/* Here we are working with some artificial multinomial data generated in the EVIEWS 4.0 manual. See Chapter 18 on "The Log Likelihood (LogL) Object" and in particular the discussion of the EVIEWS program mlogit1.prg on pp. 470 - 473. This program can be obtained from the EVIEWS example programs file located at c:/Program Files/EVIEWS4/Example Files/mlogit1.prg To make the problem interesting I will give the artificial data a "story." Let us assume that we have observations on two characteristics (X1 and X2, say age and income if you like) for 1000 consumers in a given location who choose to shop for groceries at either store 1 (st = 1), or store 2 (st = 2), or store 3 (st = 3). Here we are going to use the SAS procedure QLIM to fit an unordered multinomial logit model to the data where st is the unranked multinomial variable and x1 and x2 are the explanatory variables. */ /* Note the data dd2, dd3, x1 and x2 come directly from the the mlogit1.wf1 data set. The mlogit1.prg EVIEWS 4.0 program does the same analysis of the data. */ data multinom; input dd2 dd3 x1 x2; st1 = 1 - dd2 - dd3; st2 = dd2; st3 = dd3; if st1 = 1 then st = 1; if st2 = 1 then st = 2; if st3 = 1 then st = 3; cards; 1.000000 0.000000 0.722169 0.727069 1.000000 0.000000 0.470127 0.112331 1.000000 0.000000 0.496491 0.779999 0.000000 0.000000 0.856398 0.183000 1.000000 0.000000 0.896749 0.532288 0.000000 1.000000 0.751286 0.373546 0.000000 0.000000 0.697323 0.123087 1.000000 0.000000 0.875194 0.621618 0.000000 0.000000 0.263939 0.877520 1.000000 0.000000 0.991544 0.462648 0.000000 1.000000 0.285413 0.186541 0.000000 0.000000 0.113239 0.965509 1.000000 0.000000 0.354033 0.527105 1.000000 0.000000 0.078576 0.007189 0.000000 1.000000 0.743299 0.317848 0.000000 1.000000 0.360845 0.577589 1.000000 0.000000 0.806294 0.944559 0.000000 1.000000 0.725920 0.059160 0.000000 1.000000 0.602267 0.732394 1.000000 0.000000 0.579239 0.346234 0.000000 1.000000 0.150997 0.553879 0.000000 0.000000 0.931148 0.339316 0.000000 1.000000 0.418619 0.428275 0.000000 1.000000 0.257027 0.577114 0.000000 1.000000 0.136641 0.291068 0.000000 0.000000 0.215175 0.998314 0.000000 1.000000 0.216302 0.269323 0.000000 0.000000 0.824533 0.640215 0.000000 0.000000 0.026745 0.996465 1.000000 0.000000 0.111176 0.816662 0.000000 0.000000 0.003181 0.515140 0.000000 0.000000 0.574059 0.162105 1.000000 0.000000 0.953616 0.350346 0.000000 1.000000 0.671818 0.595081 0.000000 0.000000 0.060712 0.369721 0.000000 1.000000 0.928972 0.921109 0.000000 0.000000 0.446730 0.237835 1.000000 0.000000 0.854918 0.391212 1.000000 0.000000 0.686520 0.750855 1.000000 0.000000 0.097196 0.859034 0.000000 1.000000 0.847699 0.918693 0.000000 0.000000 0.143580 0.283657 0.000000 1.000000 0.163517 0.475886 1.000000 0.000000 0.725850 0.694231 0.000000 1.000000 0.696535 0.011076 0.000000 1.000000 0.308029 0.089858 0.000000 0.000000 0.472332 0.331997 0.000000 0.000000 0.687810 0.718515 1.000000 0.000000 0.441758 0.345939 1.000000 0.000000 0.212363 0.331115 0.000000 1.000000 0.896557 0.270564 1.000000 0.000000 0.786262 0.967781 1.000000 0.000000 0.232111 0.464212 0.000000 1.000000 0.640560 0.879285 0.000000 1.000000 0.279904 0.456732 1.000000 0.000000 0.258525 0.531761 1.000000 0.000000 0.071291 0.582134 0.000000 0.000000 0.452163 0.902529 0.000000 0.000000 0.577147 0.809068 0.000000 0.000000 0.633369 0.431969 0.000000 1.000000 0.891491 0.381172 1.000000 0.000000 0.282006 0.511312 0.000000 1.000000 0.193298 0.852625 0.000000 1.000000 0.436499 0.868630 1.000000 0.000000 0.702908 0.807893 0.000000 1.000000 0.880478 0.825174 1.000000 0.000000 0.801949 0.538532 0.000000 1.000000 0.017349 0.608606 0.000000 0.000000 0.528978 0.708335 0.000000 1.000000 0.488501 0.319101 1.000000 0.000000 0.435181 0.397642 0.000000 0.000000 0.200314 0.670337 1.000000 0.000000 0.594515 0.813313 1.000000 0.000000 0.945431 0.017805 0.000000 0.000000 0.120953 0.359790 1.000000 0.000000 0.363571 0.191520 1.000000 0.000000 0.567318 0.880923 0.000000 1.000000 0.151794 0.217733 0.000000 0.000000 0.902459 0.010506 1.000000 0.000000 0.894053 0.501058 0.000000 0.000000 0.244743 0.775384 1.000000 0.000000 0.096089 0.308936 1.000000 0.000000 0.037342 0.990804 1.000000 0.000000 0.399134 0.662831 0.000000 1.000000 0.397107 0.355018 1.000000 0.000000 0.561752 0.848264 0.000000 1.000000 0.931191 0.515293 1.000000 0.000000 0.215429 0.501589 1.000000 0.000000 0.697895 0.704843 1.000000 0.000000 0.558997 0.886352 0.000000 0.000000 0.985923 0.738630 1.000000 0.000000 0.823238 0.280933 0.000000 0.000000 0.469817 0.827526 0.000000 1.000000 0.672004 0.829967 1.000000 0.000000 0.746117 0.772181 0.000000 1.000000 0.919823 0.848066 0.000000 0.000000 0.045303 0.313521 1.000000 0.000000 0.646950 0.584946 1.000000 0.000000 0.560249 0.194908 1.000000 0.000000 0.768671 0.011946 1.000000 0.000000 0.716395 0.052911 1.000000 0.000000 0.645897 0.275589 1.000000 0.000000 0.993236 0.787930 0.000000 0.000000 0.259195 0.216779 0.000000 0.000000 0.771521 0.533932 0.000000 0.000000 0.554274 0.345258 0.000000 1.000000 0.679481 0.176801 1.000000 0.000000 0.959465 0.143899 0.000000 1.000000 0.535321 0.383868 0.000000 0.000000 0.809570 0.022265 1.000000 0.000000 0.177666 0.853792 0.000000 0.000000 0.904927 0.139821 1.000000 0.000000 0.976812 0.732479 1.000000 0.000000 0.014246 0.865976 0.000000 1.000000 0.178306 0.037609 0.000000 0.000000 0.380315 0.449132 0.000000 1.000000 0.077415 0.217273 1.000000 0.000000 0.714981 0.964535 0.000000 1.000000 0.176679 0.230124 0.000000 0.000000 0.092330 0.481300 0.000000 0.000000 0.588875 0.588986 1.000000 0.000000 0.701097 0.270040 1.000000 0.000000 0.968870 0.317035 0.000000 1.000000 0.514635 0.925364 0.000000 0.000000 0.283292 0.193864 0.000000 0.000000 0.375335 0.813123 0.000000 0.000000 0.084850 0.150076 1.000000 0.000000 0.220283 0.844194 1.000000 0.000000 0.448653 0.171872 0.000000 0.000000 0.369884 0.276873 0.000000 0.000000 0.678682 0.895358 0.000000 1.000000 0.946689 0.199886 0.000000 1.000000 0.181914 0.895159 1.000000 0.000000 0.586132 0.985075 0.000000 0.000000 0.254421 0.743780 1.000000 0.000000 0.327195 0.233346 0.000000 0.000000 0.123802 0.736307 0.000000 0.000000 0.207151 0.201822 0.000000 1.000000 0.366755 0.936392 0.000000 0.000000 0.241466 0.307246 1.000000 0.000000 0.548434 0.097370 0.000000 0.000000 0.133517 0.028658 1.000000 0.000000 0.005791 0.246012 0.000000 0.000000 0.487080 0.554821 0.000000 1.000000 0.655646 0.300158 0.000000 1.000000 0.194072 0.942989 1.000000 0.000000 0.407160 0.156476 1.000000 0.000000 0.306184 0.526451 0.000000 1.000000 0.145662 0.971119 1.000000 0.000000 0.306676 0.530554 0.000000 1.000000 0.497824 0.668050 0.000000 1.000000 0.021553 0.215090 1.000000 0.000000 0.387510 0.678881 0.000000 1.000000 0.617337 0.148058 0.000000 1.000000 0.806232 0.371925 0.000000 1.000000 0.159836 0.073795 0.000000 1.000000 0.515426 0.031641 1.000000 0.000000 0.985191 0.627004 1.000000 0.000000 0.524724 0.612624 0.000000 0.000000 0.522401 0.893787 1.000000 0.000000 0.440497 0.221091 0.000000 1.000000 0.055955 0.896484 0.000000 0.000000 0.188980 0.799662 0.000000 0.000000 0.843129 0.431124 0.000000 1.000000 0.121001 0.413453 0.000000 1.000000 0.344167 0.604151 0.000000 1.000000 0.067407 0.498747 1.000000 0.000000 0.837730 0.175220 1.000000 0.000000 0.836943 0.731935 0.000000 0.000000 0.298648 0.366436 0.000000 0.000000 0.469921 0.078448 0.000000 1.000000 0.994030 0.451149 0.000000 0.000000 0.087547 0.609675 1.000000 0.000000 0.781001 0.951159 1.000000 0.000000 0.621991 0.029681 0.000000 0.000000 0.286270 0.557889 0.000000 1.000000 0.561677 0.158445 0.000000 1.000000 0.853902 0.984729 1.000000 0.000000 0.666472 0.427255 0.000000 1.000000 0.952901 0.393732 0.000000 0.000000 0.090618 0.977198 0.000000 0.000000 0.785385 0.961088 0.000000 0.000000 0.960204 0.662187 1.000000 0.000000 0.126107 0.726754 0.000000 0.000000 0.535959 0.080985 0.000000 1.000000 0.170579 0.396000 1.000000 0.000000 0.827601 0.767206 1.000000 0.000000 0.926169 0.118384 0.000000 1.000000 0.490283 0.129245 0.000000 0.000000 0.110700 0.333276 1.000000 0.000000 0.326465 0.642849 0.000000 0.000000 0.926666 0.944050 0.000000 0.000000 0.068678 0.038370 0.000000 1.000000 0.384591 0.913248 0.000000 1.000000 0.912396 0.112948 0.000000 0.000000 0.886005 0.287804 0.000000 0.000000 0.406410 0.012689 0.000000 1.000000 0.288719 0.807628 1.000000 0.000000 0.823125 0.863246 0.000000 0.000000 0.817521 0.141485 0.000000 0.000000 0.044754 0.531858 0.000000 1.000000 0.935852 0.572639 0.000000 1.000000 0.979842 0.185232 1.000000 0.000000 0.311144 0.842699 0.000000 0.000000 0.271677 0.344552 1.000000 0.000000 0.002291 0.969261 0.000000 0.000000 0.744995 0.682992 0.000000 1.000000 0.513117 0.182153 1.000000 0.000000 0.484576 0.491521 0.000000 0.000000 0.088570 0.318149 0.000000 0.000000 0.094245 0.984680 1.000000 0.000000 0.777559 0.374707 1.000000 0.000000 0.284235 0.146263 0.000000 0.000000 0.374521 0.138612 0.000000 0.000000 0.443525 0.736892 1.000000 0.000000 0.292130 0.364052 1.000000 0.000000 0.898119 0.466840 0.000000 1.000000 0.406939 0.580087 0.000000 1.000000 0.196916 0.247249 1.000000 0.000000 0.057632 0.721075 0.000000 1.000000 0.537370 0.231487 0.000000 1.000000 0.553691 0.836823 0.000000 1.000000 0.549027 0.335053 1.000000 0.000000 0.664342 0.115515 0.000000 0.000000 0.869512 0.469784 0.000000 0.000000 0.295671 0.342722 0.000000 0.000000 0.378274 0.291171 1.000000 0.000000 0.646249 0.243112 0.000000 1.000000 0.570314 0.620657 0.000000 1.000000 0.031975 0.153393 0.000000 1.000000 0.402471 0.015406 0.000000 1.000000 0.405423 0.146267 0.000000 1.000000 0.477162 0.313868 0.000000 0.000000 0.446526 0.943840 1.000000 0.000000 0.418784 0.348290 0.000000 1.000000 0.085223 0.580431 0.000000 1.000000 0.633944 0.474952 1.000000 0.000000 0.656778 0.073827 1.000000 0.000000 0.021968 0.337486 1.000000 0.000000 0.559751 0.733834 0.000000 0.000000 0.201408 0.903421 1.000000 0.000000 0.823121 0.686318 0.000000 1.000000 0.625337 0.731127 1.000000 0.000000 0.708804 0.936169 1.000000 0.000000 0.733686 0.062378 0.000000 1.000000 0.798356 0.808776 0.000000 0.000000 0.405994 0.363526 0.000000 1.000000 0.110641 0.717066 0.000000 1.000000 0.897658 0.406060 0.000000 0.000000 0.336433 0.822822 0.000000 0.000000 0.177009 0.280973 0.000000 1.000000 0.745755 0.499538 0.000000 0.000000 0.921517 0.910283 0.000000 1.000000 0.087646 0.465101 0.000000 1.000000 0.867510 0.630235 1.000000 0.000000 0.488390 0.267849 1.000000 0.000000 0.844783 0.703172 1.000000 0.000000 0.544178 0.783647 1.000000 0.000000 0.097584 0.058403 1.000000 0.000000 0.879415 0.429821 1.000000 0.000000 0.830540 0.545052 0.000000 1.000000 0.469465 0.269268 0.000000 0.000000 0.124431 0.375300 1.000000 0.000000 0.220925 0.674488 1.000000 0.000000 0.008856 0.473990 0.000000 1.000000 0.284047 0.259453 0.000000 0.000000 0.621460 0.461918 0.000000 0.000000 0.326189 0.009589 1.000000 0.000000 0.539312 0.565594 1.000000 0.000000 0.848389 0.846862 0.000000 0.000000 0.690061 0.528124 1.000000 0.000000 0.547115 0.152323 0.000000 0.000000 0.572184 0.770290 0.000000 1.000000 0.375740 0.651443 0.000000 1.000000 0.872108 0.360750 0.000000 1.000000 0.644254 0.905016 0.000000 1.000000 0.074891 0.656711 0.000000 0.000000 0.324321 0.244018 0.000000 1.000000 0.283231 0.107565 0.000000 1.000000 0.871746 0.654656 0.000000 0.000000 0.660816 0.285681 0.000000 0.000000 0.020065 0.197095 0.000000 0.000000 0.839808 0.432200 1.000000 0.000000 0.784086 0.917215 0.000000 0.000000 0.229927 0.178022 0.000000 1.000000 0.334106 0.647284 0.000000 0.000000 0.971078 0.366300 1.000000 0.000000 0.860911 0.413408 0.000000 1.000000 0.558004 0.745810 1.000000 0.000000 0.938330 0.220384 0.000000 1.000000 0.465939 0.650157 0.000000 1.000000 0.311209 0.175151 0.000000 0.000000 0.993333 0.903007 1.000000 0.000000 0.266685 0.562184 0.000000 1.000000 0.572743 0.819688 0.000000 1.000000 0.523301 0.663745 0.000000 1.000000 0.673842 0.157288 1.000000 0.000000 0.755825 0.139505 0.000000 1.000000 0.400962 0.628085 0.000000 0.000000 0.963457 0.333740 1.000000 0.000000 0.672323 0.837286 1.000000 0.000000 0.910869 0.481728 1.000000 0.000000 0.702672 0.317673 1.000000 0.000000 0.093165 0.309426 1.000000 0.000000 0.118090 0.261790 1.000000 0.000000 0.957267 0.103830 1.000000 0.000000 0.651527 0.203103 0.000000 0.000000 0.836139 0.937588 0.000000 0.000000 0.034834 0.761834 0.000000 0.000000 0.657439 0.941998 0.000000 1.000000 0.375038 0.141160 0.000000 0.000000 0.840054 0.113641 1.000000 0.000000 0.948371 0.970927 1.000000 0.000000 0.727283 0.608189 0.000000 0.000000 0.962702 0.464200 0.000000 1.000000 0.434402 0.377169 1.000000 0.000000 0.981195 0.945571 1.000000 0.000000 0.264004 0.929008 0.000000 0.000000 0.664899 0.924382 1.000000 0.000000 0.912112 0.594077 0.000000 0.000000 0.138299 0.819338 1.000000 0.000000 0.757526 0.174930 0.000000 0.000000 0.750444 0.772690 0.000000 0.000000 0.865822 0.892814 0.000000 1.000000 0.656797 0.986452 0.000000 1.000000 0.792205 0.661353 1.000000 0.000000 0.031038 0.218050 0.000000 0.000000 0.664222 0.103980 0.000000 0.000000 0.910039 0.414246 0.000000 1.000000 0.393605 0.374381 1.000000 0.000000 0.700031 0.652340 0.000000 1.000000 0.891787 0.470801 0.000000 1.000000 0.536913 0.371822 0.000000 0.000000 0.630996 0.793407 1.000000 0.000000 0.714651 0.736742 0.000000 1.000000 0.539721 0.153949 1.000000 0.000000 0.772539 0.041385 0.000000 1.000000 0.680516 0.603994 0.000000 0.000000 0.759283 0.968351 1.000000 0.000000 0.421500 0.054186 0.000000 0.000000 0.411575 0.022780 1.000000 0.000000 0.913573 0.121480 0.000000 1.000000 0.544414 0.169196 0.000000 1.000000 0.885821 0.609494 1.000000 0.000000 0.795574 0.461308 1.000000 0.000000 0.370099 0.763375 1.000000 0.000000 0.569054 0.680409 1.000000 0.000000 0.944590 0.357776 0.000000 1.000000 0.373324 0.898743 0.000000 0.000000 0.929928 0.221172 1.000000 0.000000 0.952327 0.237678 0.000000 1.000000 0.345649 0.873873 0.000000 0.000000 0.359525 0.661064 1.000000 0.000000 0.236429 0.297495 0.000000 1.000000 0.243598 0.811430 1.000000 0.000000 0.707953 0.119539 0.000000 1.000000 0.517702 0.881970 0.000000 0.000000 0.129022 0.512888 0.000000 0.000000 0.094994 0.037643 1.000000 0.000000 0.759395 0.856317 0.000000 0.000000 0.070194 0.540033 0.000000 0.000000 0.092155 0.693031 0.000000 1.000000 0.335041 0.374493 0.000000 1.000000 0.618984 0.261091 0.000000 0.000000 0.945438 0.197401 0.000000 0.000000 0.428478 0.117541 0.000000 1.000000 0.975500 0.269781 1.000000 0.000000 0.740100 0.587792 1.000000 0.000000 0.049577 0.916927 0.000000 0.000000 0.389624 0.263881 0.000000 0.000000 0.076778 0.591318 0.000000 1.000000 0.391429 0.710466 1.000000 0.000000 0.731416 0.462077 0.000000 0.000000 0.895741 0.582951 0.000000 1.000000 0.076607 0.692090 1.000000 0.000000 0.299754 0.445889 0.000000 1.000000 0.231996 0.097852 0.000000 1.000000 0.897286 0.964810 1.000000 0.000000 0.957090 0.629208 0.000000 1.000000 0.343036 0.773899 1.000000 0.000000 0.269266 0.929384 0.000000 0.000000 0.287307 0.453693 0.000000 0.000000 0.437395 0.822282 1.000000 0.000000 0.771244 0.935196 0.000000 0.000000 0.114728 0.846342 0.000000 1.000000 0.927233 0.998690 0.000000 0.000000 0.486112 0.806394 1.000000 0.000000 0.628520 0.860442 0.000000 0.000000 0.313871 0.158769 0.000000 1.000000 0.062378 0.353104 1.000000 0.000000 0.844309 0.670770 0.000000 0.000000 0.917572 0.702292 1.000000 0.000000 0.959474 0.378777 0.000000 0.000000 0.944475 0.464744 0.000000 0.000000 0.585023 0.887724 0.000000 0.000000 0.375483 0.506312 0.000000 1.000000 0.223965 0.057430 0.000000 1.000000 0.723670 0.179119 0.000000 1.000000 0.563218 0.023701 0.000000 1.000000 0.590464 0.231737 0.000000 1.000000 0.418487 0.188516 0.000000 0.000000 0.779049 0.634806 0.000000 1.000000 0.896588 0.302311 1.000000 0.000000 0.079280 0.966883 0.000000 0.000000 0.865773 0.334537 0.000000 1.000000 0.653610 0.772602 1.000000 0.000000 0.990275 0.286966 1.000000 0.000000 0.815376 0.323241 0.000000 1.000000 0.301250 0.619390 0.000000 1.000000 0.092403 0.737858 1.000000 0.000000 0.602649 0.316127 0.000000 1.000000 0.372414 0.362153 0.000000 0.000000 0.311445 0.934805 0.000000 0.000000 0.720308 0.674326 1.000000 0.000000 0.496438 0.763639 0.000000 0.000000 0.691109 0.583944 1.000000 0.000000 0.901645 0.747849 0.000000 1.000000 0.228115 0.521842 0.000000 1.000000 0.381593 0.325175 0.000000 1.000000 0.904472 0.605697 1.000000 0.000000 0.159983 0.424181 1.000000 0.000000 0.574770 0.264107 1.000000 0.000000 0.359658 0.958788 0.000000 1.000000 0.722728 0.557899 0.000000 0.000000 0.574355 0.592886 0.000000 0.000000 0.159144 0.572899 0.000000 0.000000 0.867470 0.969940 1.000000 0.000000 0.810119 0.789159 0.000000 0.000000 0.899934 0.043172 0.000000 1.000000 0.458964 0.519324 0.000000 0.000000 0.811358 0.190427 0.000000 1.000000 0.143127 0.687407 0.000000 1.000000 0.432793 0.772229 0.000000 1.000000 0.465855 0.831147 0.000000 1.000000 0.810033 0.562917 0.000000 0.000000 0.341636 0.121977 0.000000 0.000000 0.369705 0.726387 1.000000 0.000000 0.245009 0.929995 1.000000 0.000000 0.089138 0.736729 0.000000 1.000000 0.588503 0.627433 0.000000 1.000000 0.284951 0.356795 0.000000 1.000000 0.011437 0.324204 0.000000 0.000000 0.011456 0.447091 0.000000 0.000000 0.805228 0.795756 1.000000 0.000000 0.607162 0.869503 0.000000 1.000000 0.985002 0.902464 1.000000 0.000000 0.727174 0.110002 0.000000 0.000000 0.475609 0.469415 0.000000 1.000000 0.237834 0.083150 1.000000 0.000000 0.315852 0.929616 1.000000 0.000000 0.021867 0.076400 0.000000 0.000000 0.375812 0.767153 1.000000 0.000000 0.809848 0.930852 1.000000 0.000000 0.708865 0.169413 0.000000 0.000000 0.230458 0.585183 0.000000 1.000000 0.259175 0.981932 1.000000 0.000000 0.945067 0.748211 0.000000 1.000000 0.081221 0.525656 0.000000 1.000000 0.120953 0.083622 0.000000 0.000000 0.363802 0.450356 1.000000 0.000000 0.125393 0.819609 0.000000 1.000000 0.021663 0.396120 1.000000 0.000000 0.957993 0.736983 0.000000 0.000000 0.686002 0.151299 1.000000 0.000000 0.682756 0.422495 0.000000 0.000000 0.440638 0.563647 0.000000 1.000000 0.899543 0.317322 0.000000 0.000000 0.303837 0.789779 1.000000 0.000000 0.112296 0.670672 0.000000 1.000000 0.326959 0.635407 0.000000 1.000000 0.378839 0.152254 0.000000 0.000000 0.040553 0.939301 0.000000 0.000000 0.210226 0.621021 1.000000 0.000000 0.540694 0.178989 0.000000 0.000000 0.020776 0.622430 0.000000 1.000000 0.249065 0.476110 1.000000 0.000000 0.851541 0.943414 0.000000 1.000000 0.015918 0.717072 0.000000 1.000000 0.337131 0.659217 0.000000 0.000000 0.079779 0.897585 0.000000 0.000000 0.495127 0.316996 1.000000 0.000000 0.483060 0.332852 1.000000 0.000000 0.382393 0.091381 0.000000 0.000000 0.020051 0.355251 0.000000 1.000000 0.263796 0.471742 1.000000 0.000000 0.078413 0.320415 0.000000 0.000000 0.986458 0.730142 0.000000 1.000000 0.919228 0.213029 1.000000 0.000000 0.436846 0.446009 0.000000 0.000000 0.066502 0.040878 0.000000 0.000000 0.381387 0.650533 0.000000 0.000000 0.391111 0.735083 0.000000 0.000000 0.568590 0.576163 1.000000 0.000000 0.763519 0.935728 0.000000 1.000000 0.610989 0.849408 0.000000 0.000000 0.291401 0.823024 0.000000 1.000000 0.767888 0.607601 0.000000 1.000000 0.331207 0.166252 0.000000 1.000000 0.041922 0.867120 0.000000 0.000000 0.805773 0.341969 0.000000 1.000000 0.144256 0.166550 0.000000 0.000000 0.131367 0.159755 0.000000 0.000000 0.078923 0.135426 0.000000 1.000000 0.107547 0.950870 0.000000 0.000000 0.942966 0.062559 0.000000 0.000000 0.193419 0.313206 0.000000 0.000000 0.434509 0.585069 0.000000 1.000000 0.413998 0.302135 0.000000 1.000000 0.109430 0.710025 0.000000 0.000000 0.816773 0.200941 1.000000 0.000000 0.108291 0.535047 0.000000 1.000000 0.718637 0.474233 0.000000 0.000000 0.379886 0.320780 1.000000 0.000000 0.322882 0.836818 1.000000 0.000000 0.764196 0.111400 0.000000 0.000000 0.618205 0.288340 0.000000 0.000000 0.703266 0.153745 1.000000 0.000000 0.679975 0.599301 1.000000 0.000000 0.425504 0.882262 1.000000 0.000000 0.991702 0.605963 0.000000 1.000000 0.827364 0.433254 1.000000 0.000000 0.138028 0.508475 1.000000 0.000000 0.556654 0.488878 1.000000 0.000000 0.100253 0.022614 1.000000 0.000000 0.250015 0.284407 0.000000 0.000000 0.103152 0.482508 0.000000 1.000000 0.182118 0.583745 0.000000 0.000000 0.023748 0.522195 1.000000 0.000000 0.186700 0.937439 0.000000 1.000000 0.538775 0.595411 0.000000 0.000000 0.671069 0.992736 0.000000 0.000000 0.077104 0.570369 1.000000 0.000000 0.864437 0.330746 0.000000 0.000000 0.393431 0.982450 0.000000 1.000000 0.537638 0.183952 0.000000 0.000000 0.621388 0.868639 1.000000 0.000000 0.358444 0.167281 1.000000 0.000000 0.517951 0.428456 0.000000 0.000000 0.421455 0.091155 0.000000 1.000000 0.544991 0.969234 0.000000 1.000000 0.730532 0.588783 0.000000 1.000000 0.327345 0.882593 1.000000 0.000000 0.348310 0.283558 0.000000 0.000000 0.419288 0.381249 1.000000 0.000000 0.898036 0.702191 0.000000 0.000000 0.982009 0.195492 0.000000 1.000000 0.913495 0.154397 0.000000 1.000000 0.311706 0.571432 1.000000 0.000000 0.531362 0.268780 0.000000 1.000000 0.063459 0.184990 0.000000 0.000000 0.554833 0.798204 0.000000 0.000000 0.782630 0.116122 1.000000 0.000000 0.017767 0.556265 1.000000 0.000000 0.820336 0.005002 0.000000 0.000000 0.463779 0.888909 1.000000 0.000000 0.963883 0.488963 0.000000 0.000000 0.289173 0.516203 1.000000 0.000000 0.638414 0.112638 1.000000 0.000000 0.536496 0.485446 0.000000 0.000000 0.397607 0.088100 0.000000 0.000000 0.223210 0.620690 1.000000 0.000000 0.536574 0.474683 0.000000 0.000000 0.613560 0.920255 0.000000 0.000000 0.617225 0.906664 1.000000 0.000000 0.203163 0.817948 0.000000 1.000000 0.402582 0.715819 0.000000 1.000000 0.987327 0.828515 0.000000 1.000000 0.874038 0.703846 1.000000 0.000000 0.475759 0.643031 0.000000 0.000000 0.443911 0.488231 0.000000 1.000000 0.271500 0.248830 0.000000 1.000000 0.681070 0.115841 0.000000 1.000000 0.687485 0.968830 0.000000 1.000000 0.016955 0.881198 0.000000 1.000000 0.205511 0.605011 1.000000 0.000000 0.528237 0.044769 1.000000 0.000000 0.825032 0.572299 0.000000 1.000000 0.694174 0.122153 0.000000 0.000000 0.633498 0.025441 1.000000 0.000000 0.206270 0.208802 1.000000 0.000000 0.928028 0.631258 0.000000 1.000000 0.389805 0.579822 0.000000 1.000000 0.570481 0.289327 1.000000 0.000000 0.958987 0.997330 0.000000 1.000000 0.773384 0.565807 1.000000 0.000000 0.621984 0.663723 1.000000 0.000000 0.028414 0.261638 0.000000 1.000000 0.139388 0.819465 0.000000 1.000000 0.797203 0.449517 0.000000 0.000000 0.703959 0.110151 0.000000 0.000000 0.335500 0.637880 1.000000 0.000000 0.627535 0.462075 1.000000 0.000000 0.604713 0.517587 0.000000 0.000000 0.709553 0.349850 0.000000 1.000000 0.703505 0.084515 0.000000 0.000000 0.564411 0.390871 1.000000 0.000000 0.890423 0.641825 0.000000 1.000000 0.114368 0.577844 1.000000 0.000000 0.043150 0.490592 0.000000 1.000000 0.607072 0.903563 1.000000 0.000000 0.281994 0.573469 1.000000 0.000000 0.689892 0.543140 0.000000 1.000000 0.559418 0.175703 0.000000 0.000000 0.410052 0.736572 0.000000 0.000000 0.912659 0.125886 0.000000 1.000000 0.738446 0.402136 1.000000 0.000000 0.665380 0.537070 1.000000 0.000000 0.764874 0.134680 0.000000 0.000000 0.649397 0.081505 0.000000 0.000000 0.765422 0.873147 0.000000 1.000000 0.341005 0.598644 0.000000 1.000000 0.281496 0.720297 0.000000 0.000000 0.106220 0.057260 0.000000 0.000000 0.042812 0.162400 0.000000 1.000000 0.628770 0.526638 0.000000 0.000000 0.685284 0.694233 0.000000 0.000000 0.984540 0.080658 0.000000 1.000000 0.593287 0.866968 1.000000 0.000000 0.153607 0.068486 0.000000 1.000000 0.864294 0.438999 0.000000 1.000000 0.469688 0.121999 1.000000 0.000000 0.363734 0.626217 1.000000 0.000000 0.319210 0.091892 0.000000 0.000000 0.891302 0.478767 0.000000 1.000000 0.475540 0.855269 0.000000 0.000000 0.364109 0.210617 0.000000 1.000000 0.838044 0.681260 1.000000 0.000000 0.820103 0.561107 1.000000 0.000000 0.823989 0.263466 0.000000 0.000000 0.517961 0.406827 0.000000 0.000000 0.829010 0.548415 0.000000 0.000000 0.210425 0.342115 0.000000 0.000000 0.745086 0.174126 0.000000 0.000000 0.262270 0.525400 0.000000 0.000000 0.950852 0.482701 0.000000 0.000000 0.355337 0.563117 0.000000 0.000000 0.010396 0.384569 1.000000 0.000000 0.973291 0.009793 1.000000 0.000000 0.357598 0.027207 1.000000 0.000000 0.546593 0.225939 1.000000 0.000000 0.974612 0.394469 1.000000 0.000000 0.990671 0.465912 1.000000 0.000000 0.162454 0.204309 0.000000 0.000000 0.778187 0.796149 0.000000 0.000000 0.240867 0.121732 0.000000 1.000000 0.782555 0.586080 1.000000 0.000000 0.910915 0.082931 1.000000 0.000000 0.634274 0.857075 0.000000 1.000000 0.281334 0.925804 1.000000 0.000000 0.391729 0.401248 0.000000 0.000000 0.118457 0.812061 0.000000 1.000000 0.162875 0.217493 0.000000 0.000000 0.202546 0.052926 1.000000 0.000000 0.888363 0.905371 0.000000 1.000000 0.921054 0.339076 0.000000 1.000000 0.959825 0.516511 0.000000 1.000000 0.444979 0.869815 0.000000 1.000000 0.448921 0.806355 1.000000 0.000000 0.456397 0.215585 1.000000 0.000000 0.674713 0.152277 0.000000 1.000000 0.788826 0.869830 1.000000 0.000000 0.255283 0.413893 0.000000 1.000000 0.979988 0.802003 0.000000 0.000000 0.351576 0.227087 1.000000 0.000000 0.476998 0.860526 0.000000 1.000000 0.682655 0.649873 0.000000 0.000000 0.252384 0.432028 0.000000 0.000000 0.090582 0.822612 0.000000 1.000000 0.285354 0.609651 0.000000 1.000000 0.680773 0.963817 1.000000 0.000000 0.427610 0.543347 1.000000 0.000000 0.080643 0.758666 1.000000 0.000000 0.225168 0.901581 0.000000 1.000000 0.497435 0.579450 1.000000 0.000000 0.906062 0.875916 1.000000 0.000000 0.898326 0.143786 0.000000 1.000000 0.983758 0.689415 0.000000 1.000000 0.276429 0.842816 0.000000 1.000000 0.553836 0.198198 0.000000 0.000000 0.534861 0.069439 1.000000 0.000000 0.774422 0.866906 0.000000 1.000000 0.543249 0.506485 1.000000 0.000000 0.683057 0.211484 1.000000 0.000000 0.857723 0.562309 0.000000 1.000000 0.716440 0.981052 0.000000 1.000000 0.512789 0.340915 1.000000 0.000000 0.920377 0.572209 0.000000 0.000000 0.969423 0.407898 0.000000 0.000000 0.383078 0.828505 0.000000 0.000000 0.319827 0.292304 0.000000 0.000000 0.402228 0.100802 0.000000 0.000000 0.339242 0.968431 1.000000 0.000000 0.382685 0.355937 0.000000 0.000000 0.077459 0.852174 0.000000 1.000000 0.529816 0.227056 0.000000 0.000000 0.147405 0.575366 0.000000 1.000000 0.364493 0.990763 0.000000 1.000000 0.691307 0.994536 1.000000 0.000000 0.080076 0.000411 0.000000 1.000000 0.779173 0.979076 0.000000 1.000000 0.034725 0.626302 0.000000 1.000000 0.169903 0.617778 1.000000 0.000000 0.858826 0.047994 0.000000 1.000000 0.340795 0.922445 0.000000 0.000000 0.599793 0.475904 1.000000 0.000000 0.253625 0.454666 0.000000 1.000000 0.437580 0.060677 0.000000 1.000000 0.427915 0.489048 1.000000 0.000000 0.718242 0.063331 0.000000 0.000000 0.038720 0.228267 1.000000 0.000000 0.373367 0.674778 1.000000 0.000000 0.703222 0.457925 0.000000 1.000000 0.859054 0.854099 0.000000 1.000000 0.758801 0.818287 0.000000 0.000000 0.479648 0.732310 1.000000 0.000000 0.262526 0.897134 0.000000 0.000000 0.571051 0.655104 0.000000 0.000000 0.545340 0.786223 0.000000 0.000000 0.173703 0.614293 0.000000 0.000000 0.992113 0.928855 0.000000 1.000000 0.795810 0.571340 0.000000 0.000000 0.092876 0.499174 0.000000 1.000000 0.160443 0.829067 0.000000 1.000000 0.593664 0.548002 0.000000 0.000000 0.742793 0.285175 0.000000 1.000000 0.430456 0.273023 0.000000 1.000000 0.787524 0.667482 1.000000 0.000000 0.423184 0.724241 0.000000 0.000000 0.059401 0.153096 1.000000 0.000000 0.703436 0.751428 0.000000 0.000000 0.699796 0.554122 0.000000 1.000000 0.160075 0.393344 0.000000 1.000000 0.366620 0.927302 0.000000 0.000000 0.680308 0.372220 1.000000 0.000000 0.197852 0.259852 0.000000 1.000000 0.750488 0.959466 0.000000 1.000000 0.667504 0.589920 0.000000 0.000000 0.613748 0.904811 0.000000 1.000000 0.387639 0.184294 1.000000 0.000000 0.972637 0.024930 0.000000 1.000000 0.301422 0.074828 1.000000 0.000000 0.206765 0.744834 0.000000 0.000000 0.386441 0.828034 1.000000 0.000000 0.429708 0.825277 0.000000 1.000000 0.882588 0.813547 0.000000 1.000000 0.086713 0.678260 0.000000 0.000000 0.290785 0.456927 1.000000 0.000000 0.290993 0.599165 0.000000 0.000000 0.894062 0.274614 1.000000 0.000000 0.611605 0.489274 1.000000 0.000000 0.743799 0.394845 0.000000 0.000000 0.049073 0.998516 0.000000 1.000000 0.555376 0.635084 0.000000 1.000000 0.217248 0.807645 1.000000 0.000000 0.954333 0.584508 0.000000 1.000000 0.290862 0.097357 1.000000 0.000000 0.470836 0.488198 1.000000 0.000000 0.838843 0.890891 1.000000 0.000000 0.861112 0.459583 1.000000 0.000000 0.855570 0.428323 0.000000 1.000000 0.677101 0.570287 0.000000 1.000000 0.536709 0.909744 0.000000 0.000000 0.204626 0.186306 0.000000 1.000000 0.942026 0.225804 0.000000 1.000000 0.328447 0.806716 0.000000 0.000000 0.927947 0.140188 0.000000 0.000000 0.018761 0.880484 0.000000 0.000000 0.911570 0.066777 0.000000 1.000000 0.704258 0.774904 0.000000 0.000000 0.716148 0.493402 1.000000 0.000000 0.454591 0.126302 1.000000 0.000000 0.997601 0.609718 0.000000 0.000000 0.761710 0.710125 1.000000 0.000000 0.815300 0.335752 0.000000 0.000000 0.175255 0.039142 1.000000 0.000000 0.179120 0.835435 0.000000 1.000000 0.032695 0.909971 0.000000 1.000000 0.200160 0.597898 0.000000 1.000000 0.207597 0.869074 1.000000 0.000000 0.796020 0.176743 1.000000 0.000000 0.789003 0.732580 0.000000 1.000000 0.596225 0.021317 1.000000 0.000000 0.659906 0.617376 0.000000 0.000000 0.409921 0.417059 0.000000 0.000000 0.494999 0.739770 1.000000 0.000000 0.155993 0.410442 0.000000 0.000000 0.565378 0.064626 0.000000 1.000000 0.908825 0.810482 0.000000 0.000000 0.177234 0.926666 0.000000 0.000000 0.050364 0.059857 0.000000 1.000000 0.972523 0.584725 0.000000 0.000000 0.613999 0.045717 0.000000 1.000000 0.752100 0.766442 0.000000 0.000000 0.356039 0.513679 0.000000 1.000000 0.048498 0.737886 0.000000 1.000000 0.772139 0.506167 1.000000 0.000000 0.133453 0.076854 1.000000 0.000000 0.361362 0.515248 0.000000 0.000000 0.212781 0.639492 1.000000 0.000000 0.175897 0.107760 1.000000 0.000000 0.741635 0.725912 1.000000 0.000000 0.527609 0.279413 1.000000 0.000000 0.841630 0.948328 0.000000 1.000000 0.142441 0.943550 1.000000 0.000000 0.072910 0.349583 1.000000 0.000000 0.431391 0.065486 1.000000 0.000000 0.477356 0.352768 1.000000 0.000000 0.501835 0.801531 0.000000 0.000000 0.905334 0.720522 0.000000 0.000000 0.815473 0.345923 1.000000 0.000000 0.313420 0.706225 1.000000 0.000000 0.444646 0.032007 0.000000 0.000000 0.686530 0.746949 0.000000 1.000000 0.491347 0.303807 1.000000 0.000000 0.144777 0.847781 0.000000 0.000000 0.705713 0.522559 0.000000 0.000000 0.877446 0.983006 0.000000 0.000000 0.395334 0.179425 0.000000 1.000000 0.227826 0.660453 0.000000 0.000000 0.436541 0.999014 0.000000 0.000000 0.455962 0.208260 0.000000 0.000000 0.659127 0.228340 0.000000 1.000000 0.195712 0.692558 0.000000 1.000000 0.273583 0.802544 0.000000 1.000000 0.860185 0.607742 0.000000 0.000000 0.536644 0.986556 0.000000 0.000000 0.512475 0.005911 0.000000 1.000000 0.925219 0.471802 0.000000 0.000000 0.220683 0.777417 0.000000 0.000000 0.007655 0.405538 1.000000 0.000000 0.601685 0.228755 0.000000 0.000000 0.497317 0.860043 0.000000 1.000000 0.051645 0.649569 1.000000 0.000000 0.937898 0.886486 0.000000 1.000000 0.566946 0.308974 1.000000 0.000000 0.766982 0.565000 0.000000 1.000000 0.860708 0.287861 0.000000 1.000000 0.163990 0.375746 0.000000 0.000000 0.296219 0.125496 0.000000 1.000000 0.036371 0.277092 0.000000 1.000000 0.241433 0.980783 0.000000 1.000000 0.204477 0.213169 1.000000 0.000000 0.740802 0.256279 0.000000 1.000000 0.092377 0.199909 0.000000 0.000000 0.536000 0.846872 1.000000 0.000000 0.873310 0.934832 0.000000 1.000000 0.335398 0.771481 1.000000 0.000000 0.405886 0.928657 1.000000 0.000000 0.653900 0.382741 0.000000 1.000000 0.994953 0.392812 1.000000 0.000000 0.247261 0.901684 0.000000 0.000000 0.228391 0.839058 0.000000 0.000000 0.799338 0.740564 1.000000 0.000000 0.011636 0.234423 1.000000 0.000000 0.242329 0.267186 1.000000 0.000000 0.242826 0.256504 1.000000 0.000000 0.814809 0.482930 0.000000 0.000000 0.852116 0.014363 0.000000 0.000000 0.799173 0.034225 0.000000 0.000000 0.217433 0.468232 0.000000 0.000000 0.578572 0.148377 0.000000 0.000000 0.577837 0.585401 0.000000 0.000000 0.177328 0.017477 0.000000 0.000000 0.932769 0.810286 0.000000 1.000000 0.465599 0.806647 0.000000 1.000000 0.266253 0.312280 0.000000 1.000000 0.688464 0.291064 0.000000 1.000000 0.509855 0.816607 0.000000 1.000000 0.589564 0.232777 1.000000 0.000000 0.188820 0.205458 0.000000 1.000000 0.211874 0.332539 0.000000 0.000000 0.696693 0.146547 0.000000 0.000000 0.842874 0.877364 1.000000 0.000000 0.586311 0.010365 0.000000 0.000000 0.641950 0.694890 1.000000 0.000000 0.755751 0.272186 1.000000 0.000000 0.366638 0.052778 0.000000 0.000000 0.419963 0.776791 0.000000 1.000000 0.817200 0.524612 1.000000 0.000000 0.767262 0.886822 0.000000 0.000000 0.405369 0.180678 0.000000 1.000000 0.247395 0.499571 1.000000 0.000000 0.748470 0.265988 0.000000 0.000000 0.202072 0.726633 0.000000 0.000000 0.275393 0.095339 0.000000 1.000000 0.709375 0.041928 0.000000 1.000000 0.347175 0.076263 0.000000 0.000000 0.475992 0.074651 0.000000 1.000000 0.079946 0.407589 0.000000 0.000000 0.398702 0.077317 0.000000 1.000000 0.505857 0.684842 0.000000 0.000000 0.213041 0.684097 1.000000 0.000000 0.939189 0.876110 1.000000 0.000000 0.973136 0.152142 1.000000 0.000000 0.951672 0.293708 0.000000 0.000000 0.245505 0.177949 0.000000 1.000000 0.595910 0.594934 1.000000 0.000000 0.655620 0.292947 1.000000 0.000000 0.117215 0.708479 0.000000 1.000000 0.759738 0.270520 1.000000 0.000000 0.244242 0.151038 0.000000 0.000000 0.378471 0.639367 0.000000 0.000000 0.819711 0.930700 1.000000 0.000000 0.622757 0.896142 1.000000 0.000000 0.982917 0.619201 1.000000 0.000000 0.473913 0.908223 0.000000 1.000000 0.077357 0.289909 0.000000 0.000000 0.325905 0.059299 0.000000 1.000000 0.778856 0.484676 0.000000 1.000000 0.912363 0.224922 0.000000 1.000000 0.497329 0.318841 0.000000 1.000000 0.526163 0.604556 0.000000 0.000000 0.055591 0.243655 0.000000 1.000000 0.126138 0.081930 1.000000 0.000000 0.793001 0.454619 1.000000 0.000000 0.930552 0.144194 0.000000 0.000000 0.764326 0.558292 0.000000 1.000000 0.991685 0.860310 1.000000 0.000000 0.100363 0.699952 0.000000 0.000000 0.823291 0.636777 0.000000 0.000000 0.665226 0.828206 0.000000 1.000000 0.402896 0.956491 0.000000 1.000000 0.975591 0.540315 1.000000 0.000000 0.473538 0.330192 0.000000 0.000000 0.566747 0.077455 0.000000 1.000000 0.505276 0.378538 0.000000 1.000000 0.216590 0.590747 0.000000 1.000000 0.734611 0.129197 1.000000 0.000000 0.019891 0.339411 0.000000 0.000000 0.638473 0.349948 0.000000 0.000000 0.978033 0.146451 0.000000 1.000000 0.478477 0.915285 1.000000 0.000000 0.863514 0.370899 0.000000 1.000000 0.234430 0.655186 0.000000 0.000000 0.560979 0.190335 1.000000 0.000000 0.959471 0.874449 1.000000 0.000000 0.804309 0.480719 0.000000 0.000000 0.612476 0.574624 0.000000 0.000000 0.799737 0.314642 1.000000 0.000000 0.542347 0.948917 0.000000 0.000000 0.406437 0.308249 0.000000 1.000000 0.408291 0.550323 0.000000 0.000000 0.121427 0.249677 1.000000 0.000000 0.993643 0.155415 0.000000 0.000000 0.076554 0.640840 1.000000 0.000000 0.134774 0.858614 0.000000 0.000000 0.980992 0.564994 0.000000 0.000000 0.867274 0.017622 1.000000 0.000000 0.715406 0.799933 0.000000 1.000000 0.761580 0.624966 1.000000 0.000000 0.415994 0.338861 0.000000 0.000000 0.663265 0.594767 0.000000 1.000000 0.327907 0.363219 1.000000 0.000000 0.587004 0.030184 0.000000 1.000000 0.288635 0.332993 1.000000 0.000000 0.361410 0.947257 0.000000 0.000000 0.207147 0.641101 0.000000 1.000000 0.177960 0.655628 0.000000 0.000000 0.090618 0.478953 0.000000 0.000000 0.771018 0.536784 0.000000 0.000000 0.766536 0.307203 0.000000 1.000000 0.382564 0.303700 0.000000 1.000000 0.083570 0.418310 0.000000 0.000000 0.271066 0.472715 0.000000 1.000000 0.764455 0.538415 0.000000 0.000000 0.340032 0.783867 0.000000 0.000000 0.056794 0.164050 0.000000 0.000000 0.868317 0.774675 0.000000 1.000000 0.865581 0.019738 1.000000 0.000000 0.689606 0.343362 1.000000 0.000000 0.739895 0.773954 1.000000 0.000000 0.589331 0.202117 1.000000 0.000000 0.562492 0.157211 1.000000 0.000000 0.523826 0.928867 0.000000 0.000000 0.406418 0.069797 1.000000 0.000000 0.649764 0.674146 0.000000 1.000000 0.925946 0.325556 1.000000 0.000000 0.270874 0.326460 1.000000 0.000000 0.803379 0.721098 1.000000 0.000000 0.158603 0.160879 0.000000 1.000000 0.515761 0.635826 1.000000 0.000000 0.832995 0.514543 0.000000 1.000000 0.995028 0.447127 0.000000 1.000000 0.374874 0.293784 0.000000 0.000000 0.048200 0.312283 0.000000 1.000000 0.458377 0.395427 0.000000 0.000000 0.572631 0.084020 1.000000 0.000000 0.889821 0.884600 1.000000 0.000000 0.233206 0.283870 0.000000 1.000000 0.934087 0.296965 0.000000 0.000000 0.982407 0.862615 1.000000 0.000000 0.373834 0.053334 0.000000 1.000000 0.041946 0.782587 0.000000 1.000000 0.821618 0.243780 0.000000 1.000000 0.459852 0.239384 0.000000 1.000000 0.547807 0.441019 1.000000 0.000000 0.185031 0.677158 0.000000 0.000000 0.519904 0.887228 0.000000 1.000000 0.182583 0.996921 1.000000 0.000000 0.271090 0.665462 ; proc qlim data = multinom; model st = x1 x2 / type = mlogit; run; proc iml; start mle; use multinom; read all var{dd2} into dd2; read all var{dd3} into dd3; read all var{x1} into x1; read all var{x2} into x2; Print, " Newton method to Maximum Likelihood Estimation"; /* Starting values for Beta10, Beta11, Beta12, Beta20, Beta21 and Beta22*/ theta = {.001,.001,.001,.001,.001,.001}; crit = 1; n=1000; result = j(4,9,0); /* Newton method to Maximum Likelihood Estimation*/ do iter = 1 to 20 while (crit > 1.0e-9); /* Defining Beta*/ beta20=theta[1,1]; beta21=theta[2,1]; beta22=theta[3,1]; beta30=theta[4,1]; beta31=theta[5,1]; beta32=theta[6,1]; /*Defining notations*/ xb2= beta20 + beta21#x1+ beta22#x2; xb3= beta30 + beta31#x1+ beta32#x2; exb2= exp(xb2); exb3= exp(xb3); eb= 1+ exp(xb2) + exp(xb3); /* The Log-Likelihood Function*/ logl= dd2#xb2 + dd3#xb3-log(eb); logl = sum (logl); /* Calculate the Gradient vector*/ g20= sum(dd2 - exb2/eb); g21 = sum((dd2 - exb2/eb)#x1); g22 = sum((dd2 - exb2/eb)#x2); g30= sum(dd3 - exb3/eb); g31= sum((dd3 - exb3/eb)#x1); g32= sum((dd3 - exb3/eb)#x2); g= g20//g21//g22//g30//g31//g32; /* Calculate the Hessian*/ h2020 = sum(-(exb2/eb)#(1-exb2/eb)); h2021 = sum(-((exb2/eb)#(1-exb2/eb))#x1); h2022 = sum(-((exb2/eb)#(1-exb2/eb))#x2); h2030 = sum((exb2#exb3)/(eb#eb)); h2031 = sum(((exb2#exb3)/(eb#eb))#x1); h2032 = sum(((exb2#exb3)/(eb#eb))#x2); h2121 = sum(-(exb2/eb)#(1-exb2/eb)#x1#x1); h2122 = sum(-(exb2/eb)#(1-exb2/eb)#x1#x2); h2130 = sum((exb2#exb3#x1)/(eb#eb)); h2131 = sum(((exb2#exb3#x1)/(eb#eb))#x1); h2132 = sum(((exb2#exb3#x1)/(eb#eb))#x2); h2222 = sum(-(exb2/eb)#(1- exb2/eb)#x2#x2); h2230 = sum((exb2#exb3#x2)/(eb#eb)); h2231 = sum((exb2#exb3#x2#x1)/(eb#eb)); h2232 = sum((exb2#exb3#x2#x2)/(eb#eb)); h3030 = sum(-(exb3/eb)#(1-exb3/eb)); h3031 = sum(-((exb3/eb)#(1-exb3/eb))#x1); h3032 = sum(-((exb3/eb)#(1-exb3/eb))#x2); h3131 = sum(-((exb3/eb)#(1-exb3/eb))#x1#x1); h3132 = sum(-((exb3/eb)#(1-exb3/eb))#x1#x2); h3232 = sum(-((exb3/eb)#(1-exb3/eb))#x2#x2); h1 = h2020||h2021||h2022||h2030||h2031||h2032; h2 = h2021`||h2121||h2122||h2130||h2131||h2132; h3 = h2022`||h2122`||h2222||h2230||h2231||h2232; h4 = h2030`||h2130`||h2230`||h3030||h3031||h3032; h5 = h2031`||h2131`||h2231`||h3031`||h3131||h3132; h6 = h2032`||h2132`||h2232`||h3032`||h3132`||h3232; h = h1//h2//h3//h4//h5//h6; /* The Newton two step */ db = -inv(h)*g; thetanew = theta + db; crit = sqrt(ssq(thetanew - theta)); /* Place the result of this iteration in the result matrix */ result[iter,] = iter||(theta`)||crit||logl; theta = thetanew; end; cnames = {iter,beta20, beta21,beta22, beta30, beta31, beta32, crit,logL}; print "result",result [colname=cnames]; finish; run mle; quit;