data: d:\work\develope\apps\PsiStatsPro\data\s24_3.loglinear date: Thu 24 Mar 2005 17:03:45 excluded variables as follows: - none ---- three-way contingency table analysis by log-linear model list of models sorted, AIC, chi square, degree of freedom model number: log-linear models sorted , AIC , chi , freedom 2: u+uA(i)+uB(j)+uC(k)+uAB(ij)+uAC(ik) , -4.702, 7.298, 6 1: u+uA(i)+uB(j)+uC(k)+uAB(ij)+uAC(ik)+uBC(jk), -2.188, 5.812, 4 6: u+uA(i)+uB(j)+uC(k) +uAC(ik) , 3.450, 19.450, 8 4: u+uA(i)+uB(j)+uC(k) +uAC(ik)+uBC(jk), 7.137, 19.137, 6 10: u+uA(i) +uC(k) +uAC(ik) , 22.710, 40.710, 9 5: u+uA(i)+uB(j)+uC(k)+uAB(ij) , 108.767, 128.767, 10 3: u+uA(i)+uB(j)+uC(k)+uAB(ij) +uBC(jk), 112.454, 128.454, 8 8: u+uA(i)+uB(j)+uC(k) , 116.919, 140.919, 12 7: u+uA(i)+uB(j)+uC(k) +uBC(jk), 120.606, 140.606, 10 9: u+uA(i)+uB(j) +uAB(ij) , 127.915, 151.915, 12 12: u+uA(i)+uB(j) , 136.067, 164.067, 14 13: u+uA(i) +uC(k) , 136.179, 162.179, 13 15: u+uA(i) , 155.326, 185.326, 15 14: u +uB(j)+uC(k) , 724.363, 752.363, 14 11: u +uB(j)+uC(k) +uBC(jk), 728.050, 752.050, 12 16: u +uB(j) , 743.510, 775.510, 16 17: u +uC(k) , 743.622, 773.622, 15 18: u , 762.770, 796.770, 17 estimated parameters of the saturated model - main effect, two and three-factors interaction - i , uA(i) , Std.E. , Std.uA(i) 1. , -1.460827403, 0.089303956, -16.357924841 2. , 0.752905766, 0.054644695, 13.778204258 3. , 0.707921636, 0.055356241, 12.788470232 j , uB(j) , Std.E. , Std.uB(j) 1. , 0.048724682, 0.048348652, 1.007777484 2. , -0.048724682, 0.048348652, -1.007777484 k , uC(k) , Std.E. , Std.uC(k) 1. , -0.132096138, 0.069842619, -1.891339982 2. , 0.192995085, 0.065968245, 2.925575567 3. , -0.060898947, 0.069251367, -0.879389815 i j , uAB(ij) , Std.E. , S.uAB(ij) 1 1 ,-0.234161853360, 0.089303956151,-2.622077043970 1 2 , 0.234161853360, 0.089303956151, 2.622077043970 2 1 , 0.042066071940, 0.054644694779, 0.769810721973 2 2 ,-0.042066071940, 0.054644694779,-0.769810721973 3 1 , 0.192095781420, 0.055356240704, 3.470173895088 3 2 ,-0.192095781420, 0.055356240704,-3.470173895088 i k , uAC(ik) , Std.E. , S.uAC(ik) 1 1 , 0.089914366529, 0.128224497793, 0.701226115730 1 2 ,-0.108631542446, 0.122679971364,-0.885487184567 1 3 , 0.018717175917, 0.127903410031, 0.146338365115 2 1 , 0.405423864534, 0.077368584308, 5.240161341478 2 2 , 0.038518034103, 0.074008595315, 0.520453522185 2 3 ,-0.443941898637, 0.080331102238,-5.526401185435 3 1 ,-0.495338231063, 0.082707490044,-5.989037157302 3 2 , 0.070113508342, 0.074720869397, 0.938339033100 3 3 , 0.425224722720, 0.077214914856, 5.507028318452 j k , uBC(jk) , Std.E. , S.uBC(jk) 1 1 , 0.001936356409, 0.069842619011, 0.027724567561 1 2 , 0.040449330891, 0.065968244731, 0.613163667696 1 3 ,-0.042385687300, 0.069251367448,-0.612055600666 2 1 ,-0.001936356409, 0.069842619011,-0.027724567561 2 2 ,-0.040449330891, 0.065968244731,-0.613163667696 2 3 , 0.042385687300, 0.069251367448, 0.612055600666 i j k , uABC(ijk) , Std.E. , S.uABC(ijk) 1 1 1 ,-0.071911997336, 0.128224497793,-0.560828847636 1 1 2 , 0.099501950962, 0.122679971364, 0.811069238575 1 1 3 ,-0.027589953626, 0.127903410031,-0.215709288905 1 2 1 , 0.071911997336, 0.128224497793, 0.560828847636 1 2 2 ,-0.099501950962, 0.122679971364,-0.811069238575 1 2 3 , 0.027589953626, 0.127903410031, 0.215709288905 2 1 1 , 0.001815867688, 0.077368584308, 0.023470349161 2 1 2 ,-0.114071016445, 0.074008595315,-1.541321193296 2 1 3 , 0.112255148757, 0.080331102238, 1.397405807077 2 2 1 ,-0.001815867688, 0.077368584308,-0.023470349161 2 2 2 , 0.114071016445, 0.074008595315, 1.541321193296 2 2 3 ,-0.112255148757, 0.080331102238,-1.397405807077 3 1 1 , 0.070096129648, 0.082707490044, 0.847518521125 3 1 2 , 0.014569065482, 0.074720869397, 0.194979871082 3 1 3 ,-0.084665195130, 0.077214914856,-1.096487579997 3 2 1 ,-0.070096129648, 0.082707490044,-0.847518521125 3 2 2 ,-0.014569065482, 0.074720869397,-0.194979871082 3 2 3 , 0.084665195130, 0.077214914856, 1.096487579997 comparison of models model number: log-linear models sorted , chi , freedom 2: u+uA(i)+uB(j)+uC(k)+uAB(ij)+uAC(ik) , 7.298460, 6 1: u+uA(i)+uB(j)+uC(k)+uAB(ij)+uAC(ik)+uBC(jk), 5.812165, 4 difference , 1.486294, 2 frequency cross table of observed and expected, residual , LLM( 2) , , , LLM( 1) , C 1, C 2, C 3, C 1, C 2, C 3 A 1 - B 1 , 7, 10, 7, 7, 10, 7 , 7.729, 8.542, 7.729, 8.075, 8.676, 7.249 , -0.729, 1.458, -0.729, -1.075, 1.324, -0.249 B 2 , 12, 11, 12, 12, 11, 12 , 11.271, 12.458, 11.271, 10.925, 12.324, 11.751 , 0.729, -1.458, 0.729, 1.075, -1.324, 0.249 A 2 - B 1 , 133, 118, 65, 133, 118, 65 , 130.814, 124.893, 60.293, 134.063, 125.189, 56.748 , 2.186, -6.893, 4.707, -1.063, -7.189, 8.252 B 2 , 110, 114, 47, 110, 114, 47 , 112.186, 107.107, 51.707, 108.937, 106.811, 55.252 , -2.186, 6.893, -4.707, 1.063, 7.189, -8.252 A 3 - B 1 , 64, 154, 142, 64, 154, 142 , 59.595, 145.338, 155.068, 61.862, 148.136, 150.003 , 4.405, 8.662, -13.068, 2.138, 5.864, -8.003 B 2 , 34, 85, 113, 34, 85, 113 , 38.405, 93.662, 99.932, 36.138, 90.864, 104.997 , -4.405, -8.662, 13.068, -2.138, -5.864, 8.003 estimated parameters of LLM( 2) and LLM( 1) - main effect, two and three-factors interaction - , LLM( 2) , LLM( 1) i , uA(i), uA(i) 1 ,-1.491074416679,-1.490630763621 2 , 0.765300208795, 0.766661223991 3 , 0.725774207884, 0.723969539629 j , uB(j), uB(j) 1 , 0.035949303558, 0.035539263638 2 ,-0.035949303558,-0.035539263638 k , uC(k), uC(k) 1 ,-0.125220994954,-0.126559333664 2 , 0.189864158427, 0.189993660370 3 ,-0.064643163473,-0.063434326706 i j , uAB(ij), uAB(ij) 1 1 ,-0.224596419129,-0.224929085417 1 2 , 0.224596419129, 0.224929085417 2 1 , 0.040862392795, 0.029964558615 2 2 ,-0.040862392795,-0.029964558615 3 1 , 0.183734026334, 0.194964526802 3 2 ,-0.183734026334,-0.194964526802 i k , uAC(ik), uAC(ik) 1 1 , 0.091859842102, 0.100352207206 1 2 ,-0.123141852723,-0.120065656253 1 3 , 0.031282010621, 0.019713449047 2 1 , 0.398849876194, 0.397683890551 2 2 , 0.037440651138, 0.037034291610 2 3 ,-0.436290527332,-0.434718182161 3 1 ,-0.490709718296,-0.498036097757 3 2 , 0.085701201584, 0.083031364643 3 3 , 0.405008516711, 0.415004733114 j k , uBC(jk), uBC(jk) 1 1 , 0.000000000000, 0.038268080446 1 2 , 0.000000000000, 0.013875352809 1 3 , 0.000000000000,-0.052143433255 2 1 , 0.000000000000,-0.038268080446 2 2 , 0.000000000000,-0.013875352809 2 3 , 0.000000000000, 0.052143433255