M1: Full model fit with PROC GLIMMIX, ML with AGQ 1 The GLIMMIX Procedure Model Information Data Set WORK.EPILEPS Response Variable seizures Response Distribution Poisson Link Function Log Variance Function Default Variance Matrix Blocked By id Estimation Technique Maximum Likelihood Likelihood Approximation Gauss-Hermite Quadrature Degrees of Freedom Method Containment Class Level Information Class Levels Values id 59 101 102 103 104 106 107 108 110 111 112 113 114 116 117 118 121 122 123 124 126 128 129 130 135 137 139 141 143 145 147 201 202 203 204 205 206 207 208 209 210 211 213 214 215 217 218 219 220 221 222 225 226 227 228 230 232 234 236 238 trt 2 0 1 time 4 1 2 3 4 Number of Observations Read 236 Number of Observations Used 236 Dimensions G-side Cov. Parameters 1 Columns in X 30 Columns in Z per Subject 1 Subjects (Blocks in V) 59 Max Obs per Subject 4 Optimization Information Optimization Technique Dual Quasi-Newton Parameters in Optimization 17 Lower Boundaries 1 Upper Boundaries 0 Fixed Effects Not Profiled Starting From GLM estimates Quadrature Points 1 M1: Full model fit with PROC GLIMMIX, ML with AGQ 2 The GLIMMIX Procedure Iteration History Objective Max Iteration Restarts Evaluations Function Change Gradient 0 0 4 1321.425524 . 112.5453 1 0 4 1317.4189516 4.00657233 43.30585 2 0 2 1316.5678605 0.85109111 40.15178 3 0 2 1315.801856 0.76600447 19.56654 4 0 2 1315.6826407 0.11921534 13.8309 5 0 2 1315.5889736 0.09366708 13.27267 6 0 2 1315.5051574 0.08381617 14.20445 7 0 2 1315.4157378 0.08941970 17.09838 8 0 4 1315.2343009 0.18143686 14.9958 9 0 2 1315.1587077 0.07559324 22.41285 10 0 2 1315.0675971 0.09111051 3.642066 11 0 2 1314.9889243 0.07867285 7.352381 12 0 2 1314.9310035 0.05792080 6.731285 13 0 3 1314.8909883 0.04001514 3.608913 14 0 4 1314.7628053 0.12818303 4.023196 15 0 3 1314.7178922 0.04491315 3.436772 16 0 2 1314.6614963 0.05639587 5.04204 17 0 4 1314.4920326 0.16946369 5.770447 18 0 3 1314.4206651 0.07136751 1.506549 19 0 3 1314.4119393 0.00872578 2.397241 20 0 4 1314.3764747 0.03546463 3.048539 21 0 3 1314.3631508 0.01332392 0.886389 22 0 3 1314.3614854 0.00166531 0.558321 23 0 4 1314.3411104 0.02037505 5.275335 24 0 3 1314.3308269 0.01028346 0.26979 25 0 2 1314.3237395 0.00708743 1.524068 26 0 3 1314.3211324 0.00260708 0.500362 27 0 3 1314.3209956 0.00013680 0.183412 28 0 4 1314.3190909 0.00190477 1.798924 29 0 2 1314.3172612 0.00182965 0.758909 30 0 2 1314.3157613 0.00149985 1.746121 31 0 4 1314.3100715 0.00568984 1.447916 32 0 2 1314.3044086 0.00566287 0.321836 33 0 3 1314.3041131 0.00029557 0.234085 34 0 4 1314.3025005 0.00161262 0.191484 35 0 3 1314.3023874 0.00011308 0.173246 36 0 4 1314.3012544 0.00113292 0.133853 37 0 2 1314.3006709 0.00058359 0.37812 38 0 3 1314.3005128 0.00015805 0.019192 39 0 3 1314.3005083 0.00000447 0.008981 Convergence criterion (GCONV=1E-8) satisfied. M1: Full model fit with PROC GLIMMIX, ML with AGQ 3 The GLIMMIX Procedure Adaptiveness of Quadrature at Solution Quadrature Objective ---Relative Difference to--- Points Function Converged Previous 1 1314.3005083 3 1314.4254895 0.0000950933 0.0000950933 5 1314.1578821 -0.000108519 -0.000203593 7 1314.1549526 -0.000110748 -2.229194E-6 9 1314.1550919 -0.000110642 1.0606664E-7 11 1314.1550632 -0.000110664 -2.188706E-8 21 1314.1550617 -0.000110665 -1.13737E-9 31 1314.1550617 -0.000110665 7.95887E-15 Fit Statistics -2 Log Likelihood 1314.30 AIC (smaller is better) 1348.30 AICC (smaller is better) 1351.11 BIC (smaller is better) 1383.62 CAIC (smaller is better) 1400.62 HQIC (smaller is better) 1362.09 Fit Statistics for Conditional Distribution -2 log L(seizures | r. effects) 1153.81 Pearson Chi-Square 343.12 Pearson Chi-Square / DF 1.45 Covariance Parameter Estimates Standard Cov Parm Subject Estimate Error Intercept id 0.2644 0.06065 Solutions for Fixed Effects Standard Effect trt time Estimate Error DF t Value Pr > |t| Intercept -0.7701 0.3615 55 -2.13 0.0376 logbase 1.1617 0.1665 165 6.98 <.0001 trt 0 0.9741 0.4848 165 2.01 0.0462 trt 1 0 . . . . logbase*trt 0 -0.2911 0.2273 165 -1.28 0.2021 logbase*trt 1 0 . . . . M1: Full model fit with PROC GLIMMIX, ML with AGQ 4 The GLIMMIX Procedure Solutions for Fixed Effects Standard Effect trt time Estimate Error DF t Value Pr > |t| time 1 -0.2732 0.3065 165 -0.89 0.3740 time 2 0.6760 0.2940 165 2.30 0.0228 time 3 0.1698 0.3021 165 0.56 0.5748 time 4 0 . . . . logbase*time 1 0.1980 0.1117 165 1.77 0.0782 logbase*time 2 -0.1802 0.1116 165 -1.61 0.1083 logbase*time 3 0.008656 0.1123 165 0.08 0.9387 logbase*time 4 0 . . . . trt*time 0 1 0.4417 0.4244 165 1.04 0.2995 trt*time 0 2 -0.5607 0.4201 165 -1.33 0.1838 trt*time 0 3 -0.3577 0.4304 165 -0.83 0.4072 trt*time 0 4 0 . . . . trt*time 1 1 0 . . . . trt*time 1 2 0 . . . . trt*time 1 3 0 . . . . trt*time 1 4 0 . . . . logbase*trt*time 0 1 -0.2011 0.1648 165 -1.22 0.2240 logbase*trt*time 0 2 0.1472 0.1670 165 0.88 0.3792 logbase*trt*time 0 3 0.1137 0.1681 165 0.68 0.4998 logbase*trt*time 0 4 0 . . . . logbase*trt*time 1 1 0 . . . . logbase*trt*time 1 2 0 . . . . logbase*trt*time 1 3 0 . . . . logbase*trt*time 1 4 0 . . . . Type III Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F logbase 1 165 105.67 105.67 <.0001 <.0001 trt 1 165 4.55 4.55 0.0329 0.0344 logbase*trt 1 165 1.90 1.90 0.1684 0.1703 time 3 165 6.40 2.13 0.0936 0.0979 logbase*time 3 165 7.54 2.51 0.0565 0.0603 trt*time 3 165 6.97 2.32 0.0729 0.0769 logbase*trt*time 3 165 5.86 1.95 0.1185 0.1230 M1a: Full model with alt par'zation fit with PROC GLIMMIX, ML w/ AGQ 5 The GLIMMIX Procedure Model Information Data Set WORK.EPILEPS Response Variable seizures Response Distribution Poisson Link Function Log Variance Function Default Variance Matrix Blocked By id Estimation Technique Maximum Likelihood Likelihood Approximation Gauss-Hermite Quadrature Degrees of Freedom Method Containment Class Level Information Class Levels Values id 59 101 102 103 104 106 107 108 110 111 112 113 114 116 117 118 121 122 123 124 126 128 129 130 135 137 139 141 143 145 147 201 202 203 204 205 206 207 208 209 210 211 213 214 215 217 218 219 220 221 222 225 226 227 228 230 232 234 236 238 Number of Observations Read 236 Number of Observations Used 236 Dimensions G-side Cov. Parameters 1 Columns in X 16 Columns in Z per Subject 1 Subjects (Blocks in V) 59 Max Obs per Subject 4 Optimization Information Optimization Technique Dual Quasi-Newton Parameters in Optimization 17 Lower Boundaries 1 Upper Boundaries 0 Fixed Effects Not Profiled Starting From GLM estimates Quadrature Points 1 M1a: Full model with alt par'zation fit with PROC GLIMMIX, ML w/ AGQ 6 The GLIMMIX Procedure Iteration History Objective Max Iteration Restarts Evaluations Function Change Gradient 0 0 4 1321.425524 . 81.5267 1 0 3 1319.4549326 1.97059131 100.9325 2 0 2 1317.5420108 1.91292181 28.1374 3 0 4 1316.3247536 1.21725724 51.64273 4 0 3 1315.9245563 0.40019728 22.55754 5 0 2 1315.6110219 0.31353442 9.411401 6 0 3 1315.5304209 0.08060104 13.44055 7 0 2 1315.4360126 0.09440829 6.143514 8 0 3 1315.3892021 0.04681043 7.30122 9 0 2 1315.3254105 0.06379163 7.149528 10 0 4 1315.1881249 0.13728564 12.78427 11 0 2 1315.1483938 0.03973104 15.2009 12 0 4 1315.0144737 0.13392010 1.849229 13 0 3 1314.9944387 0.02003499 5.621575 14 0 4 1314.947702 0.04673670 2.577671 15 0 4 1314.7746609 0.17304119 4.020669 16 0 2 1314.4944405 0.28022039 6.303588 17 0 3 1314.3273086 0.16713184 2.433679 18 0 3 1314.3186482 0.00866041 0.594513 19 0 2 1314.3078989 0.01074931 1.72006 20 0 3 1314.3015823 0.00631662 0.188476 21 0 3 1314.3015335 0.00004880 0.082502 22 0 4 1314.3010861 0.00044737 0.126199 23 0 3 1314.3010181 0.00006796 0.06419 24 0 4 1314.3007604 0.00025770 0.115599 25 0 3 1314.3006322 0.00012822 0.070559 26 0 2 1314.3005155 0.00011673 0.048093 27 0 3 1314.3005013 0.00001416 0.004698 28 0 3 1314.3004999 0.00000146 0.000655 Convergence criterion (GCONV=1E-8) satisfied. Fit Statistics -2 Log Likelihood 1314.30 AIC (smaller is better) 1348.30 AICC (smaller is better) 1351.11 BIC (smaller is better) 1383.62 CAIC (smaller is better) 1400.62 HQIC (smaller is better) 1362.09 M1a: Full model with alt par'zation fit with PROC GLIMMIX, ML w/ AGQ 7 The GLIMMIX Procedure Fit Statistics for Conditional Distribution -2 log L(seizures | r. effects) 1153.81 Pearson Chi-Square 343.12 Pearson Chi-Square / DF 1.45 Covariance Parameter Estimates Standard Cov Parm Subject Estimate Error Intercept id 0.2644 0.06065 Solutions for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| trttim11 0.3724 0.3122 165 1.19 0.2346 trttim12 0.3191 0.3181 165 1.00 0.3172 trttim13 0.01639 0.3258 165 0.05 0.9599 trttim14 0.2042 0.3233 165 0.63 0.5285 trttim21 -1.0431 0.3577 165 -2.92 0.0040 trttim22 -0.09386 0.3380 165 -0.28 0.7816 trttim23 -0.6006 0.3497 165 -1.72 0.0878 trttim24 -0.7699 0.3615 165 -2.13 0.0347 trttim11*logbase 0.8675 0.1507 165 5.75 <.0001 trttim12*logbase 0.8377 0.1531 165 5.47 <.0001 trttim13*logbase 0.9929 0.1545 165 6.43 <.0001 trttim14*logbase 0.8706 0.1547 165 5.63 <.0001 trttim21*logbase 1.3596 0.1642 165 8.28 <.0001 trttim22*logbase 0.9814 0.1605 165 6.11 <.0001 trttim23*logbase 1.1705 0.1630 165 7.18 <.0001 trttim24*logbase 1.1617 0.1665 165 6.98 <.0001 Type III Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F trttim11 1 165 1.42 1.42 0.2329 0.2346 trttim12 1 165 1.01 1.01 0.3158 0.3172 trttim13 1 165 0.00 0.00 0.9599 0.9599 trttim14 1 165 0.40 0.40 0.5277 0.5285 trttim21 1 165 8.50 8.50 0.0035 0.0040 trttim22 1 165 0.08 0.08 0.7812 0.7816 trttim23 1 165 2.95 2.95 0.0859 0.0878 trttim24 1 165 4.54 4.54 0.0332 0.0347 M1a: Full model with alt par'zation fit with PROC GLIMMIX, ML w/ AGQ 8 The GLIMMIX Procedure Type III Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F trttim11*logbase 1 165 33.12 33.12 <.0001 <.0001 trttim12*logbase 1 165 29.94 29.94 <.0001 <.0001 trttim13*logbase 1 165 41.30 41.30 <.0001 <.0001 trttim14*logbase 1 165 31.69 31.69 <.0001 <.0001 trttim21*logbase 1 165 68.55 68.55 <.0001 <.0001 trttim22*logbase 1 165 37.38 37.38 <.0001 <.0001 trttim23*logbase 1 165 51.59 51.59 <.0001 <.0001 trttim24*logbase 1 165 48.66 48.66 <.0001 <.0001 M1b: Full model with alt par'zation fit with PROC GLIMMIX, PQL 9 The GLIMMIX Procedure Model Information Data Set WORK.EPILEPS Response Variable seizures Response Distribution Poisson Link Function Log Variance Function Default Variance Matrix Blocked By id Estimation Technique PL Degrees of Freedom Method Kenward-Roger Fixed Effects SE Adjustment Kenward-Roger Class Level Information Class Levels Values id 59 101 102 103 104 106 107 108 110 111 112 113 114 116 117 118 121 122 123 124 126 128 129 130 135 137 139 141 143 145 147 201 202 203 204 205 206 207 208 209 210 211 213 214 215 217 218 219 220 221 222 225 226 227 228 230 232 234 236 238 Number of Observations Read 236 Number of Observations Used 236 Dimensions G-side Cov. Parameters 1 Columns in X 16 Columns in Z per Subject 1 Subjects (Blocks in V) 59 Max Obs per Subject 4 Optimization Information Optimization Technique Dual Quasi-Newton Parameters in Optimization 1 Lower Boundaries 1 Upper Boundaries 0 Fixed Effects Profiled Starting From Data M1b: Full model with alt par'zation fit with PROC GLIMMIX, PQL 10 The GLIMMIX Procedure Iteration History Objective Max Iteration Restarts Subiterations Function Change Gradient 0 0 4 469.31429859 2.00000000 3.003E-6 1 0 4 539.87222529 0.51768201 5.635E-7 2 0 2 548.29790705 0.01285681 0.000062 3 0 1 548.48045629 0.00015057 5.908E-6 4 0 1 548.48163913 0.00000148 8.574E-8 5 0 0 548.48164985 0.00000000 1.432E-6 Convergence criterion (PCONV=1.11022E-8) satisfied. Fit Statistics -2 Log Pseudo-Likelihood 548.48 Generalized Chi-Square 390.36 Gener. Chi-Square / DF 1.65 Covariance Parameter Estimates Standard Cov Parm Subject Estimate Error Intercept id 0.2572 0.05836 Solutions for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| trttim11 0.4147 0.3093 123.3 1.34 0.1824 trttim12 0.3615 0.3153 133.2 1.15 0.2537 trttim13 0.05861 0.3230 146.2 0.18 0.8563 trttim14 0.2465 0.3205 142.2 0.77 0.4432 trttim21 -0.9831 0.3542 139 -2.78 0.0063 trttim22 -0.03336 0.3341 112.3 -0.10 0.9207 trttim23 -0.5404 0.3461 127.8 -1.56 0.1209 trttim24 -0.7097 0.3580 146.4 -1.98 0.0493 trttim11*logbase 0.8554 0.1492 86.82 5.73 <.0001 trttim12*logbase 0.8257 0.1516 92.55 5.45 <.0001 trttim13*logbase 0.9809 0.1530 95.73 6.41 <.0001 trttim14*logbase 0.8585 0.1532 96.4 5.61 <.0001 trttim21*logbase 1.3415 0.1625 87.9 8.25 <.0001 trttim22*logbase 0.9631 0.1587 81.19 6.07 <.0001 trttim23*logbase 1.1523 0.1612 85.72 7.15 <.0001 trttim24*logbase 1.1435 0.1648 93.7 6.94 <.0001 M1b: Full model with alt par'zation fit with PROC GLIMMIX, PQL 11 The GLIMMIX Procedure Type III Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F trttim11 1 123.3 1.80 1.80 0.1799 0.1824 trttim12 1 133.2 1.31 1.31 0.2516 0.2537 trttim13 1 146.2 0.03 0.03 0.8560 0.8563 trttim14 1 142.2 0.59 0.59 0.4419 0.4432 trttim21 1 139 7.70 7.70 0.0055 0.0063 trttim22 1 112.3 0.01 0.01 0.9205 0.9207 trttim23 1 127.8 2.44 2.44 0.1184 0.1209 trttim24 1 146.4 3.93 3.93 0.0474 0.0493 trttim11*logbase 1 86.82 32.87 32.87 <.0001 <.0001 trttim12*logbase 1 92.55 29.67 29.67 <.0001 <.0001 trttim13*logbase 1 95.73 41.10 41.10 <.0001 <.0001 trttim14*logbase 1 96.4 31.42 31.42 <.0001 <.0001 trttim21*logbase 1 87.9 68.13 68.13 <.0001 <.0001 trttim22*logbase 1 81.19 36.81 36.81 <.0001 <.0001 trttim23*logbase 1 85.72 51.08 51.08 <.0001 <.0001 trttim24*logbase 1 93.7 48.12 48.12 <.0001 <.0001 M1c: NLMIXED fit of Model M1b 12 The NLMIXED Procedure Specifications Data Set WORK.EPILEPS Dependent Variable seizures Distribution for Dependent Variable Poisson Random Effects b Distribution for Random Effects Normal Subject Variable id Optimization Technique Dual Quasi-Newton Integration Method Adaptive Gaussian Quadrature Dimensions Observations Used 236 Observations Not Used 0 Total Observations 236 Subjects 59 Max Obs Per Subject 4 Parameters 17 Quadrature Points 1 Parameters lam11 lam12 lam13 lam14 lam21 lam22 lam23 lam24 beta11 0.41 0.36 0.059 0.25 -0.98 -0.033 -0.54 -0.71 0.86 Parameters beta12 beta13 beta14 beta21 beta22 beta23 beta24 th1 NegLogLike 0.83 0.98 0.86 1.34 0.96 1.15 1.14 0.26 657.225417 Iteration History Iter Calls NegLogLike Diff MaxGrad Slope 1 5 657.207839 0.017578 1.117196 -68.3103 2 7 657.196523 0.011316 2.997418 -0.01007 3 8 657.179603 0.01692 0.512185 -0.06435 4 10 657.178559 0.001044 0.764563 -0.00492 5 11 657.17735 0.001209 0.344358 -0.00358 6 13 657.177103 0.000246 0.326411 -0.00097 7 15 657.174696 0.002407 0.769231 -0.00129 8 16 657.171697 0.002999 1.812577 -0.00373 9 18 657.16246 0.009237 1.092308 -0.01544 M1c: NLMIXED fit of Model M1b 13 The NLMIXED Procedure Iteration History Iter Calls NegLogLike Diff MaxGrad Slope 10 20 657.16008 0.00238 0.694305 -0.00686 11 22 657.158561 0.001519 1.080143 -0.00376 12 23 657.156082 0.002479 0.413764 -0.00665 13 25 657.154558 0.001524 0.290583 -0.00205 14 26 657.152411 0.002147 0.526143 -0.00054 15 27 657.151121 0.001289 0.132988 -0.00175 16 29 657.150599 0.000522 0.02504 -0.00103 17 31 657.150503 0.000096 0.168314 -7.04E-6 18 33 657.150441 0.000063 0.027755 -0.00007 19 35 657.150282 0.000158 0.107704 -7.28E-6 20 37 657.150253 0.000029 0.006236 -0.00005 21 38 657.150251 1.774E-6 0.009007 -3.66E-7 NOTE: GCONV convergence criterion satisfied. Fit Statistics -2 Log Likelihood 1314.3 AIC (smaller is better) 1348.3 AICC (smaller is better) 1351.1 BIC (smaller is better) 1383.6 Parameter Estimates Standard Parameter Estimate Error DF t Value Pr > |t| Alpha Lower Upper Gradient lam11 0.3725 0.3122 58 1.19 0.2377 0.05 -0.2524 0.9973 0.005089 lam12 0.3189 0.3181 58 1.00 0.3203 0.05 -0.3179 0.9556 -0.00261 lam13 0.01608 0.3258 58 0.05 0.9608 0.05 -0.6360 0.6682 -0.00376 lam14 0.2040 0.3233 58 0.63 0.5306 0.05 -0.4432 0.8511 -0.00132 lam21 -1.0432 0.3577 58 -2.92 0.0050 0.05 -1.7592 -0.3272 -0.00094 lam22 -0.09395 0.3380 58 -0.28 0.7820 0.05 -0.7705 0.5826 -0.00076 lam23 -0.6008 0.3497 58 -1.72 0.0911 0.05 -1.3008 0.09922 -0.00115 lam24 -0.7702 0.3615 58 -2.13 0.0374 0.05 -1.4937 -0.04660 -0.00151 beta11 0.8675 0.1507 58 5.76 <.0001 0.05 0.5658 1.1692 0.002466 beta12 0.8378 0.1531 58 5.47 <.0001 0.05 0.5314 1.1443 -0.00096 beta13 0.9930 0.1545 58 6.43 <.0001 0.05 0.6838 1.3023 -0.00136 beta14 0.8707 0.1547 58 5.63 <.0001 0.05 0.5611 1.1802 0.00009 beta21 1.3596 0.1642 58 8.28 <.0001 0.05 1.0309 1.6883 -0.00244 beta22 0.9814 0.1605 58 6.11 <.0001 0.05 0.6601 1.3027 -0.0043 beta23 1.1706 0.1630 58 7.18 <.0001 0.05 0.8444 1.4967 -0.00071 beta24 1.1617 0.1665 58 6.98 <.0001 0.05 0.8284 1.4951 0.001671 th1 0.2644 0.06063 58 4.36 <.0001 0.05 0.1430 0.3858 -0.00901 M2: equal slopes for logbase across groups. Fit with PROC GLIMMIX, ML 14 The GLIMMIX Procedure Model Information Data Set WORK.EPILEPS Response Variable seizures Response Distribution Poisson Link Function Log Variance Function Default Variance Matrix Blocked By id Estimation Technique Maximum Likelihood Likelihood Approximation Gauss-Hermite Quadrature Degrees of Freedom Method Containment Class Level Information Class Levels Values id 59 101 102 103 104 106 107 108 110 111 112 113 114 116 117 118 121 122 123 124 126 128 129 130 135 137 139 141 143 145 147 201 202 203 204 205 206 207 208 209 210 211 213 214 215 217 218 219 220 221 222 225 226 227 228 230 232 234 236 238 trt 2 0 1 time 4 1 2 3 4 Number of Observations Read 236 Number of Observations Used 236 Dimensions G-side Cov. Parameters 1 Columns in X 19 Columns in Z per Subject 1 Subjects (Blocks in V) 59 Max Obs per Subject 4 Optimization Information Optimization Technique Dual Quasi-Newton Parameters in Optimization 13 Lower Boundaries 1 Upper Boundaries 0 Fixed Effects Not Profiled Starting From GLM estimates Quadrature Points 1 M2: equal slopes for logbase across groups. Fit with PROC GLIMMIX, ML 15 The GLIMMIX Procedure Iteration History Objective Max Iteration Restarts Evaluations Function Change Gradient 0 0 4 1329.3092722 . 98.02804 1 0 3 1326.3445651 2.96470711 54.13719 2 0 2 1325.9149475 0.42961764 72.48443 3 0 4 1324.9016632 1.01328432 26.85016 4 0 2 1324.4279213 0.47374191 29.71535 5 0 2 1323.6077525 0.82016879 23.84177 6 0 2 1322.6145563 0.99319620 16.13632 7 0 3 1322.4421831 0.17237322 9.840619 8 0 2 1322.2826647 0.15951834 6.974314 9 0 3 1322.2453056 0.03735915 2.976531 10 0 4 1322.1673253 0.07798032 5.013607 11 0 3 1322.1293919 0.03793334 3.252928 12 0 2 1322.0736432 0.05574868 2.981927 13 0 3 1322.0385158 0.03512747 0.962144 14 0 3 1322.0357321 0.00278364 1.017285 15 0 4 1321.9980949 0.03763726 1.126523 16 0 3 1321.9946438 0.00345104 1.053239 17 0 4 1321.9864457 0.00819809 0.686875 18 0 3 1321.9848446 0.00160109 1.214833 19 0 4 1321.9672801 0.01756456 0.884446 20 0 3 1321.9666476 0.00063247 0.527473 21 0 2 1321.9662415 0.00040615 0.52279 22 0 3 1321.9659734 0.00026805 0.24082 23 0 4 1321.9650612 0.00091224 0.051778 24 0 3 1321.965032 0.00002923 0.006808 25 0 3 1321.9650319 0.00000009 0.001662 Convergence criterion (GCONV=1E-8) satisfied. Adaptiveness of Quadrature at Solution Quadrature Objective ---Relative Difference to--- Points Function Converged Previous 1 1321.9650319 3 1322.0885784 0.0000934568 0.0000934568 5 1321.8143512 -0.000113982 -0.00020742 7 1321.8111852 -0.000116377 -2.395202E-6 9 1321.8113334 -0.000116265 1.1208188E-7 11 1321.8113025 -0.000116289 -2.334381E-8 21 1321.8113008 -0.00011629 -1.303304E-9 31 1321.8113008 -0.00011629 1.186916E-14 M2: equal slopes for logbase across groups. Fit with PROC GLIMMIX, ML 16 The GLIMMIX Procedure Fit Statistics -2 Log Likelihood 1321.97 AIC (smaller is better) 1347.97 AICC (smaller is better) 1349.60 BIC (smaller is better) 1374.97 CAIC (smaller is better) 1387.97 HQIC (smaller is better) 1358.51 Fit Statistics for Conditional Distribution -2 log L(seizures | r. effects) 1159.45 Pearson Chi-Square 347.14 Pearson Chi-Square / DF 1.47 Covariance Parameter Estimates Standard Cov Parm Subject Estimate Error Intercept id 0.2739 0.06254 Solutions for Fixed Effects Standard Effect trt time Estimate Error DF t Value Pr > |t| logbase 0.9992 0.1142 168 8.75 <.0001 time 1 -0.4961 0.2590 168 -1.92 0.0571 time 2 0.05655 0.2517 168 0.22 0.8225 time 3 -0.4167 0.2593 168 -1.61 0.1100 time 4 -0.4588 0.2647 168 -1.73 0.0849 logbase*time 1 0.1097 0.08242 168 1.33 0.1848 logbase*time 2 -0.1152 0.08251 168 -1.40 0.1644 logbase*time 3 0.05843 0.08319 168 0.70 0.4834 logbase*time 4 0 . . . . trt 0 0.4277 0.1740 168 2.46 0.0150 trt 1 0 . . . . trt*time 0 1 -0.05880 0.1314 168 -0.45 0.6551 trt*time 0 2 -0.2128 0.1334 168 -1.60 0.1125 trt*time 0 3 -0.08013 0.1330 168 -0.60 0.5478 trt*time 0 4 0 . . . . trt*time 1 1 0 . . . . trt*time 1 2 0 . . . . trt*time 1 3 0 . . . . trt*time 1 4 0 . . . . M2: equal slopes for logbase across groups. Fit with PROC GLIMMIX, ML 17 The GLIMMIX Procedure Type III Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F logbase 1 168 100.53 100.53 <.0001 <.0001 time 3 168 7.09 2.36 0.0690 0.0729 logbase*time 3 168 8.96 2.99 0.0299 0.0328 trt 1 168 5.04 5.04 0.0248 0.0261 trt*time 3 168 2.80 0.93 0.4227 0.4251 Least Squares Means Estimates Standard Effect Label Estimate Error DF t Value Pr > |t| trt*time 1 0.3398 0.1514 168 2.24 0.0261 trt*time 2 0.03884 0.1033 168 0.38 0.7073 trt*time 3 -0.1727 0.1128 168 -1.53 0.1278 trt*time 4 -0.08013 0.1330 168 -0.60 0.5478 F Test for Least Squares Means Estimates Num Den Effect DF DF F Value Pr > F trt*time 4 168 1.92 0.1089 M3: equal slopes for logbase across groups, time. Fit with PROC GLIMMIX, ML 18 The GLIMMIX Procedure Model Information Data Set WORK.EPILEPS Response Variable seizures Response Distribution Poisson Link Function Log Variance Function Default Variance Matrix Blocked By id Estimation Technique Maximum Likelihood Likelihood Approximation Gauss-Hermite Quadrature Degrees of Freedom Method Containment Class Level Information Class Levels Values id 59 101 102 103 104 106 107 108 110 111 112 113 114 116 117 118 121 122 123 124 126 128 129 130 135 137 139 141 143 145 147 201 202 203 204 205 206 207 208 209 210 211 213 214 215 217 218 219 220 221 222 225 226 227 228 230 232 234 236 238 trt 2 0 1 time 4 1 2 3 4 Number of Observations Read 236 Number of Observations Used 236 Dimensions G-side Cov. Parameters 1 Columns in X 15 Columns in Z per Subject 1 Subjects (Blocks in V) 59 Max Obs per Subject 4 Optimization Information Optimization Technique Dual Quasi-Newton Parameters in Optimization 10 Lower Boundaries 1 Upper Boundaries 0 Fixed Effects Not Profiled Starting From GLM estimates Quadrature Points 1 M3: equal slopes for logbase across groups, time. Fit with PROC GLIMMIX, ML 19 The GLIMMIX Procedure Iteration History Objective Max Iteration Restarts Evaluations Function Change Gradient 0 0 4 1337.9411516 . 97.73567 1 0 3 1334.2414142 3.69973740 28.69507 2 0 3 1332.3981527 1.84326147 13.74908 3 0 5 1332.2425088 0.15564390 17.641 4 0 3 1332.1016069 0.14090190 17.89809 5 0 2 1331.7159962 0.38561070 12.34725 6 0 2 1331.1996548 0.51634140 13.13453 7 0 3 1331.0030969 0.19655790 5.469193 8 0 3 1330.9461489 0.05694806 1.956293 9 0 3 1330.9442982 0.00185073 1.171442 10 0 4 1330.9384123 0.00588585 0.213198 11 0 4 1330.9383289 0.00008337 0.209131 12 0 2 1330.938239 0.00008998 0.035254 13 0 3 1330.9382364 0.00000252 0.00187 Convergence criterion (GCONV=1E-8) satisfied. Adaptiveness of Quadrature at Solution Quadrature Objective ---Relative Difference to--- Points Function Converged Previous 1 1330.9382364 3 1331.0618063 0.0000928442 0.0000928442 5 1330.7873951 -0.000113335 -0.00020616 7 1330.7842233 -0.000115718 -2.383418E-6 9 1330.7843717 -0.000115606 1.1152445E-7 11 1330.7843408 -0.000115629 -2.323816E-8 21 1330.7843391 -0.000115631 -1.299273E-9 31 1330.7843391 -0.000115631 1.195998E-14 Fit Statistics -2 Log Likelihood 1330.94 AIC (smaller is better) 1350.94 AICC (smaller is better) 1351.92 BIC (smaller is better) 1371.71 CAIC (smaller is better) 1381.71 HQIC (smaller is better) 1359.05 M3: equal slopes for logbase across groups, time. Fit with PROC GLIMMIX, ML 20 The GLIMMIX Procedure Fit Statistics for Conditional Distribution -2 log L(seizures | r. effects) 1168.36 Pearson Chi-Square 355.50 Pearson Chi-Square / DF 1.51 Covariance Parameter Estimates Standard Cov Parm Subject Estimate Error Intercept id 0.2743 0.06260 Solutions for Fixed Effects Standard Effect trt time Estimate Error DF t Value Pr > |t| logbase 1.0112 0.1010 171 10.01 <.0001 trt 0 -0.06025 0.2193 171 -0.27 0.7839 trt 1 -0.4899 0.2271 171 -2.16 0.0324 time 1 0.2460 0.09256 171 2.66 0.0086 time 2 0.2270 0.09295 171 2.44 0.0156 time 3 0.1919 0.09368 171 2.05 0.0420 time 4 0 . . . . trt*time 0 1 -0.08478 0.1299 171 -0.65 0.5148 trt*time 0 2 -0.1874 0.1320 171 -1.42 0.1576 trt*time 0 3 -0.09373 0.1316 171 -0.71 0.4774 trt*time 0 4 0 . . . . trt*time 1 1 0 . . . . trt*time 1 2 0 . . . . trt*time 1 3 0 . . . . trt*time 1 4 0 . . . . Type III Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F logbase 1 171 100.27 100.27 <.0001 <.0001 trt 1 171 4.99 4.99 0.0256 0.0269 time 3 171 10.22 3.41 0.0168 0.0190 trt*time 3 171 2.03 0.68 0.5654 0.5667 NLMIXED fit of M4: same as M3 but w/ random intercept & slope on logbase 21 The NLMIXED Procedure Specifications Data Set WORK.EPILEPS Dependent Variable seizures Distribution for Dependent Variable Poisson Random Effects b1 b2 Distribution for Random Effects Normal Subject Variable id Optimization Technique Dual Quasi-Newton Integration Method Adaptive Gaussian Quadrature Dimensions Observations Used 236 Observations Not Used 0 Total Observations 236 Subjects 59 Max Obs Per Subject 4 Parameters 12 Quadrature Points 1 Parameters lam11 lam12 lam13 lam14 lam21 lam22 lam23 lam24 beta 0.1745 0.05292 0.1115 0.01329 -0.1896 -0.2086 -0.2436 -0.4355 0.9771 Parameters th1 th2 th3 NegLogLike 0.1709 0.02322 0.003156 665.210939 Iteration History Iter Calls NegLogLike Diff MaxGrad Slope 1 321 665.210858 0.000081 1.405956 -245E158 2 371 665.210639 0.000219 0.426307 -0.00004 3 396 665.210598 0.000041 1.001975 -0.00013 4 421 665.210579 0.000019 0.72826 -0.00003 5 471 665.210554 0.000025 1.024825 -0.00001 6 496 665.210537 0.000017 0.489372 -0.00004 7 521 665.210517 0.00002 0.814136 -0.00003 8 546 665.210502 0.000016 0.364233 -8.67E-6 9 596 665.21043 0.000071 0.468287 -0.00004 NLMIXED fit of M4: same as M3 but w/ random intercept & slope on logbase 22 The NLMIXED Procedure Iteration History Iter Calls NegLogLike Diff MaxGrad Slope 10 622 665.210428 2.032E-6 0.342294 -4.21E-6 NOTE: GCONV convergence criterion satisfied. Fit Statistics -2 Log Likelihood 1330.4 AIC (smaller is better) 1354.4 AICC (smaller is better) 1355.8 BIC (smaller is better) 1379.4 Parameter Estimates Standard Parameter Estimate Error DF t Value Pr > |t| Alpha Lower Upper Gradient lam11 0.1745 0.2581 57 0.68 0.5017 0.05 -0.3423 0.6913 -0.01107 lam12 0.05292 0.2590 57 0.20 0.8388 0.05 -0.4658 0.5716 -0.00395 lam13 0.1115 0.2586 57 0.43 0.6679 0.05 -0.4062 0.6292 -0.00744 lam14 0.01329 0.2594 57 0.05 0.9593 0.05 -0.5061 0.5327 -0.01727 lam21 -0.1896 0.2440 57 -0.78 0.4403 0.05 -0.6782 0.2990 0.009226 lam22 -0.2086 0.2441 57 -0.85 0.3965 0.05 -0.6975 0.2803 0.003219 lam23 -0.2436 0.2444 57 -1.00 0.3231 0.05 -0.7331 0.2458 0.024511 lam24 -0.4355 0.2461 57 -1.77 0.0822 0.05 -0.9284 0.05737 0.01866 beta 0.9771 0.1197 57 8.16 <.0001 0.05 0.7374 1.2168 0.182991 th1 0.1701 0.4110 57 0.41 0.6804 0.05 -0.6528 0.9931 0.288011 th2 0.02245 0.2095 57 0.11 0.9151 0.05 -0.3971 0.4420 -0.34229 th3 0.004396 0.09773 57 0.04 0.9643 0.05 -0.1913 0.2001 0.341148