -3.255e-07 b_brand_Supermarket_best -7.317e-07 1.195e-17 b_brand_Supermarket_worst 7.106e-18 -4.096e-07 b_brand_PainAway_best -2.471e-07 7.619e-18 b_brand_PainAway_worst 5.620e-18 -1.974e-07 b_country_CH_best -1.367e-07 4.432e-18 b_country_CH_worst 1.050e-17 -6.450e-08 b_country_DK_best -5.300e-08 5.732e-18 b_country_DK_worst 1.887e-17 -4.484e-08 b_country_IND_best 1.661e-07 -1.663e-18 b_country_IND_worst 1.656e-17 -5.460e-08 b_country_RUS_best 1.745e-07 -3.241e-18 b_country_RUS_worst 8.562e-18 1.399e-07 b_country_BRA_best 9.617e-08 -3.476e-18 b_country_BRA_worst 4.734e-18 4.997e-09 b_char_fast_best -1.217e-07 8.863e-19 b_char_fast_worst 8.674e-19 -8.794e-08 b_char_double_best -9.387e-08 3.018e-18 b_char_double_worst -2.050e-18 -6.690e-08 b_risk_best 3.250e-09 -1.116e-21 b_risk_worst -1.116e-21 1.291e-09 b_price_best 1.172e-07 6.343e-19 b_price_worst 1.939e-18 1.533e-07 b_price_best b_price_worst b_brand_Novum_best 3.442e-05 7.184e-16 b_brand_Novum_worst -2.914e-15 1.2194e-04 b_brand_BestValue_best 3.2726e-04 -1.451e-15 b_brand_worstValue_worst -3.577e-15 4.8866e-04 b_brand_Supermarket_best 2.9919e-04 -2.928e-15 b_brand_Supermarket_worst -3.693e-15 4.7512e-04 b_brand_PainAway_best 3.8506e-04 1.398e-15 b_brand_PainAway_worst -2.790e-15 4.8893e-04 b_country_CH_best -7.871e-05 -2.453e-15 b_country_CH_worst -1.404e-15 -1.7711e-04 b_country_DK_best -2.947e-05 -1.518e-15 b_country_DK_worst 3.068e-15 -1.116e-05 b_country_IND_best 3.306e-05 -2.088e-15 b_country_IND_worst 3.068e-15 6.014e-05 b_country_RUS_best 4.211e-05 1.467e-15 b_country_RUS_worst 2.691e-15 1.1422e-04 b_country_BRA_best 7.203e-05 3.188e-16 b_country_BRA_worst 2.365e-15 1.3300e-04 b_char_fast_best -6.687e-05 -5.942e-16 b_char_fast_worst -6.984e-16 -1.1796e-04 b_char_double_best -1.0604e-04 -1.203e-15 b_char_double_worst -6.005e-16 -1.1134e-04 b_risk_best 1.172e-07 1.939e-18 b_risk_worst 6.343e-19 1.533e-07 b_price_best 3.1443e-04 4.229e-16 b_price_worst 4.229e-16 3.8197e-04 Robust covariance matrix: b_brand_Novum_best b_brand_Novum_worst b_brand_Novum_best 9.7504e-04 -4.798e-05 b_brand_Novum_worst -4.798e-05 0.001729 b_brand_BestValue_best 4.5007e-04 -1.8460e-04 b_brand_worstValue_worst -6.124e-05 0.001149 b_brand_Supermarket_best 5.6059e-04 -5.651e-05 b_brand_Supermarket_worst -3.950e-05 0.001229 b_brand_PainAway_best 4.1297e-04 1.255e-05 b_brand_PainAway_worst -4.672e-05 0.001156 b_country_CH_best -1.1109e-04 -7.892e-05 b_country_CH_worst -8.875e-06 -1.2269e-04 b_country_DK_best -4.496e-05 -9.779e-05 b_country_DK_worst 1.917e-05 -1.3250e-04 b_country_IND_best -7.218e-05 1.0514e-04 b_country_IND_worst 2.055e-06 3.765e-05 b_country_RUS_best -6.119e-05 1.1634e-04 b_country_RUS_worst -4.519e-06 1.834e-05 b_country_BRA_best 2.379e-05 7.697e-05 b_country_BRA_worst 4.648e-05 1.616e-05 b_char_fast_best -5.244e-05 -1.170e-05 b_char_fast_worst 1.456e-05 -6.370e-05 b_char_double_best -9.396e-06 -4.222e-05 b_char_double_worst 2.534e-05 1.7183e-04 b_risk_best 1.190e-07 -1.344e-07 b_risk_worst -4.144e-08 -6.143e-08 b_price_best 3.764e-05 5.816e-06 b_price_worst -1.348e-05 1.4086e-04 b_brand_BestValue_best b_brand_worstValue_worst b_brand_Novum_best 4.5007e-04 -6.124e-05 b_brand_Novum_worst -1.8460e-04 0.001149 b_brand_BestValue_best 0.003966 4.738e-05 b_brand_worstValue_worst 4.738e-05 0.004757 b_brand_Supermarket_best 0.002895 1.7814e-04 b_brand_Supermarket_worst 1.0843e-04 0.004219 b_brand_PainAway_best 0.002630 8.118e-05 b_brand_PainAway_worst 1.2906e-04 0.004125 b_country_CH_best 5.7083e-04 -7.850e-05 b_country_CH_worst 1.088e-05 0.001260 b_country_DK_best 4.5966e-04 -1.4400e-04 b_country_DK_worst 5.090e-05 0.001408 b_country_IND_best -0.001551 2.1846e-04 b_country_IND_worst 2.237e-05 -0.001240 b_country_RUS_best -0.001664 1.1462e-04 b_country_RUS_worst 1.729e-05 -0.001137 b_country_BRA_best -0.001461 1.1620e-04 b_country_BRA_worst -3.908e-05 -0.001172 b_char_fast_best -1.207e-05 9.990e-06 b_char_fast_worst -2.859e-06 -7.864e-05 b_char_double_best 3.1121e-04 8.876e-06 b_char_double_worst -1.9518e-04 4.3047e-04 b_risk_best -5.210e-07 6.259e-08 b_risk_worst -7.485e-09 -4.812e-07 b_price_best 3.2054e-04 -2.858e-05 b_price_worst -6.295e-05 5.3287e-04 b_brand_Supermarket_best b_brand_Supermarket_worst b_brand_Novum_best 5.6059e-04 -3.950e-05 b_brand_Novum_worst -5.651e-05 0.001229 b_brand_BestValue_best 0.002895 1.0843e-04 b_brand_worstValue_worst 1.7814e-04 0.004219 b_brand_Supermarket_best 0.004365 2.5306e-04 b_brand_Supermarket_worst 2.5306e-04 0.005321 b_brand_PainAway_best 0.002849 3.953e-05 b_brand_PainAway_worst 2.6009e-04 0.004274 b_country_CH_best 6.0841e-04 -9.511e-05 b_country_CH_worst -1.927e-05 0.001367 b_country_DK_best 5.7064e-04 -1.8287e-04 b_country_DK_worst 8.246e-05 0.001434 b_country_IND_best -0.001603 1.7731e-04 b_country_IND_worst 2.791e-05 -0.001230 b_country_RUS_best -0.001605 3.219e-05 b_country_RUS_worst -4.492e-06 -0.001164 b_country_BRA_best -0.001834 5.520e-05 b_country_BRA_worst 5.611e-05 -0.001231 b_char_fast_best 1.1875e-04 1.051e-05 b_char_fast_worst -1.455e-07 -3.042e-05 b_char_double_best 3.6970e-04 5.688e-05 b_char_double_worst -2.0374e-04 6.1894e-04 b_risk_best -6.423e-07 5.221e-08 b_risk_worst -3.825e-08 -5.740e-07 b_price_best 2.9534e-04 -2.394e-05 b_price_worst -7.943e-05 5.1816e-04 b_brand_PainAway_best b_brand_PainAway_worst b_brand_Novum_best 4.1297e-04 -4.672e-05 b_brand_Novum_worst 1.255e-05 0.001156 b_brand_BestValue_best 0.002630 1.2906e-04 b_brand_worstValue_worst 8.118e-05 0.004125 b_brand_Supermarket_best 0.002849 2.6009e-04 b_brand_Supermarket_worst 3.953e-05 0.004274 b_brand_PainAway_best 0.004109 1.2458e-04 b_brand_PainAway_worst 1.2458e-04 0.005034 b_country_CH_best 4.6797e-04 -1.836e-05 b_country_CH_worst 7.853e-06 0.001383 b_country_DK_best 4.7548e-04 -7.895e-05 b_country_DK_worst -3.909e-05 0.001548 b_country_IND_best -0.001317 2.8010e-04 b_country_IND_worst 1.1316e-04 -0.001324 b_country_RUS_best -0.001435 7.520e-05 b_country_RUS_worst 1.0692e-04 -0.001214 b_country_BRA_best -0.001357 1.2898e-04 b_country_BRA_worst 5.858e-05 -0.001265 b_char_fast_best -4.831e-05 -1.110e-05 b_char_fast_worst 1.0059e-04 -1.7527e-04 b_char_double_best 1.5739e-04 4.447e-05 b_char_double_worst -1.0926e-04 4.4331e-04 b_risk_best -3.210e-07 3.838e-08 b_risk_worst -2.246e-08 -3.797e-07 b_price_best 3.7438e-04 -1.595e-05 b_price_worst -9.635e-05 5.0680e-04 b_country_CH_best b_country_CH_worst b_brand_Novum_best -1.1109e-04 -8.875e-06 b_brand_Novum_worst -7.892e-05 -1.2269e-04 b_brand_BestValue_best 5.7083e-04 1.088e-05 b_brand_worstValue_worst -7.850e-05 0.001260 b_brand_Supermarket_best 6.0841e-04 -1.927e-05 b_brand_Supermarket_worst -9.511e-05 0.001367 b_brand_PainAway_best 4.6797e-04 7.853e-06 b_brand_PainAway_worst -1.836e-05 0.001383 b_country_CH_best 0.001447 4.232e-07 b_country_CH_worst 4.232e-07 0.002944 b_country_DK_best 6.5935e-04 -6.010e-05 b_country_DK_worst 4.426e-05 0.001411 b_country_IND_best -2.231e-05 9.035e-05 b_country_IND_worst 4.336e-05 -3.2097e-04 b_country_RUS_best -1.4535e-04 -7.675e-05 b_country_RUS_worst 1.104e-05 -1.7459e-04 b_country_BRA_best -8.616e-05 2.295e-05 b_country_BRA_worst -5.562e-06 -2.3130e-04 b_char_fast_best 1.0154e-04 -6.376e-05 b_char_fast_worst 1.308e-06 1.4356e-04 b_char_double_best 1.0687e-04 -1.641e-05 b_char_double_worst -4.817e-06 4.232e-05 b_risk_best 1.979e-08 1.061e-07 b_risk_worst 5.059e-08 -7.433e-08 b_price_best -7.239e-05 2.642e-05 b_price_worst 1.088e-05 -1.4705e-04 b_country_DK_best b_country_DK_worst b_brand_Novum_best -4.496e-05 1.917e-05 b_brand_Novum_worst -9.779e-05 -1.3250e-04 b_brand_BestValue_best 4.5966e-04 5.090e-05 b_brand_worstValue_worst -1.4400e-04 0.001408 b_brand_Supermarket_best 5.7064e-04 8.246e-05 b_brand_Supermarket_worst -1.8287e-04 0.001434 b_brand_PainAway_best 4.7548e-04 -3.909e-05 b_brand_PainAway_worst -7.895e-05 0.001548 b_country_CH_best 6.5935e-04 4.426e-05 b_country_CH_worst -6.010e-05 0.001411 b_country_DK_best 0.001347 5.926e-06 b_country_DK_worst 5.926e-06 0.002726 b_country_IND_best 6.341e-05 3.696e-05 b_country_IND_worst 2.240e-05 -6.441e-05 b_country_RUS_best -1.285e-05 -1.3354e-04 b_country_RUS_worst 8.255e-05 -1.4555e-04 b_country_BRA_best -2.902e-06 7.396e-06 b_country_BRA_worst 1.082e-06 -2.3714e-04 b_char_fast_best 1.094e-05 -5.421e-06 b_char_fast_worst -7.057e-06 1.1551e-04 b_char_double_best 4.424e-06 6.047e-06 b_char_double_worst 8.226e-06 -6.346e-05 b_risk_best 1.125e-07 1.249e-07 b_risk_worst 4.689e-08 -1.795e-08 b_price_best -3.426e-05 1.234e-05 b_price_worst 5.731e-07 5.400e-05 b_country_IND_best b_country_IND_worst b_brand_Novum_best -7.218e-05 2.055e-06 b_brand_Novum_worst 1.0514e-04 3.765e-05 b_brand_BestValue_best -0.001551 2.237e-05 b_brand_worstValue_worst 2.1846e-04 -0.001240 b_brand_Supermarket_best -0.001603 2.791e-05 b_brand_Supermarket_worst 1.7731e-04 -0.001230 b_brand_PainAway_best -0.001317 1.1316e-04 b_brand_PainAway_worst 2.8010e-04 -0.001324 b_country_CH_best -2.231e-05 4.336e-05 b_country_CH_worst 9.035e-05 -3.2097e-04 b_country_DK_best 6.341e-05 2.240e-05 b_country_DK_worst 3.696e-05 -6.441e-05 b_country_IND_best 0.003175 2.724e-05 b_country_IND_worst 2.724e-05 0.002421 b_country_RUS_best 0.001317 -4.796e-05 b_country_RUS_worst 7.591e-05 0.001157 b_country_BRA_best 0.001665 -7.488e-05 b_country_BRA_worst -1.342e-06 0.001276 b_char_fast_best -1.2561e-04 1.618e-05 b_char_fast_worst -3.252e-05 -8.814e-05 b_char_double_best -5.716e-05 -1.6544e-04 b_char_double_worst 1.8013e-04 -1.7281e-04 b_risk_best 3.047e-07 9.295e-09 b_risk_worst 4.116e-08 -7.258e-08 b_price_best 4.109e-05 2.023e-05 b_price_worst 4.327e-05 7.710e-05 b_country_RUS_best b_country_RUS_worst b_brand_Novum_best -6.119e-05 -4.519e-06 b_brand_Novum_worst 1.1634e-04 1.834e-05 b_brand_BestValue_best -0.001664 1.729e-05 b_brand_worstValue_worst 1.1462e-04 -0.001137 b_brand_Supermarket_best -0.001605 -4.492e-06 b_brand_Supermarket_worst 3.219e-05 -0.001164 b_brand_PainAway_best -0.001435 1.0692e-04 b_brand_PainAway_worst 7.520e-05 -0.001214 b_country_CH_best -1.4535e-04 1.104e-05 b_country_CH_worst -7.675e-05 -1.7459e-04 b_country_DK_best -1.285e-05 8.255e-05 b_country_DK_worst -1.3354e-04 -1.4555e-04 b_country_IND_best 0.001317 7.591e-05 b_country_IND_worst -4.796e-05 0.001157 b_country_RUS_best 0.003470 1.564e-05 b_country_RUS_worst 1.564e-05 0.002008 b_country_BRA_best 0.001713 -3.815e-05 b_country_BRA_worst 3.591e-05 0.001236 b_char_fast_best -1.4589e-04 -4.166e-05 b_char_fast_worst -3.716e-05 -1.4564e-04 b_char_double_best -8.703e-05 -1.3585e-04 b_char_double_worst 8.539e-05 -6.043e-05 b_risk_best 2.187e-07 -2.083e-08 b_risk_worst 5.975e-09 1.898e-07 b_price_best 1.038e-05 4.671e-05 b_price_worst 2.716e-05 1.0412e-04 b_country_BRA_best b_country_BRA_worst b_brand_Novum_best 2.379e-05 4.648e-05 b_brand_Novum_worst 7.697e-05 1.616e-05 b_brand_BestValue_best -0.001461 -3.908e-05 b_brand_worstValue_worst 1.1620e-04 -0.001172 b_brand_Supermarket_best -0.001834 5.611e-05 b_brand_Supermarket_worst 5.520e-05 -0.001231 b_brand_PainAway_best -0.001357 5.858e-05 b_brand_PainAway_worst 1.2898e-04 -0.001265 b_country_CH_best -8.616e-05 -5.562e-06 b_country_CH_worst 2.295e-05 -2.3130e-04 b_country_DK_best -2.902e-06 1.082e-06 b_country_DK_worst 7.396e-06 -2.3714e-04 b_country_IND_best 0.001665 -1.342e-06 b_country_IND_worst -7.488e-05 0.001276 b_country_RUS_best 0.001713 3.591e-05 b_country_RUS_worst -3.815e-05 0.001236 b_country_BRA_best 0.003557 -6.371e-05 b_country_BRA_worst -6.371e-05 0.002357 b_char_fast_best -1.8792e-04 -2.061e-07 b_char_fast_worst -2.426e-05 -8.939e-05 b_char_double_best -1.3930e-04 -1.4328e-04 b_char_double_worst 9.911e-05 -1.1520e-04 b_risk_best 1.329e-07 -2.703e-08 b_risk_worst 4.132e-08 2.803e-08 b_price_best 5.608e-05 2.198e-05 b_price_worst 2.475e-05 1.2563e-04 b_char_fast_best b_char_fast_worst b_brand_Novum_best -5.244e-05 1.456e-05 b_brand_Novum_worst -1.170e-05 -6.370e-05 b_brand_BestValue_best -1.207e-05 -2.859e-06 b_brand_worstValue_worst 9.990e-06 -7.864e-05 b_brand_Supermarket_best 1.1875e-04 -1.455e-07 b_brand_Supermarket_worst 1.051e-05 -3.042e-05 b_brand_PainAway_best -4.831e-05 1.0059e-04 b_brand_PainAway_worst -1.110e-05 -1.7527e-04 b_country_CH_best 1.0154e-04 1.308e-06 b_country_CH_worst -6.376e-05 1.4356e-04 b_country_DK_best 1.094e-05 -7.057e-06 b_country_DK_worst -5.421e-06 1.1551e-04 b_country_IND_best -1.2561e-04 -3.252e-05 b_country_IND_worst 1.618e-05 -8.814e-05 b_country_RUS_best -1.4589e-04 -3.716e-05 b_country_RUS_worst -4.166e-05 -1.4564e-04 b_country_BRA_best -1.8792e-04 -2.426e-05 b_country_BRA_worst -2.061e-07 -8.939e-05 b_char_fast_best 7.7596e-04 -2.288e-05 b_char_fast_worst -2.288e-05 8.0992e-04 b_char_double_best 4.3530e-04 1.659e-05 b_char_double_worst -3.896e-05 3.8148e-04 b_risk_best -1.318e-07 9.796e-09 b_risk_worst 6.877e-08 -4.049e-08 b_price_best -6.636e-05 -1.254e-06 b_price_worst 2.400e-05 -1.2086e-04 b_char_double_best b_char_double_worst b_brand_Novum_best -9.396e-06 2.534e-05 b_brand_Novum_worst -4.222e-05 1.7183e-04 b_brand_BestValue_best 3.1121e-04 -1.9518e-04 b_brand_worstValue_worst 8.876e-06 4.3047e-04 b_brand_Supermarket_best 3.6970e-04 -2.0374e-04 b_brand_Supermarket_worst 5.688e-05 6.1894e-04 b_brand_PainAway_best 1.5739e-04 -1.0926e-04 b_brand_PainAway_worst 4.447e-05 4.4331e-04 b_country_CH_best 1.0687e-04 -4.817e-06 b_country_CH_worst -1.641e-05 4.232e-05 b_country_DK_best 4.424e-06 8.226e-06 b_country_DK_worst 6.047e-06 -6.346e-05 b_country_IND_best -5.716e-05 1.8013e-04 b_country_IND_worst -1.6544e-04 -1.7281e-04 b_country_RUS_best -8.703e-05 8.539e-05 b_country_RUS_worst -1.3585e-04 -6.043e-05 b_country_BRA_best -1.3930e-04 9.911e-05 b_country_BRA_worst -1.4328e-04 -1.1520e-04 b_char_fast_best 4.3530e-04 -3.896e-05 b_char_fast_worst 1.659e-05 3.8148e-04 b_char_double_best 0.001274 -8.457e-05 b_char_double_worst -8.457e-05 0.002673 b_risk_best 6.823e-10 1.071e-07 b_risk_worst 2.622e-08 -4.153e-08 b_price_best -1.0975e-04 2.028e-05 b_price_worst 1.712e-06 -1.0729e-04 b_risk_best b_risk_worst b_brand_Novum_best 1.190e-07 -4.144e-08 b_brand_Novum_worst -1.344e-07 -6.143e-08 b_brand_BestValue_best -5.210e-07 -7.485e-09 b_brand_worstValue_worst 6.259e-08 -4.812e-07 b_brand_Supermarket_best -6.423e-07 -3.825e-08 b_brand_Supermarket_worst 5.221e-08 -5.740e-07 b_brand_PainAway_best -3.210e-07 -2.246e-08 b_brand_PainAway_worst 3.838e-08 -3.797e-07 b_country_CH_best 1.979e-08 5.059e-08 b_country_CH_worst 1.061e-07 -7.433e-08 b_country_DK_best 1.125e-07 4.689e-08 b_country_DK_worst 1.249e-07 -1.795e-08 b_country_IND_best 3.047e-07 4.116e-08 b_country_IND_worst 9.295e-09 -7.258e-08 b_country_RUS_best 2.187e-07 5.975e-09 b_country_RUS_worst -2.083e-08 1.898e-07 b_country_BRA_best 1.329e-07 4.132e-08 b_country_BRA_worst -2.703e-08 2.803e-08 b_char_fast_best -1.318e-07 6.877e-08 b_char_fast_worst 9.796e-09 -4.049e-08 b_char_double_best 6.823e-10 2.622e-08 b_char_double_worst 1.071e-07 -4.153e-08 b_risk_best 3.304e-09 -1.019e-10 b_risk_worst -1.019e-10 1.265e-09 b_price_best 9.904e-08 -3.108e-09 b_price_worst -2.634e-08 8.876e-08 b_price_best b_price_worst b_brand_Novum_best 3.764e-05 -1.348e-05 b_brand_Novum_worst 5.816e-06 1.4086e-04 b_brand_BestValue_best 3.2054e-04 -6.295e-05 b_brand_worstValue_worst -2.858e-05 5.3287e-04 b_brand_Supermarket_best 2.9534e-04 -7.943e-05 b_brand_Supermarket_worst -2.394e-05 5.1816e-04 b_brand_PainAway_best 3.7438e-04 -9.635e-05 b_brand_PainAway_worst -1.595e-05 5.0680e-04 b_country_CH_best -7.239e-05 1.088e-05 b_country_CH_worst 2.642e-05 -1.4705e-04 b_country_DK_best -3.426e-05 5.731e-07 b_country_DK_worst 1.234e-05 5.400e-05 b_country_IND_best 4.109e-05 4.327e-05 b_country_IND_worst 2.023e-05 7.710e-05 b_country_RUS_best 1.038e-05 2.716e-05 b_country_RUS_worst 4.671e-05 1.0412e-04 b_country_BRA_best 5.608e-05 2.475e-05 b_country_BRA_worst 2.198e-05 1.2563e-04 b_char_fast_best -6.636e-05 2.400e-05 b_char_fast_worst -1.254e-06 -1.2086e-04 b_char_double_best -1.0975e-04 1.712e-06 b_char_double_worst 2.028e-05 -1.0729e-04 b_risk_best 9.904e-08 -2.634e-08 b_risk_worst -3.108e-09 8.876e-08 b_price_best 2.8799e-04 -2.243e-05 b_price_worst -2.243e-05 3.7175e-04 Classical correlation matrix: b_brand_Novum_best b_brand_Novum_worst b_brand_Novum_best 1.000000 -4.864e-12 b_brand_Novum_worst -4.864e-12 1.00000 b_brand_BestValue_best 0.243663 2.318e-12 b_brand_worstValue_worst -4.097e-12 0.39943 b_brand_Supermarket_best 0.297273 -6.935e-14 b_brand_Supermarket_worst -5.403e-12 0.40178 b_brand_PainAway_best 0.257101 9.074e-13 b_brand_PainAway_worst -4.347e-12 0.40145 b_country_CH_best -0.053734 7.503e-13 b_country_CH_worst -4.826e-12 -0.07517 b_country_DK_best -0.046709 3.604e-13 b_country_DK_worst -1.652e-12 -0.06370 b_country_IND_best -0.030436 -5.539e-12 b_country_IND_worst -7.055e-12 -0.02398 b_country_RUS_best -0.037163 -1.559e-12 b_country_RUS_worst -1.955e-13 0.01854 b_country_BRA_best -0.003842 -3.851e-12 b_country_BRA_worst 3.176e-13 0.01537 b_char_fast_best 0.015053 2.016e-13 b_char_fast_worst 7.884e-13 -0.03471 b_char_double_best 0.065061 2.254e-12 b_char_double_worst -1.940e-12 0.06952 b_risk_best 0.001136 2.579e-14 b_risk_worst 3.648e-12 0.03296 b_price_best 0.063980 -3.833e-12 b_price_worst 1.212e-12 0.14553 b_brand_BestValue_best b_brand_worstValue_worst b_brand_Novum_best 0.2437 -4.097e-12 b_brand_Novum_worst 2.318e-12 0.39943 b_brand_BestValue_best 1.0000 -8.894e-12 b_brand_worstValue_worst -8.894e-12 1.00000 b_brand_Supermarket_best 0.6941 -1.602e-11 b_brand_Supermarket_worst -8.721e-12 0.81567 b_brand_PainAway_best 0.6200 -8.066e-12 b_brand_PainAway_worst -6.824e-12 0.82465 b_country_CH_best 0.3113 -6.031e-12 b_country_CH_worst -1.514e-11 0.30850 b_country_DK_best 0.2866 -4.905e-12 b_country_DK_worst -2.317e-11 0.36653 b_country_IND_best -0.4272 8.133e-12 b_country_IND_worst -1.654e-11 -0.37424 b_country_RUS_best -0.4107 9.711e-12 b_country_RUS_worst -6.129e-12 -0.35989 b_country_BRA_best -0.3767 8.610e-12 b_country_BRA_worst -3.388e-12 -0.34499 b_char_fast_best 6.7096e-04 7.247e-12 b_char_fast_worst -3.696e-12 0.01056 b_char_double_best 0.1786 8.337e-13 b_char_double_worst -1.764e-12 0.16604 b_risk_best -0.1979 1.915e-12 b_risk_worst 5.889e-12 -0.13735 b_price_best 0.3027 -3.059e-12 b_price_worst -1.217e-12 0.37912 b_brand_Supermarket_best b_brand_Supermarket_worst b_brand_Novum_best 0.29727 -5.403e-12 b_brand_Novum_worst -6.935e-14 0.401777 b_brand_BestValue_best 0.69410 -8.721e-12 b_brand_worstValue_worst -1.602e-11 0.815674 b_brand_Supermarket_best 1.00000 -1.628e-11 b_brand_Supermarket_worst -1.628e-11 1.000000 b_brand_PainAway_best 0.63045 -8.034e-12 b_brand_PainAway_worst -1.420e-11 0.817417 b_country_CH_best 0.30362 -5.994e-12 b_country_CH_worst -1.932e-11 0.313620 b_country_DK_best 0.29936 -5.968e-12 b_country_DK_worst -2.867e-11 0.361111 b_country_IND_best -0.43843 6.805e-12 b_country_IND_worst -1.098e-11 -0.357642 b_country_RUS_best -0.41723 8.214e-12 b_country_RUS_worst -3.050e-12 -0.349370 b_country_BRA_best -0.44164 8.062e-12 b_country_BRA_worst 7.043e-13 -0.356890 b_char_fast_best 0.06167 6.333e-12 b_char_fast_worst -3.005e-12 0.008178 b_char_double_best 0.21148 1.416e-13 b_char_double_worst -3.475e-12 0.182253 b_risk_best -0.20703 1.851e-12 b_risk_worst 5.364e-12 -0.169227 b_price_best 0.27214 -3.092e-12 b_price_worst -2.417e-12 0.360950 b_brand_PainAway_best b_brand_PainAway_worst b_brand_Novum_best 0.25710 -4.347e-12 b_brand_Novum_worst 9.074e-13 0.40145 b_brand_BestValue_best 0.61996 -6.824e-12 b_brand_worstValue_worst -8.066e-12 0.82465 b_brand_Supermarket_best 0.63045 -1.420e-11 b_brand_Supermarket_worst -8.034e-12 0.81742 b_brand_PainAway_best 1.00000 -6.370e-12 b_brand_PainAway_worst -6.370e-12 1.00000 b_country_CH_best 0.24520 -4.297e-12 b_country_CH_worst -1.056e-11 0.32393 b_country_DK_best 0.24566 -3.272e-12 b_country_DK_worst -1.434e-11 0.38581 b_country_IND_best -0.37968 7.564e-12 b_country_IND_worst -5.033e-12 -0.38040 b_country_RUS_best -0.34613 8.655e-12 b_country_RUS_worst 2.329e-13 -0.36353 b_country_BRA_best -0.36259 7.846e-12 b_country_BRA_worst 2.910e-12 -0.36085 b_char_fast_best -0.03172 6.926e-12 b_char_fast_worst -3.512e-12 -0.05909 b_char_double_best 0.13670 1.098e-12 b_char_double_worst -1.452e-12 0.15812 b_risk_best -0.06966 1.490e-12 b_risk_worst 3.408e-12 -0.08301 b_price_best 0.34904 -2.378e-12 b_price_worst 1.150e-12 0.37815 b_country_CH_best b_country_CH_worst b_brand_Novum_best -0.053734 -4.826e-12 b_brand_Novum_worst 7.503e-13 -0.07517 b_brand_BestValue_best 0.311346 -1.514e-11 b_brand_worstValue_worst -6.031e-12 0.30850 b_brand_Supermarket_best 0.303617 -1.932e-11 b_brand_Supermarket_worst -5.994e-12 0.31362 b_brand_PainAway_best 0.245202 -1.056e-11 b_brand_PainAway_worst -4.297e-12 0.32393 b_country_CH_best 1.000000 1.369e-13 b_country_CH_worst 1.369e-13 1.00000 b_country_DK_best 0.496771 1.687e-12 b_country_DK_worst -4.816e-12 0.47369 b_country_IND_best 0.004139 1.845e-11 b_country_IND_worst 1.445e-13 -0.08169 b_country_RUS_best -0.028292 1.698e-11 b_country_RUS_worst 2.106e-12 -0.06958 b_country_BRA_best -0.036568 1.555e-11 b_country_BRA_worst 3.044e-12 -0.09573 b_char_fast_best 0.068251 4.865e-12 b_char_fast_worst -5.154e-13 0.14143 b_char_double_best 0.083519 -3.461e-12 b_char_double_worst -1.315e-12 0.03132 b_risk_best -0.061253 3.450e-12 b_risk_worst 3.152e-12 -0.03362 b_price_best -0.113414 -1.483e-12 b_price_worst -3.207e-12 -0.16973 b_country_DK_best b_country_DK_worst b_brand_Novum_best -0.046709 -1.652e-12 b_brand_Novum_worst 3.604e-13 -0.063700 b_brand_BestValue_best 0.286576 -2.317e-11 b_brand_worstValue_worst -4.905e-12 0.366533 b_brand_Supermarket_best 0.299363 -2.867e-11 b_brand_Supermarket_worst -5.968e-12 0.361111 b_brand_PainAway_best 0.245664 -1.434e-11 b_brand_PainAway_worst -3.272e-12 0.385807 b_country_CH_best 0.496771 -4.816e-12 b_country_CH_worst 1.687e-12 0.473693 b_country_DK_best 1.000000 -1.695e-12 b_country_DK_worst -1.695e-12 1.000000 b_country_IND_best 0.043369 2.847e-11 b_country_IND_worst 1.078e-12 -0.022083 b_country_RUS_best 0.004773 2.815e-11 b_country_RUS_worst 2.396e-12 -0.033660 b_country_BRA_best 0.001867 2.341e-11 b_country_BRA_worst 3.820e-12 -0.087023 b_char_fast_best 0.030265 5.563e-12 b_char_fast_worst -7.142e-13 0.120480 b_char_double_best 0.021427 -8.193e-12 b_char_double_worst -1.882e-12 0.007745 b_risk_best -0.024679 6.495e-12 b_risk_worst 4.234e-12 -0.024485 b_price_best -0.044111 3.395e-12 b_price_worst -2.062e-12 -0.011201 b_country_IND_best b_country_IND_worst b_brand_Novum_best -0.030436 -7.055e-12 b_brand_Novum_worst -5.539e-12 -0.02398 b_brand_BestValue_best -0.427239 -1.654e-11 b_brand_worstValue_worst 8.133e-12 -0.37424 b_brand_Supermarket_best -0.438427 -1.098e-11 b_brand_Supermarket_worst 6.805e-12 -0.35764 b_brand_PainAway_best -0.379678 -5.033e-12 b_brand_PainAway_worst 7.564e-12 -0.38040 b_country_CH_best 0.004139 1.445e-13 b_country_CH_worst 1.845e-11 -0.08169 b_country_DK_best 0.043369 1.078e-12 b_country_DK_worst 2.847e-11 -0.02208 b_country_IND_best 1.000000 7.785e-12 b_country_IND_worst 7.785e-12 1.00000 b_country_RUS_best 0.445409 1.015e-11 b_country_RUS_worst 2.609e-12 0.53202 b_country_BRA_best 0.466378 6.204e-12 b_country_BRA_worst 4.071e-13 0.54339 b_char_fast_best -0.062867 -1.291e-11 b_char_fast_worst 4.580e-12 -0.05275 b_char_double_best -0.032131 -1.496e-11 b_char_double_worst 9.253e-13 -0.01304 b_risk_best 0.052470 6.047e-12 b_risk_worst -8.333e-13 -0.03163 b_price_best 0.033579 3.603e-12 b_price_worst -1.924e-12 0.06406 b_country_RUS_best b_country_RUS_worst b_brand_Novum_best -0.037163 -1.955e-13 b_brand_Novum_worst -1.559e-12 0.01854 b_brand_BestValue_best -0.410692 -6.129e-12 b_brand_worstValue_worst 9.711e-12 -0.35989 b_brand_Supermarket_best -0.417227 -3.050e-12 b_brand_Supermarket_worst 8.214e-12 -0.34937 b_brand_PainAway_best -0.346133 2.329e-13 b_brand_PainAway_worst 8.655e-12 -0.36353 b_country_CH_best -0.028292 2.106e-12 b_country_CH_worst 1.698e-11 -0.06958 b_country_DK_best 0.004773 2.396e-12 b_country_DK_worst 2.815e-11 -0.03366 b_country_IND_best 0.445409 2.609e-12 b_country_IND_worst 1.015e-11 0.53202 b_country_RUS_best 1.000000 6.790e-12 b_country_RUS_worst 6.790e-12 1.00000 b_country_BRA_best 0.420087 2.860e-12 b_country_BRA_worst 3.812e-12 0.55677 b_char_fast_best -0.062615 -7.459e-12 b_char_fast_worst 2.503e-12 -0.10886 b_char_double_best -0.028126 -7.495e-12 b_char_double_worst 7.459e-14 -0.03183 b_risk_best 0.050833 3.311e-12 b_risk_worst -1.498e-12 0.08583 b_price_best 0.039431 3.346e-12 b_price_worst 1.246e-12 0.12884 b_country_BRA_best b_country_BRA_worst b_brand_Novum_best -0.003842 3.176e-13 b_brand_Novum_worst -3.851e-12 0.015366 b_brand_BestValue_best -0.376739 -3.388e-12 b_brand_worstValue_worst 8.610e-12 -0.344987 b_brand_Supermarket_best -0.441635 7.043e-13 b_brand_Supermarket_worst 8.062e-12 -0.356890 b_brand_PainAway_best -0.362589 2.910e-12 b_brand_PainAway_worst 7.846e-12 -0.360850 b_country_CH_best -0.036568 3.044e-12 b_country_CH_worst 1.555e-11 -0.095734 b_country_DK_best 0.001867 3.820e-12 b_country_DK_worst 2.341e-11 -0.087023 b_country_IND_best 0.466378 4.071e-13 b_country_IND_worst 6.204e-12 0.543391 b_country_RUS_best 0.420087 3.812e-12 b_country_RUS_worst 2.860e-12 0.556774 b_country_BRA_best 1.000000 1.022e-12 b_country_BRA_worst 1.022e-12 1.000000 b_char_fast_best -0.072453 -7.134e-12 b_char_fast_worst 4.198e-12 -0.068899 b_char_double_best -0.044938 -5.996e-12 b_char_double_worst 1.364e-12 -0.044963 b_risk_best 0.028992 1.756e-12 b_risk_worst -1.662e-12 0.002940 b_price_best 0.069802 2.819e-12 b_price_worst 2.803e-13 0.143873 b_char_fast_best b_char_fast_worst b_brand_Novum_best 0.01505 7.884e-13 b_brand_Novum_worst 2.016e-13 -0.034713 b_brand_BestValue_best 6.7096e-04 -3.696e-12 b_brand_worstValue_worst 7.247e-12 0.010562 b_brand_Supermarket_best 0.06167 -3.005e-12 b_brand_Supermarket_worst 6.333e-12 0.008178 b_brand_PainAway_best -0.03172 -3.512e-12 b_brand_PainAway_worst 6.926e-12 -0.059094 b_country_CH_best 0.06825 -5.154e-13 b_country_CH_worst 4.865e-12 0.141428 b_country_DK_best 0.03027 -7.142e-13 b_country_DK_worst 5.563e-12 0.120480 b_country_IND_best -0.06287 4.580e-12 b_country_IND_worst -1.291e-11 -0.052753 b_country_RUS_best -0.06262 2.503e-12 b_country_RUS_worst -7.459e-12 -0.108862 b_country_BRA_best -0.07245 4.198e-12 b_country_BRA_worst -7.134e-12 -0.068899 b_char_fast_best 1.00000 3.714e-12 b_char_fast_worst 3.714e-12 1.000000 b_char_double_best 0.45286 2.284e-12 b_char_double_worst 1.069e-12 0.243685 b_risk_best -0.07500 5.321e-13 b_risk_worst 8.667e-13 -0.085565 b_price_best -0.13253 -1.377e-12 b_price_worst -1.068e-12 -0.211041 b_char_double_best b_char_double_worst b_brand_Novum_best 0.06506 -1.940e-12 b_brand_Novum_worst 2.254e-12 0.069523 b_brand_BestValue_best 0.17858 -1.764e-12 b_brand_worstValue_worst 8.337e-13 0.166041 b_brand_Supermarket_best 0.21148 -3.475e-12 b_brand_Supermarket_worst 1.416e-13 0.182253 b_brand_PainAway_best 0.13670 -1.452e-12 b_brand_PainAway_worst 1.098e-12 0.158117 b_country_CH_best 0.08352 -1.315e-12 b_country_CH_worst -3.461e-12 0.031323 b_country_DK_best 0.02143 -1.882e-12 b_country_DK_worst -8.193e-12 0.007745 b_country_IND_best -0.03213 9.253e-13 b_country_IND_worst -1.496e-11 -0.013045 b_country_RUS_best -0.02813 7.459e-14 b_country_RUS_worst -7.495e-12 -0.031829 b_country_BRA_best -0.04494 1.364e-12 b_country_BRA_worst -5.996e-12 -0.044963 b_char_fast_best 0.45286 1.069e-12 b_char_fast_worst 2.284e-12 0.243685 b_char_double_best 1.00000 -2.105e-13 b_char_double_worst -2.105e-13 1.000000 b_risk_best -0.04469 -6.908e-13 b_risk_worst 2.279e-12 -0.035763 b_price_best -0.16229 -6.506e-13 b_price_worst -1.670e-12 -0.109443 b_risk_best b_risk_worst b_brand_Novum_best 0.001136 3.648e-12 b_brand_Novum_worst 2.579e-14 0.032959 b_brand_BestValue_best -0.197859 5.889e-12 b_brand_worstValue_worst 1.915e-12 -0.137352 b_brand_Supermarket_best -0.207033 5.364e-12 b_brand_Supermarket_worst 1.851e-12 -0.169227 b_brand_PainAway_best -0.069660 3.408e-12 b_brand_PainAway_worst 1.490e-12 -0.083013 b_country_CH_best -0.061253 3.152e-12 b_country_CH_worst 3.450e-12 -0.033617 b_country_DK_best -0.024679 4.234e-12 b_country_DK_worst 6.495e-12 -0.024485 b_country_IND_best 0.052470 -8.333e-13 b_country_IND_worst 6.047e-12 -0.031632 b_country_RUS_best 0.050833 -1.498e-12 b_country_RUS_worst 3.311e-12 0.085827 b_country_BRA_best 0.028992 -1.662e-12 b_country_BRA_worst 1.756e-12 0.002940 b_char_fast_best -0.074999 8.667e-13 b_char_fast_worst 5.321e-13 -0.085565 b_char_double_best -0.044686 2.279e-12 b_char_double_worst -6.908e-13 -0.035763 b_risk_best 1.000000 -5.447e-13 b_risk_worst -5.447e-13 1.000000 b_price_best 0.115957 9.955e-13 b_price_worst 1.741e-12 0.218281 b_price_best b_price_worst b_brand_Novum_best 0.06398 1.212e-12 b_brand_Novum_worst -3.833e-12 0.14553 b_brand_BestValue_best 0.30266 -1.217e-12 b_brand_worstValue_worst -3.059e-12 0.37912 b_brand_Supermarket_best 0.27214 -2.417e-12 b_brand_Supermarket_worst -3.092e-12 0.36095 b_brand_PainAway_best 0.34904 1.150e-12 b_brand_PainAway_worst -2.378e-12 0.37815 b_country_CH_best -0.11341 -3.207e-12 b_country_CH_worst -1.483e-12 -0.16973 b_country_DK_best -0.04411 -2.062e-12 b_country_DK_worst 3.395e-12 -0.01120 b_country_IND_best 0.03358 -1.924e-12 b_country_IND_worst 3.603e-12 0.06406 b_country_RUS_best 0.03943 1.246e-12 b_country_RUS_worst 3.346e-12 0.12884 b_country_BRA_best 0.06980 2.803e-13 b_country_BRA_worst 2.819e-12 0.14387 b_char_fast_best -0.13253 -1.068e-12 b_char_fast_worst -1.377e-12 -0.21104 b_char_double_best -0.16229 -1.670e-12 b_char_double_worst -6.506e-13 -0.10944 b_risk_best 0.11596 1.741e-12 b_risk_worst 9.955e-13 0.21828 b_price_best 1.00000 1.220e-12 b_price_worst 1.220e-12 1.00000 Robust correlation matrix: b_brand_Novum_best b_brand_Novum_worst b_brand_Novum_best 1.000000 -0.036950 b_brand_Novum_worst -0.036950 1.000000 b_brand_BestValue_best 0.228874 -0.070490 b_brand_worstValue_worst -0.028438 0.400541 b_brand_Supermarket_best 0.271719 -0.020569 b_brand_Supermarket_worst -0.017342 0.405258 b_brand_PainAway_best 0.206313 0.004709 b_brand_PainAway_worst -0.021090 0.391645 b_country_CH_best -0.093544 -0.049902 b_country_CH_worst -0.005238 -0.054372 b_country_DK_best -0.039232 -0.064079 b_country_DK_worst 0.011758 -0.061024 b_country_IND_best -0.041026 0.044871 b_country_IND_worst 0.001338 0.018399 b_country_RUS_best -0.033269 0.047494 b_country_RUS_worst -0.003229 0.009842 b_country_BRA_best 0.012772 0.031032 b_country_BRA_worst 0.030662 0.008005 b_char_fast_best -0.060292 -0.010099 b_char_fast_worst 0.016385 -0.053829 b_char_double_best -0.008429 -0.028442 b_char_double_worst 0.015700 0.079926 b_risk_best 0.066326 -0.056243 b_risk_worst -0.037312 -0.041531 b_price_best 0.071027 0.008242 b_price_worst -0.022390 0.175681 b_brand_BestValue_best b_brand_worstValue_worst b_brand_Novum_best 0.228874 -0.028438 b_brand_Novum_worst -0.070490 0.400541 b_brand_BestValue_best 1.000000 0.010907 b_brand_worstValue_worst 0.010907 1.000000 b_brand_Supermarket_best 0.695652 0.039091 b_brand_Supermarket_worst 0.023603 0.838591 b_brand_PainAway_best 0.651435 0.018361 b_brand_PainAway_worst 0.028885 0.842959 b_country_CH_best 0.238323 -0.029927 b_country_CH_worst 0.003183 0.336702 b_country_DK_best 0.198888 -0.056891 b_country_DK_worst 0.015480 0.391066 b_country_IND_best -0.437139 0.056214 b_country_IND_worst 0.007219 -0.365487 b_country_RUS_best -0.448461 0.028211 b_country_RUS_worst 0.006125 -0.367841 b_country_BRA_best -0.389077 0.028247 b_country_BRA_worst -0.012783 -0.349997 b_char_fast_best -0.006882 0.005200 b_char_fast_worst -0.001595 -0.040063 b_char_double_best 0.138429 0.003605 b_char_double_worst -0.059946 0.120722 b_risk_best -0.143926 0.015789 b_risk_worst -0.003342 -0.196130 b_price_best 0.299931 -0.024419 b_price_worst -0.051846 0.400706 b_brand_Supermarket_best b_brand_Supermarket_worst b_brand_Novum_best 0.271719 -0.017342 b_brand_Novum_worst -0.020569 0.405258 b_brand_BestValue_best 0.695652 0.023603 b_brand_worstValue_worst 0.039091 0.838591 b_brand_Supermarket_best 1.000000 0.052505 b_brand_Supermarket_worst 0.052505 1.000000 b_brand_PainAway_best 0.672671 0.008454 b_brand_PainAway_worst 0.055482 0.825784 b_country_CH_best 0.242118 -0.034282 b_country_CH_worst -0.005374 0.345383 b_country_DK_best 0.235340 -0.068310 b_country_DK_worst 0.023903 0.376520 b_country_IND_best -0.430705 0.043138 b_country_IND_worst 0.008585 -0.342573 b_country_RUS_best -0.412456 0.007491 b_country_RUS_worst -0.001517 -0.355949 b_country_BRA_best -0.465520 0.012686 b_country_BRA_worst 0.017494 -0.347484 b_char_fast_best 0.064523 0.005171 b_char_fast_worst -7.736e-05 -0.014655 b_char_double_best 0.156743 0.021843 b_char_double_worst -0.059645 0.164112 b_risk_best -0.169143 0.012452 b_risk_worst -0.016275 -0.221237 b_price_best 0.263406 -0.019338 b_price_worst -0.062349 0.368398 b_brand_PainAway_best b_brand_PainAway_worst b_brand_Novum_best 0.206313 -0.021090 b_brand_Novum_worst 0.004709 0.391645 b_brand_BestValue_best 0.651435 0.028885 b_brand_worstValue_worst 0.018361 0.842959 b_brand_Supermarket_best 0.672671 0.055482 b_brand_Supermarket_worst 0.008454 0.825784 b_brand_PainAway_best 1.000000 0.027391 b_brand_PainAway_worst 0.027391 1.000000 b_country_CH_best 0.191947 -0.006803 b_country_CH_worst 0.002258 0.359145 b_country_DK_best 0.202117 -0.030319 b_country_DK_worst -0.011680 0.417847 b_country_IND_best -0.364747 0.070063 b_country_IND_worst 0.035876 -0.379355 b_country_RUS_best -0.379995 0.017994 b_country_RUS_worst 0.037220 -0.381721 b_country_BRA_best -0.354932 0.030479 b_country_BRA_worst 0.018826 -0.367301 b_char_fast_best -0.027056 -0.005615 b_char_fast_worst 0.055136 -0.086805 b_char_double_best 0.068779 0.017555 b_char_double_worst -0.032969 0.120855 b_risk_best -0.087119 0.009410 b_risk_worst -0.009849 -0.150476 b_price_best 0.344146 -0.013244 b_price_worst -0.077953 0.370470 b_country_CH_best b_country_CH_worst b_brand_Novum_best -0.093544 -0.005238 b_brand_Novum_worst -0.049902 -0.054372 b_brand_BestValue_best 0.238323 0.003183 b_brand_worstValue_worst -0.029927 0.336702 b_brand_Supermarket_best 0.242118 -0.005374 b_brand_Supermarket_worst -0.034282 0.345383 b_brand_PainAway_best 0.191947 0.002258 b_brand_PainAway_worst -0.006803 0.359145 b_country_CH_best 1.000000 2.0507e-04 b_country_CH_worst 2.0507e-04 1.000000 b_country_DK_best 0.472391 -0.030180 b_country_DK_worst 0.022290 0.498102 b_country_IND_best -0.010413 0.029552 b_country_IND_worst 0.023168 -0.120220 b_country_RUS_best -0.064879 -0.024012 b_country_RUS_worst 0.006479 -0.071801 b_country_BRA_best -0.037985 0.007093 b_country_BRA_worst -0.003013 -0.087809 b_char_fast_best 0.095846 -0.042184 b_char_fast_worst 0.001208 0.092968 b_char_double_best 0.078711 -0.008472 b_char_double_worst -0.002450 0.015087 b_risk_best 0.009055 0.034025 b_risk_worst 0.037399 -0.038512 b_price_best -0.112151 0.028690 b_price_worst 0.014840 -0.140555 b_country_DK_best b_country_DK_worst b_brand_Novum_best -0.039232 0.011758 b_brand_Novum_worst -0.064079 -0.061024 b_brand_BestValue_best 0.198888 0.015480 b_brand_worstValue_worst -0.056891 0.391066 b_brand_Supermarket_best 0.235340 0.023903 b_brand_Supermarket_worst -0.068310 0.376520 b_brand_PainAway_best 0.202117 -0.011680 b_brand_PainAway_worst -0.030319 0.417847 b_country_CH_best 0.472391 0.022290 b_country_CH_worst -0.030180 0.498102 b_country_DK_best 1.000000 0.003093 b_country_DK_worst 0.003093 1.000000 b_country_IND_best 0.030663 0.012563 b_country_IND_worst 0.012404 -0.025073 b_country_RUS_best -0.005945 -0.043417 b_country_RUS_worst 0.050197 -0.062208 b_country_BRA_best -0.001326 0.002375 b_country_BRA_worst 6.0751e-04 -0.093559 b_char_fast_best 0.010702 -0.003727 b_char_fast_worst -0.006757 0.077736 b_char_double_best 0.003377 0.003244 b_char_double_worst 0.004336 -0.023509 b_risk_best 0.053328 0.041611 b_risk_worst 0.035920 -0.009666 b_price_best -0.055015 0.013928 b_price_worst 8.0994e-04 0.053639 b_country_IND_best b_country_IND_worst b_brand_Novum_best -0.041026 0.001338 b_brand_Novum_worst 0.044871 0.018399 b_brand_BestValue_best -0.437139 0.007219 b_brand_worstValue_worst 0.056214 -0.365487 b_brand_Supermarket_best -0.430705 0.008585 b_brand_Supermarket_worst 0.043138 -0.342573 b_brand_PainAway_best -0.364747 0.035876 b_brand_PainAway_worst 0.070063 -0.379355 b_country_CH_best -0.010413 0.023168 b_country_CH_worst 0.029552 -0.120220 b_country_DK_best 0.030663 0.012404 b_country_DK_worst 0.012563 -0.025073 b_country_IND_best 1.000000 0.009825 b_country_IND_worst 0.009825 1.000000 b_country_RUS_best 0.396879 -0.016545 b_country_RUS_worst 0.030064 0.524926 b_country_BRA_best 0.495533 -0.025517 b_country_BRA_worst -4.9053e-04 0.534270 b_char_fast_best -0.080030 0.011801 b_char_fast_worst -0.020280 -0.062940 b_char_double_best -0.028414 -0.094184 b_char_double_worst 0.061833 -0.067931 b_risk_best 0.094069 0.003287 b_risk_worst 0.020539 -0.041471 b_price_best 0.042975 0.024222 b_price_worst 0.039833 0.081270 b_country_RUS_best b_country_RUS_worst b_brand_Novum_best -0.033269 -0.003229 b_brand_Novum_worst 0.047494 0.009842 b_brand_BestValue_best -0.448461 0.006125 b_brand_worstValue_worst 0.028211 -0.367841 b_brand_Supermarket_best -0.412456 -0.001517 b_brand_Supermarket_worst 0.007491 -0.355949 b_brand_PainAway_best -0.379995 0.037220 b_brand_PainAway_worst 0.017994 -0.381721 b_country_CH_best -0.064879 0.006479 b_country_CH_worst -0.024012 -0.071801 b_country_DK_best -0.005945 0.050197 b_country_DK_worst -0.043417 -0.062208 b_country_IND_best 0.396879 0.030064 b_country_IND_worst -0.016545 0.524926 b_country_RUS_best 1.000000 0.005926 b_country_RUS_worst 0.005926 1.000000 b_country_BRA_best 0.487489 -0.014272 b_country_BRA_worst 0.012557 0.568176 b_char_fast_best -0.088910 -0.033370 b_char_fast_worst -0.022168 -0.114199 b_char_double_best -0.041385 -0.084921 b_char_double_worst 0.028038 -0.026085 b_risk_best 0.064597 -0.008088 b_risk_worst 0.002852 0.119066 b_price_best 0.010384 0.061419 b_price_worst 0.023909 0.120501 b_country_BRA_best b_country_BRA_worst b_brand_Novum_best 0.012772 0.030662 b_brand_Novum_worst 0.031032 0.008005 b_brand_BestValue_best -0.389077 -0.012783 b_brand_worstValue_worst 0.028247 -0.349997 b_brand_Supermarket_best -0.465520 0.017494 b_brand_Supermarket_worst 0.012686 -0.347484 b_brand_PainAway_best -0.354932 0.018826 b_brand_PainAway_worst 0.030479 -0.367301 b_country_CH_best -0.037985 -0.003013 b_country_CH_worst 0.007093 -0.087809 b_country_DK_best -0.001326 6.0751e-04 b_country_DK_worst 0.002375 -0.093559 b_country_IND_best 0.495533 -4.9053e-04 b_country_IND_worst -0.025517 0.534270 b_country_RUS_best 0.487489 0.012557 b_country_RUS_worst -0.014272 0.568176 b_country_BRA_best 1.000000 -0.022003 b_country_BRA_worst -0.022003 1.000000 b_char_fast_best -0.113108 -1.5239e-04 b_char_fast_worst -0.014290 -0.064703 b_char_double_best -0.065424 -0.082680 b_char_double_worst 0.032140 -0.045900 b_risk_best 0.038763 -0.009686 b_risk_worst 0.019476 0.016234 b_price_best 0.055410 0.026687 b_price_worst 0.021522 0.134221 b_char_fast_best b_char_fast_worst b_brand_Novum_best -0.060292 0.016385 b_brand_Novum_worst -0.010099 -0.053829 b_brand_BestValue_best -0.006882 -0.001595 b_brand_worstValue_worst 0.005200 -0.040063 b_brand_Supermarket_best 0.064523 -7.736e-05 b_brand_Supermarket_worst 0.005171 -0.014655 b_brand_PainAway_best -0.027056 0.055136 b_brand_PainAway_worst -0.005615 -0.086805 b_country_CH_best 0.095846 0.001208 b_country_CH_worst -0.042184 0.092968 b_country_DK_best 0.010702 -0.006757 b_country_DK_worst -0.003727 0.077736 b_country_IND_best -0.080030 -0.020280 b_country_IND_worst 0.011801 -0.062940 b_country_RUS_best -0.088910 -0.022168 b_country_RUS_worst -0.033370 -0.114199 b_country_BRA_best -0.113108 -0.014290 b_country_BRA_worst -1.5239e-04 -0.064703 b_char_fast_best 1.000000 -0.028866 b_char_fast_worst -0.028866 1.000000 b_char_double_best 0.437735 0.016334 b_char_double_worst -0.027051 0.259278 b_risk_best -0.082321 0.005989 b_risk_worst 0.069404 -0.039996 b_price_best -0.140369 -0.002597 b_price_worst 0.044690 -0.220264 b_char_double_best b_char_double_worst b_brand_Novum_best -0.008429 0.015700 b_brand_Novum_worst -0.028442 0.079926 b_brand_BestValue_best 0.138429 -0.059946 b_brand_worstValue_worst 0.003605 0.120722 b_brand_Supermarket_best 0.156743 -0.059645 b_brand_Supermarket_worst 0.021843 0.164112 b_brand_PainAway_best 0.068779 -0.032969 b_brand_PainAway_worst 0.017555 0.120855 b_country_CH_best 0.078711 -0.002450 b_country_CH_worst -0.008472 0.015087 b_country_DK_best 0.003377 0.004336 b_country_DK_worst 0.003244 -0.023509 b_country_IND_best -0.028414 0.061833 b_country_IND_worst -0.094184 -0.067931 b_country_RUS_best -0.041385 0.028038 b_country_RUS_worst -0.084921 -0.026085 b_country_BRA_best -0.065424 0.032140 b_country_BRA_worst -0.082680 -0.045900 b_char_fast_best 0.437735 -0.027051 b_char_fast_worst 0.016334 0.259278 b_char_double_best 1.000000 -0.045824 b_char_double_worst -0.045824 1.000000 b_risk_best 3.3250e-04 0.036030 b_risk_worst 0.020646 -0.022586 b_price_best -0.181153 0.023120 b_price_worst 0.002487 -0.107636 b_risk_best b_risk_worst b_brand_Novum_best 0.066326 -0.037312 b_brand_Novum_worst -0.056243 -0.041531 b_brand_BestValue_best -0.143926 -0.003342 b_brand_worstValue_worst 0.015789 -0.196130 b_brand_Supermarket_best -0.169143 -0.016275 b_brand_Supermarket_worst 0.012452 -0.221237 b_brand_PainAway_best -0.087119 -0.009849 b_brand_PainAway_worst 0.009410 -0.150476 b_country_CH_best 0.009055 0.037399 b_country_CH_worst 0.034025 -0.038512 b_country_DK_best 0.053328 0.035920 b_country_DK_worst 0.041611 -0.009666 b_country_IND_best 0.094069 0.020539 b_country_IND_worst 0.003287 -0.041471 b_country_RUS_best 0.064597 0.002852 b_country_RUS_worst -0.008088 0.119066 b_country_BRA_best 0.038763 0.019476 b_country_BRA_worst -0.009686 0.016234 b_char_fast_best -0.082321 0.069404 b_char_fast_worst 0.005989 -0.039996 b_char_double_best 3.3250e-04 0.020646 b_char_double_worst 0.036030 -0.022586 b_risk_best 1.000000 -0.049859 b_risk_worst -0.049859 1.000000 b_price_best 0.101535 -0.005148 b_price_worst -0.023765 0.129419 b_price_best b_price_worst b_brand_Novum_best 0.071027 -0.022390 b_brand_Novum_worst 0.008242 0.175681 b_brand_BestValue_best 0.299931 -0.051846 b_brand_worstValue_worst -0.024419 0.400706 b_brand_Supermarket_best 0.263406 -0.062349 b_brand_Supermarket_worst -0.019338 0.368398 b_brand_PainAway_best 0.344146 -0.077953 b_brand_PainAway_worst -0.013244 0.370470 b_country_CH_best -0.112151 0.014840 b_country_CH_worst 0.028690 -0.140555 b_country_DK_best -0.055015 8.0994e-04 b_country_DK_worst 0.013928 0.053639 b_country_IND_best 0.042975 0.039833 b_country_IND_worst 0.024222 0.081270 b_country_RUS_best 0.010384 0.023909 b_country_RUS_worst 0.061419 0.120501 b_country_BRA_best 0.055410 0.021522 b_country_BRA_worst 0.026687 0.134221 b_char_fast_best -0.140369 0.044690 b_char_fast_worst -0.002597 -0.220264 b_char_double_best -0.181153 0.002487 b_char_double_worst 0.023120 -0.107636 b_risk_best 0.101535 -0.023765 b_risk_worst -0.005148 0.129419 b_price_best 1.000000 -0.068559 b_price_worst -0.068559 1.000000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 593 0.04419081 875 0.04709950 367 0.04763586 859 0.05609218 947 0.05645199 499 0.05874615 476 0.05891200 933 0.06078124 678 0.06128873 70 0.06129397 8 0.06333876 288 0.06372274 240 0.06375514 565 0.06376885 163 0.06410289 1000 0.06416929 524 0.06418130 118 0.06421143 127 0.06493393 287 0.06515614 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Best-worst model on drug choice data, using different parameters for best and worst choices" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "BW_joint_model_diff_params" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" 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_best 0.269840040 b_brand_Novum_worst 0.285961152 b_brand_BestValue_best 0.461959261 b_brand_worstValue_worst 0.586512365 b_brand_Supermarket_best 0.154960300 b_brand_Supermarket_worst 0.418166331 b_brand_PainAway_best 1.099518292 b_brand_PainAway_worst 0.977448123 b_country_CH_best 0.642622755 b_country_CH_worst 0.319067370 b_country_DK_best 0.330873729 b_country_DK_worst 0.098947944 b_country_IND_best 0.305614738 b_country_IND_worst 0.091536064 b_country_RUS_best 0.849571077 b_country_RUS_worst 0.540562570 b_country_BRA_best 0.632877180 b_country_BRA_worst 0.342120878 b_char_fast_best 0.739516761 b_char_fast_worst 0.462362634 b_char_double_best 1.171769902 b_char_double_worst 0.715424894 b_risk_best 0.001528073 b_risk_worst 0.001037535 b_price_best 0.704463004 b_price_worst 0.512147975 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() ### List of utilities for the "best" choice V_best = list() V_best[["alt1"]] = ( b_brand_Artemis_best*(brand_1=="Artemis") + b_brand_Novum_best*(brand_1=="Novum") + b_country_CH_best*(country_1=="Switzerland") + b_country_DK_best*(country_1=="Denmark") + b_country_USA_best*(country_1=="USA") + b_char_standard_best*(char_1=="standard") + b_char_fast_best*(char_1=="fast acting") + b_char_double_best*(char_1=="double strength") + b_risk_best*side_effects_1 + b_price_best*price_1) V_best[["alt2"]] = ( b_brand_Artemis_best*(brand_2=="Artemis") + b_brand_Novum_best*(brand_2=="Novum") + b_country_CH_best*(country_2=="Switzerland") + b_country_DK_best*(country_2=="Denmark") + b_country_USA_best*(country_2=="USA") + b_char_standard_best*(char_2=="standard") + b_char_fast_best*(char_2=="fast acting") + b_char_double_best*(char_2=="double strength") + b_risk_best*side_effects_2 + b_price_best*price_2) V_best[["alt3"]] = ( b_brand_BestValue_best*(brand_3=="BestValue") + b_brand_Supermarket_best*(brand_3=="Supermarket") + b_brand_PainAway_best*(brand_3=="PainAway") + b_country_USA_best*(country_3=="USA") + b_country_IND_best*(country_3=="India") + b_country_RUS_best*(country_3=="Russia") + b_country_BRA_best*(country_3=="Brazil") + b_char_standard_best*(char_3=="standard") + b_char_fast_best*(char_3=="fast acting") + b_risk_best*side_effects_3 + b_price_best*price_3 ) V_best[["alt4"]] = ( b_brand_BestValue_best*(brand_4=="BestValue") + b_brand_Supermarket_best*(brand_4=="Supermarket") + b_brand_PainAway_best*(brand_4=="PainAway") + b_country_USA_best*(country_4=="USA") + b_country_IND_best*(country_4=="India") + b_country_RUS_best*(country_4=="Russia") + b_country_BRA_best*(country_4=="Brazil") + b_char_standard_best*(char_4=="standard") + b_char_fast_best*(char_4=="fast acting") + b_risk_best*side_effects_4 + b_price_best*price_4 ) ### Compute probabilities for "best" choice using MNL model mnl_settings_best = 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_best ) P[["choice_best"]] = apollo_mnl(mnl_settings_best, functionality) ### List of utilities for the "worse" choice V_worst = list() V_worst[["alt1"]] = ( b_brand_Artemis_worst*(brand_1=="Artemis") + b_brand_Novum_worst*(brand_1=="Novum") + b_country_CH_worst*(country_1=="Switzerland") + b_country_DK_worst*(country_1=="Denmark") + b_country_USA_worst*(country_1=="USA") + b_char_standard_worst*(char_1=="standard") + b_char_fast_worst*(char_1=="fast acting") + b_char_double_worst*(char_1=="double strength") + b_risk_worst*side_effects_1 + b_price_worst*price_1) V_worst[["alt2"]] = ( b_brand_Artemis_worst*(brand_2=="Artemis") + b_brand_Novum_worst*(brand_2=="Novum") + b_country_CH_worst*(country_2=="Switzerland") + b_country_DK_worst*(country_2=="Denmark") + b_country_USA_worst*(country_2=="USA") + b_char_standard_worst*(char_2=="standard") + b_char_fast_worst*(char_2=="fast acting") + b_char_double_worst*(char_2=="double strength") + b_risk_worst*side_effects_2 + b_price_worst*price_2) V_worst[["alt3"]] = ( b_brand_worstValue_worst*(brand_3=="BestValue") + b_brand_Supermarket_worst*(brand_3=="Supermarket") + b_brand_PainAway_worst*(brand_3=="PainAway") + b_country_USA_worst*(country_3=="USA") + b_country_IND_worst*(country_3=="India") + b_country_RUS_worst*(country_3=="Russia") + b_country_BRA_worst*(country_3=="Brazil") + b_char_standard_worst*(char_3=="standard") + b_char_fast_worst*(char_3=="fast acting") + b_risk_worst*side_effects_3 + b_price_worst*price_3 ) V_worst[["alt4"]] = ( b_brand_worstValue_worst*(brand_4=="BestValue") + b_brand_Supermarket_worst*(brand_4=="Supermarket") + b_brand_PainAway_worst*(brand_4=="PainAway") + b_country_USA_worst*(country_4=="USA") + b_country_IND_worst*(country_4=="India") + b_country_RUS_worst*(country_4=="Russia") + b_country_BRA_worst*(country_4=="Brazil") + b_char_standard_worst*(char_4=="standard") + b_char_fast_worst*(char_4=="fast acting") + b_risk_worst*side_effects_4 + b_price_worst*price_4 ) ### Compute probabilities for "worst" choice using MNL model mnl_settings_worst = list( alternatives = c(alt1=1, alt2=2, alt3=3, alt4=4), avail = list(alt1=(best!=1), alt2=(best!=2), alt3=(best!=3), alt4=(best!=4)), choiceVar = worst, utilities = list(alt1 = -V_worst[["alt1"]], alt2 = -V_worst[["alt2"]], alt3 = -V_worst[["alt3"]], alt4 = -V_worst[["alt4"]]) ) P[["choice_worst"]] = apollo_mnl(mnl_settings_worst, functionality) ### Combined model P = apollo_combineModels(P, apollo_inputs, functionality) ### Take product across observation for same individual P = apollo_panelProd(P, apollo_inputs, functionality) ### Prepare and return outputs of function P = apollo_prepareProb(P, apollo_inputs, functionality) return(P) }