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 : MDCEV_with_outside_good Model description : MDCEV model on time use data, alpha-gamma profile with outside good and socio-demographics Model run at : 2025-09-19 11:49:39.537623 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -2.91289 reciprocal of condition number : 0.00196158 Number of individuals : 447 Number of rows in database : 2826 Number of modelled outcomes : 2826 Number of cores used : 1 Model without mixing LL(start) : -24707.23 LL at equal shares, LL(0) : NA LL at observed shares, LL(C) : NA LL(final) : -15007.36 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 : 30042.72 BIC : 30125.97 Estimated parameters : 14 Time taken (hh:mm:ss) : 00:00:1.78 pre-estimation : 00:00:0.3 estimation : 00:00:0.6 post-estimation : 00:00:0.87 Iterations : 15 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) alpha_generic 0.0000 NA NA NA NA gamma_work 4.8990 0.29747 16.469 0.28122 17.420 gamma_school 3.0985 0.58589 5.288 0.54811 5.653 gamma_shopping 0.4264 0.02697 15.813 0.03088 13.808 gamma_private 0.6200 0.05038 12.307 0.06763 9.168 gamma_leisure 2.0958 0.11402 18.381 0.12634 16.589 delta_work -3.7172 0.07070 -52.578 0.11544 -32.201 delta_school -7.4183 0.22459 -33.030 0.34573 -21.457 delta_shopping -3.8044 0.04154 -91.583 0.05212 -72.999 delta_private -4.2786 0.04785 -89.417 0.06188 -69.148 delta_leisure -3.4001 0.04423 -76.873 0.05645 -60.227 delta_work_FT 1.3248 0.08157 16.242 0.13484 9.825 delta_work_wknd -2.8609 0.14288 -20.023 0.19540 -14.641 delta_school_young 2.3442 0.25751 9.103 0.40178 5.834 delta_leisure_wknd 0.2949 0.07139 4.130 0.07397 3.987 sig 1.0000 NA NA NA NA Overview of choices for MDCEV model component : outside work school shopping private leisure Times available 2826.00 2826.00 2826.00 2826.0 2826.00 2826.00 Observations in which chosen 2826.00 1139.00 85.00 783.0 535.00 1174.00 Average consumption when available 18.21 2.89 0.11 0.5 0.44 1.85 Average consumption when chosen 18.21 7.17 3.52 1.8 2.34 4.45 Classical covariance matrix: gamma_work gamma_school gamma_shopping gamma_private gamma_work 0.088486 -4.7924e-04 -3.032e-05 -5.858e-05 gamma_school -4.7924e-04 0.343267 -4.527e-06 -1.887e-05 gamma_shopping -3.032e-05 -4.527e-06 7.2722e-04 3.073e-07 gamma_private -5.858e-05 -1.887e-05 3.073e-07 0.002538 gamma_leisure -5.8257e-04 -1.7296e-04 -2.712e-06 -1.060e-05 delta_work -0.002152 1.2332e-04 4.550e-06 6.644e-06 delta_school -1.0683e-04 -2.2871e-04 2.068e-06 7.243e-07 delta_shopping -6.179e-05 3.825e-06 -1.6228e-04 -6.348e-07 delta_private -5.703e-05 1.861e-06 3.029e-07 -2.1535e-04 delta_leisure -4.348e-05 3.478e-05 -2.691e-06 -8.952e-07 delta_work_FT -0.004915 -1.0582e-04 -6.964e-06 -7.118e-06 delta_work_wknd 0.006179 -7.759e-05 1.055e-05 6.501e-06 delta_school_young 7.567e-05 -0.003040 -4.637e-06 -4.827e-07 delta_leisure_wknd 8.532e-05 -6.774e-05 1.083e-05 7.624e-06 gamma_leisure delta_work delta_school delta_shopping gamma_work -5.8257e-04 -0.002152 -1.0683e-04 -6.179e-05 gamma_school -1.7296e-04 1.2332e-04 -2.2871e-04 3.825e-06 gamma_shopping -2.712e-06 4.550e-06 2.068e-06 -1.6228e-04 gamma_private -1.060e-05 6.644e-06 7.243e-07 -6.348e-07 gamma_leisure 0.01300 4.640e-05 -1.805e-05 -2.059e-05 delta_work 4.640e-05 0.004998 3.8083e-04 3.9197e-04 delta_school -1.805e-05 3.8083e-04 0.05044 3.8366e-04 delta_shopping -2.059e-05 3.9197e-04 3.8366e-04 0.001726 delta_private -1.487e-05 3.8867e-04 3.8732e-04 3.8697e-04 delta_leisure -8.8798e-04 5.1000e-04 3.7852e-04 3.8833e-04 delta_work_FT -2.780e-05 -0.004564 2.160e-06 -7.659e-06 delta_work_wknd -2.842e-05 -8.7597e-04 3.903e-05 3.423e-06 delta_school_young 1.453e-07 2.841e-05 -0.05022 4.725e-06 delta_leisure_wknd -5.3947e-04 -3.6577e-04 5.464e-05 2.392e-05 delta_private delta_leisure delta_work_FT delta_work_wknd gamma_work -5.703e-05 -4.348e-05 -0.004915 0.006179 gamma_school 1.861e-06 3.478e-05 -1.0582e-04 -7.759e-05 gamma_shopping 3.029e-07 -2.691e-06 -6.964e-06 1.055e-05 gamma_private -2.1535e-04 -8.952e-07 -7.118e-06 6.501e-06 gamma_leisure -1.487e-05 -8.8798e-04 -2.780e-05 -2.842e-05 delta_work 3.8867e-04 5.1000e-04 -0.004564 -8.7597e-04 delta_school 3.8732e-04 3.7852e-04 2.160e-06 3.903e-05 delta_shopping 3.8697e-04 3.8833e-04 -7.659e-06 3.423e-06 delta_private 0.002290 3.8100e-04 -1.094e-05 2.608e-05 delta_leisure 3.8100e-04 0.001956 -3.145e-06 -3.6992e-04 delta_work_FT -1.094e-05 -3.145e-06 0.006653 -0.001224 delta_work_wknd 2.608e-05 -3.6992e-04 -0.001224 0.020415 delta_school_young -6.547e-06 -7.159e-06 -5.774e-05 -1.384e-05 delta_leisure_wknd 4.254e-05 -0.001715 -1.488e-06 0.001190 delta_school_young delta_leisure_wknd gamma_work 7.567e-05 8.532e-05 gamma_school -0.003040 -6.774e-05 gamma_shopping -4.637e-06 1.083e-05 gamma_private -4.827e-07 7.624e-06 gamma_leisure 1.453e-07 -5.3947e-04 delta_work 2.841e-05 -3.6577e-04 delta_school -0.050221 5.464e-05 delta_shopping 4.725e-06 2.392e-05 delta_private -6.547e-06 4.254e-05 delta_leisure -7.159e-06 -0.001715 delta_work_FT -5.774e-05 -1.488e-06 delta_work_wknd -1.384e-05 0.001190 delta_school_young 0.066311 6.147e-06 delta_leisure_wknd 6.147e-06 0.005097 Robust covariance matrix: gamma_work gamma_school gamma_shopping gamma_private gamma_work 0.079087 0.011724 -3.0699e-04 0.001014 gamma_school 0.011724 0.300423 -6.2118e-04 7.5429e-04 gamma_shopping -3.0699e-04 -6.2118e-04 9.5370e-04 1.3060e-04 gamma_private 0.001014 7.5429e-04 1.3060e-04 0.004574 gamma_leisure 0.003811 0.001502 4.8376e-04 -4.5307e-04 delta_work -0.002909 -0.002683 2.3988e-04 -7.3747e-04 delta_school 0.009100 0.045073 4.1162e-04 1.0307e-04 delta_shopping -9.9807e-04 0.001006 -2.4729e-04 -2.4935e-04 delta_private 0.001046 0.001523 -7.425e-05 -1.2225e-04 delta_leisure -0.001758 0.002269 -5.745e-05 -2.1639e-04 delta_work_FT -0.012014 0.003376 -1.3693e-04 4.7885e-04 delta_work_wknd 0.020237 0.001382 8.684e-05 6.9015e-04 delta_school_young -0.004020 -0.046997 -1.4011e-04 2.4372e-04 delta_leisure_wknd 9.0877e-04 0.001588 -6.766e-05 3.241e-05 gamma_leisure delta_work delta_school delta_shopping gamma_work 0.003811 -0.002909 0.009100 -9.9807e-04 gamma_school 0.001502 -0.002683 0.045073 0.001006 gamma_shopping 4.8376e-04 2.3988e-04 4.1162e-04 -2.4729e-04 gamma_private -4.5307e-04 -7.3747e-04 1.0307e-04 -2.4935e-04 gamma_leisure 0.015962 8.2700e-04 0.005252 -6.8352e-04 delta_work 8.2700e-04 0.013326 0.004197 5.7882e-04 delta_school 0.005252 0.004197 0.119529 -3.5687e-04 delta_shopping -6.8352e-04 5.7882e-04 -3.5687e-04 0.002716 delta_private -6.2051e-04 -4.0312e-04 8.7801e-04 7.1245e-04 delta_leisure -0.001664 8.540e-05 3.5046e-04 8.8867e-04 delta_work_FT -0.001236 -0.013172 -0.005041 -2.0933e-04 delta_work_wknd 0.003071 9.7588e-04 0.011725 -0.001205 delta_school_young -0.004576 -0.008306 -0.119814 4.4857e-04 delta_leisure_wknd 4.1978e-04 1.5146e-04 -1.7540e-04 2.4589e-04 delta_private delta_leisure delta_work_FT delta_work_wknd gamma_work 0.001046 -0.001758 -0.012014 0.020237 gamma_school 0.001523 0.002269 0.003376 0.001382 gamma_shopping -7.425e-05 -5.745e-05 -1.3693e-04 8.684e-05 gamma_private -1.2225e-04 -2.1639e-04 4.7885e-04 6.9015e-04 gamma_leisure -6.2051e-04 -0.001664 -0.001236 0.003071 delta_work -4.0312e-04 8.540e-05 -0.013172 9.7588e-04 delta_school 8.7801e-04 3.5046e-04 -0.005041 0.011725 delta_shopping 7.1245e-04 8.8867e-04 -2.0933e-04 -0.001205 delta_private 0.003829 0.001031 4.0090e-04 -2.5945e-04 delta_leisure 0.001031 0.003187 5.8628e-04 -8.7440e-04 delta_work_FT 4.0090e-04 5.8628e-04 0.018181 -0.006396 delta_work_wknd -2.5945e-04 -8.7440e-04 -0.006396 0.038180 delta_school_young -0.001116 -2.9208e-04 0.008273 -0.005667 delta_leisure_wknd 4.568e-06 -0.001780 -3.0016e-04 2.4377e-04 delta_school_young delta_leisure_wknd gamma_work -0.004020 9.0877e-04 gamma_school -0.046997 0.001588 gamma_shopping -1.4011e-04 -6.766e-05 gamma_private 2.4372e-04 3.241e-05 gamma_leisure -0.004576 4.1978e-04 delta_work -0.008306 1.5146e-04 delta_school -0.119814 -1.7540e-04 delta_shopping 4.4857e-04 2.4589e-04 delta_private -0.001116 4.568e-06 delta_leisure -2.9208e-04 -0.001780 delta_work_FT 0.008273 -3.0016e-04 delta_work_wknd -0.005667 2.4377e-04 delta_school_young 0.161431 0.001891 delta_leisure_wknd 0.001891 0.005471 Classical correlation matrix: gamma_work gamma_school gamma_shopping gamma_private gamma_work 1.000000 -0.002750 -0.003780 -0.003909 gamma_school -0.002750 1.000000 -2.8653e-04 -6.3945e-04 gamma_shopping -0.003780 -2.8653e-04 1.000000 2.2618e-04 gamma_private -0.003909 -6.3945e-04 2.2618e-04 1.000000 gamma_leisure -0.017177 -0.002589 -8.8209e-04 -0.001845 delta_work -0.102326 0.002977 0.002387 0.001865 delta_school -0.001599 -0.001738 3.4143e-04 6.401e-05 delta_shopping -0.005001 1.5715e-04 -0.144862 -3.0334e-04 delta_private -0.004007 6.639e-05 2.3472e-04 -0.089333 delta_leisure -0.003304 0.001342 -0.002256 -4.0174e-04 delta_work_FT -0.202558 -0.002214 -0.003166 -0.001732 delta_work_wknd 0.145372 -9.2689e-04 0.002737 9.0312e-04 delta_school_young 9.8792e-04 -0.020152 -6.6779e-04 -3.721e-05 delta_leisure_wknd 0.004018 -0.001619 0.005627 0.002120 gamma_leisure delta_work delta_school delta_shopping gamma_work -0.017177 -0.102326 -0.001599 -0.005001 gamma_school -0.002589 0.002977 -0.001738 1.5715e-04 gamma_shopping -8.8209e-04 0.002387 3.4143e-04 -0.144862 gamma_private -0.001845 0.001865 6.401e-05 -3.0334e-04 gamma_leisure 1.000000 0.005755 -7.0495e-04 -0.004347 delta_work 0.005755 1.000000 0.023984 0.133468 delta_school -7.0495e-04 0.023984 1.000000 0.041123 delta_shopping -0.004347 0.133468 0.041123 1.000000 delta_private -0.002725 0.114888 0.036041 0.194679 delta_leisure -0.176080 0.163094 0.038104 0.211358 delta_work_FT -0.002989 -0.791505 1.1793e-04 -0.002260 delta_work_wknd -0.001745 -0.086716 0.001216 5.7665e-04 delta_school_young 4.947e-06 0.001560 -0.868352 4.4176e-04 delta_leisure_wknd -0.066272 -0.072464 0.003408 0.008064 delta_private delta_leisure delta_work_FT delta_work_wknd gamma_work -0.004007 -0.003304 -0.202558 0.145372 gamma_school 6.639e-05 0.001342 -0.002214 -9.2689e-04 gamma_shopping 2.3472e-04 -0.002256 -0.003166 0.002737 gamma_private -0.089333 -4.0174e-04 -0.001732 9.0312e-04 gamma_leisure -0.002725 -0.176080 -0.002989 -0.001745 delta_work 0.114888 0.163094 -0.791505 -0.086716 delta_school 0.036041 0.038104 1.1793e-04 0.001216 delta_shopping 0.194679 0.211358 -0.002260 5.7665e-04 delta_private 1.000000 0.180019 -0.002804 0.003815 delta_leisure 0.180019 1.000000 -8.7162e-04 -0.058535 delta_work_FT -0.002804 -8.7162e-04 1.000000 -0.104998 delta_work_wknd 0.003815 -0.058535 -0.104998 1.000000 delta_school_young -5.3131e-04 -6.2852e-04 -0.002749 -3.7627e-04 delta_leisure_wknd 0.012453 -0.543125 -2.5554e-04 0.116656 delta_school_young delta_leisure_wknd gamma_work 9.8792e-04 0.004018 gamma_school -0.020152 -0.001619 gamma_shopping -6.6779e-04 0.005627 gamma_private -3.721e-05 0.002120 gamma_leisure 4.947e-06 -0.066272 delta_work 0.001560 -0.072464 delta_school -0.868352 0.003408 delta_shopping 4.4176e-04 0.008064 delta_private -5.3131e-04 0.012453 delta_leisure -6.2852e-04 -0.543125 delta_work_FT -0.002749 -2.5554e-04 delta_work_wknd -3.7627e-04 0.116656 delta_school_young 1.000000 3.3434e-04 delta_leisure_wknd 3.3434e-04 1.000000 Robust correlation matrix: gamma_work gamma_school gamma_shopping gamma_private gamma_work 1.00000 0.07606 -0.03535 0.053336 gamma_school 0.07606 1.00000 -0.03670 0.020349 gamma_shopping -0.03535 -0.03670 1.00000 0.062530 gamma_private 0.05334 0.02035 0.06253 1.000000 gamma_leisure 0.10727 0.02169 0.12399 -0.053027 delta_work -0.08961 -0.04240 0.06729 -0.094464 delta_school 0.09360 0.23786 0.03855 0.004408 delta_shopping -0.06810 0.03522 -0.15365 -0.070747 delta_private 0.06009 0.04491 -0.03886 -0.029214 delta_leisure -0.11072 0.07331 -0.03295 -0.056677 delta_work_FT -0.31683 0.04567 -0.03288 0.052511 delta_work_wknd 0.36828 0.01290 0.01439 0.052227 delta_school_young -0.03558 -0.21341 -0.01129 0.008969 delta_leisure_wknd 0.04369 0.03918 -0.02962 0.006480 gamma_leisure delta_work delta_school delta_shopping gamma_work 0.10727 -0.08961 0.093595 -0.06810 gamma_school 0.02169 -0.04240 0.237856 0.03522 gamma_shopping 0.12399 0.06729 0.038553 -0.15365 gamma_private -0.05303 -0.09446 0.004408 -0.07075 gamma_leisure 1.00000 0.05670 0.120244 -0.10381 delta_work 0.05670 1.00000 0.105148 0.09621 delta_school 0.12024 0.10515 1.000000 -0.01981 delta_shopping -0.10381 0.09621 -0.019807 1.00000 delta_private -0.07938 -0.05644 0.041043 0.22094 delta_leisure -0.23334 0.01310 0.017956 0.30205 delta_work_FT -0.07255 -0.84620 -0.108125 -0.02979 delta_work_wknd 0.12439 0.04326 0.173569 -0.11837 delta_school_young -0.09016 -0.17908 -0.862534 0.02142 delta_leisure_wknd 0.04492 0.01774 -0.006859 0.06379 delta_private delta_leisure delta_work_FT delta_work_wknd gamma_work 0.06009 -0.11072 -0.31683 0.36828 gamma_school 0.04491 0.07331 0.04567 0.01290 gamma_shopping -0.03886 -0.03295 -0.03288 0.01439 gamma_private -0.02921 -0.05668 0.05251 0.05223 gamma_leisure -0.07938 -0.23334 -0.07255 0.12439 delta_work -0.05644 0.01310 -0.84620 0.04326 delta_school 0.04104 0.01796 -0.10813 0.17357 delta_shopping 0.22094 0.30205 -0.02979 -0.11837 delta_private 1.00000 0.29516 0.04805 -0.02146 delta_leisure 0.29516 1.00000 0.07702 -0.07927 delta_work_FT 0.04805 0.07702 1.00000 -0.24276 delta_work_wknd -0.02146 -0.07927 -0.24276 1.00000 delta_school_young -0.04490 -0.01288 0.15271 -0.07219 delta_leisure_wknd 9.9809e-04 -0.42630 -0.03009 0.01687 delta_school_young delta_leisure_wknd gamma_work -0.035578 0.043687 gamma_school -0.213407 0.039181 gamma_shopping -0.011292 -0.029619 gamma_private 0.008969 0.006480 gamma_leisure -0.090157 0.044920 delta_work -0.179080 0.017738 delta_school -0.862534 -0.006859 delta_shopping 0.021423 0.063786 delta_private -0.044897 9.9809e-04 delta_leisure -0.012877 -0.426302 delta_work_FT 0.152707 -0.030095 delta_work_wknd -0.072190 0.016866 delta_school_young 1.000000 0.063645 delta_leisure_wknd 0.063645 1.000000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 2146576 1.310647e-06 9902059 1.643746e-05 9880000 2.639039e-05 6292582 3.777530e-05 3051038 6.564058e-05 8415029 6.887043e-05 8530000 7.160606e-05 9230000 7.424680e-05 7560000 8.725064e-05 8494828 9.341750e-05 1226238 9.510128e-05 5436896 9.791490e-05 7177352 9.978865e-05 6689995 1.057270e-04 1566942 1.153992e-04 3730000 1.300520e-04 2942411 1.303239e-04 9216479 1.404914e-04 6490000 1.465976e-04 2119561 1.511240e-04 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "MDCEV model on time use data, alpha-gamma profile with outside good and socio-demographics" indivID "indivID" outputDirectory "output/" debug "FALSE" modelName "MDCEV_with_outside_good" 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 second derivative of LL (using numDeriv) Scaling used in computing Hessian --------------------------------- Value gamma_work 4.8989650 gamma_school 3.0984709 gamma_shopping 0.4264225 gamma_private 0.6200180 gamma_leisure 2.0957931 delta_work 3.7172154 delta_school 7.4182683 delta_shopping 3.8043552 delta_private 4.2786348 delta_leisure 3.4000987 delta_work_FT 1.3248269 delta_work_wknd 2.8608918 delta_school_young 2.3441698 delta_leisure_wknd 0.2948772 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() ### Define individual alternatives alternatives = c("outside", "work", "school", "shopping", "private", "leisure") ### Define availabilities avail = list(outside = 1, work = 1, school = 1, shopping = 1, private = 1, leisure = 1) ### Define continuous consumption for individual alternatives continuousChoice = list(outside = t_outside/60, work = t_a02/60, school = t_a03/60, shopping = t_a04/60, private = t_a05/60, leisure = t_leisure/60) ### Define utilities for individual alternatives V = list() V[["outside"]] = 0 V[["work"]] = delta_work + delta_work_FT * occ_full_time + delta_work_wknd * weekend V[["school"]] = delta_school + delta_school_young * (age<=30) V[["shopping"]] = delta_shopping V[["private"]] = delta_private V[["leisure"]] = delta_leisure + delta_leisure_wknd*weekend ### Define alpha parameters alpha = list(outside = alpha_generic, work = alpha_generic, school = alpha_generic, shopping = alpha_generic, private = alpha_generic, leisure = alpha_generic) ### Define gamma parameters gamma = list(work = gamma_work, school = gamma_school, shopping = gamma_shopping, private = gamma_private, leisure = gamma_leisure) ### Define costs for individual alternatives cost = list(outside = 1, work = 1, school = 1, shopping = 1, private = 1, leisure = 1) ### Define settings for MDCEV model mdcev_settings = list(alternatives = alternatives, avail = avail, continuousChoice = continuousChoice, utilities = V, alpha = alpha, gamma = gamma, sigma = sig, cost = cost, budget = 24) ### Compute probabilities using MDCEV model P[["model"]] = apollo_mdcev(mdcev_settings, 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) }