Model 1-exch - Sandwich var-based inference 1 The GENMOD Procedure Model Information Data Set WORK.TWO Distribution Poisson Link Function Log Dependent Variable y Number of Observations Read 212 Number of Observations Used 212 Class Level Information Class Value Design Variables sex F 0 M 1 quarter 1 0 0 0 2 1 0 0 3 0 1 0 4 0 0 1 Parameter Information Parameter Effect sex quarter Prm1 Intercept Prm2 quarter 2 Prm3 quarter 3 Prm4 quarter 4 Prm5 sex M Prm6 agecent Prm7 agecent*sex M Algorithm converged. GEE Model Information Correlation Structure Exchangeable Within-Subject Effect quarter (4 levels) Subject Effect id (53 levels) Number of Clusters 53 Correlation Matrix Dimension 4 Maximum Cluster Size 4 Minimum Cluster Size 4 Model 1-exch - Sandwich var-based inference 2 The GENMOD Procedure Algorithm converged. Working Correlation Matrix Col1 Col2 Col3 Col4 Row1 1.0000 0.1422 0.1422 0.1422 Row2 0.1422 1.0000 0.1422 0.1422 Row3 0.1422 0.1422 1.0000 0.1422 Row4 0.1422 0.1422 0.1422 1.0000 Exchangeable Working Correlation Correlation 0.1422221807 GEE Fit Criteria QIC 252.9882 QICu 252.1742 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept 0.2974 0.2175 -0.1289 0.7238 1.37 0.1715 quarter 2 -0.4055 0.2402 -0.8762 0.0653 -1.69 0.0914 quarter 3 -0.2400 0.2259 -0.6826 0.2027 -1.06 0.2880 quarter 4 -1.1394 0.2220 -1.5746 -0.7043 -5.13 <.0001 sex M 0.0249 0.2103 -0.3873 0.4371 0.12 0.9059 agecent 0.0268 0.0088 0.0096 0.0440 3.06 0.0022 agecent*sex M -0.0269 0.0119 -0.0502 -0.0036 -2.26 0.0236 Score Statistics For Type 3 GEE Analysis Chi- Source DF Square Pr > ChiSq quarter 3 19.79 0.0002 sex 1 0.01 0.9069 agecent 1 5.19 0.0227 agecent*sex 1 4.28 0.0386 Model 1-exch - Model var-based inference 3 The GENMOD Procedure Model Information Data Set WORK.TWO Distribution Poisson Link Function Log Dependent Variable y Number of Observations Read 212 Number of Observations Used 212 Class Level Information Class Value Design Variables sex F 0 M 1 quarter 1 0 0 0 2 1 0 0 3 0 1 0 4 0 0 1 Parameter Information Parameter Effect sex quarter Prm1 Intercept Prm2 quarter 2 Prm3 quarter 3 Prm4 quarter 4 Prm5 sex M Prm6 agecent Prm7 agecent*sex M Algorithm converged. GEE Model Information Correlation Structure Exchangeable Within-Subject Effect quarter (4 levels) Subject Effect id (53 levels) Number of Clusters 53 Correlation Matrix Dimension 4 Maximum Cluster Size 4 Minimum Cluster Size 4 Model 1-exch - Model var-based inference 4 The GENMOD Procedure Algorithm converged. Working Correlation Matrix Col1 Col2 Col3 Col4 Row1 1.0000 0.1422 0.1422 0.1422 Row2 0.1422 1.0000 0.1422 0.1422 Row3 0.1422 0.1422 1.0000 0.1422 Row4 0.1422 0.1422 0.1422 1.0000 Exchangeable Working Correlation Correlation 0.1422221807 GEE Fit Criteria QIC 252.9882 QICu 252.1742 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept 0.2974 0.2175 -0.1289 0.7238 1.37 0.1715 quarter 2 -0.4055 0.2402 -0.8762 0.0653 -1.69 0.0914 quarter 3 -0.2400 0.2259 -0.6826 0.2027 -1.06 0.2880 quarter 4 -1.1394 0.2220 -1.5746 -0.7043 -5.13 <.0001 sex M 0.0249 0.2103 -0.3873 0.4371 0.12 0.9059 agecent 0.0268 0.0088 0.0096 0.0440 3.06 0.0022 agecent*sex M -0.0269 0.0119 -0.0502 -0.0036 -2.26 0.0236 Analysis Of GEE Parameter Estimates Model-Based Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept 0.2974 0.2411 -0.1751 0.7700 1.23 0.2174 quarter 2 -0.4055 0.2155 -0.8278 0.0169 -1.88 0.0599 quarter 3 -0.2400 0.2052 -0.6421 0.1622 -1.17 0.2422 quarter 4 -1.1394 0.2796 -1.6875 -0.5914 -4.08 <.0001 sex M 0.0249 0.2507 -0.4665 0.5162 0.10 0.9210 Model 1-exch - Model var-based inference 5 The GENMOD Procedure Analysis Of GEE Parameter Estimates Model-Based Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| agecent 0.0268 0.0130 0.0013 0.0523 2.06 0.0394 agecent*sex M -0.0269 0.0149 -0.0561 0.0022 -1.81 0.0703 Scale 1.2723 . . . . . NOTE: The scale parameter was held fixed. Score Statistics For Type 3 GEE Analysis Chi- Source DF Square Pr > ChiSq quarter 3 19.79 0.0002 sex 1 0.01 0.9069 agecent 1 5.19 0.0227 agecent*sex 1 4.28 0.0386 M2a: Poisson GLMM with random intercept 6 Fit with PROC GLIMMIX, PQL The GLIMMIX Procedure Model Information Data Set WORK.TWO Response Variable y 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 53 1 2 3 4 5 6 7 8 9 10 11 12 13 17 18 20 21 22 24 25 27 28 29 30 36 39 40 41 42 43 45 46 47 48 49 50 51 52 53 54 55 58 59 60 62 63 64 67 69 70 71 72 73 sex 2 F M msmoke 1 Yes quarter 4 1 2 3 4 Number of Observations Read 212 Number of Observations Used 212 Dimensions G-side Cov. Parameters 1 Columns in X 10 Columns in Z per Subject 1 Subjects (Blocks in V) 53 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 M2a: Poisson GLMM with random intercept 7 Fit with PROC GLIMMIX, PQL The GLIMMIX Procedure Iteration History Objective Max Iteration Restarts Subiterations Function Change Gradient 0 0 4 592.31822462 2.00000000 8.275E-6 1 0 4 683.19356841 1.91461688 2.046E-6 2 0 3 703.08854694 2.00000000 0.000035 3 0 2 704.414405 0.06079073 8.185E-6 4 0 2 704.49291215 0.00416651 0.001567 5 0 2 704.49798429 0.00014271 0.000053 6 0 1 704.49781378 0.00000762 0.000013 7 0 1 704.49782291 0.00000502 8.735E-6 8 0 0 704.4978169 0.00000000 7.481E-6 Convergence criterion (PCONV=1E-6) satisfied. Fit Statistics -2 Log Pseudo-Likelihood 704.50 Generalized Chi-Square 233.55 Gener. Chi-Square / DF 1.10 Covariance Parameter Estimates Standard Cov Parm Subject Estimate Error Intercept id 0.2884 0.1063 Solutions for Fixed Effects Standard Effect sex quarter Estimate Error DF t Value Pr > |t| Intercept -0.8947 0.2278 212 -3.93 0.0001 quarter 1 1.1394 0.2345 212 4.86 <.0001 quarter 2 0.7340 0.2483 212 2.96 0.0035 quarter 3 0.8995 0.2421 212 3.72 0.0003 quarter 4 0 . . . . sex F -0.04466 0.2446 60.97 -0.18 0.8557 sex M 0 . . . . agecent 0.000048 0.007122 52.9 0.01 0.9947 agecent*sex F 0.03136 0.01587 52.14 1.98 0.0535 agecent*sex M 0 . . . . M2a: Poisson GLMM with random intercept 8 Fit with PROC GLIMMIX, PQL The GLIMMIX Procedure Type III Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F quarter 3 1 8.14 0.2508 sex 1 60.97 0.03 0.8557 agecent 1 52.14 3.93 0.0528 agecent*sex 1 52.14 3.90 0.0535 Contrasts Num Den Label DF DF F Value Pr > F sex*agecent 1 52.14 3.90 0.0535 sex 1 60.97 0.03 0.8557 agecent 1 52.14 3.93 0.0528 quarter 3 1 8.14 0.2508 M2b: Poisson GLMM with random intercept 9 Same model as M2a, but fit with ML The NLMIXED Procedure Specifications Data Set WORK.TWO Dependent Variable y 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 212 Observations Not Used 0 Total Observations 212 Subjects 53 Max Obs Per Subject 4 Parameters 8 Quadrature Points 1 Parameters b bagecentsex Intercept bquarter1 bquarter2 bquarter3 bsexF bagecent F sigb -0.8947 1.1394 0.734 0.8995 -0.04466 0.000048 0.03136 0.1 Parameters NegLogLike 292.297006 Iteration History Iter Calls NegLogLike Diff MaxGrad Slope 1 5 292.175796 0.121211 26.01687 -629.336 2 7 288.096058 4.079738 140.1881 -46.0139 3 11 286.652054 1.444003 85.50345 -878.638 4 12 285.142105 1.509949 107.3088 -21.1591 5 14 282.383349 2.758756 29.70107 -3.96203 6 16 281.793323 0.590026 21.2093 -2.04465 7 18 281.643191 0.150132 4.914673 -0.23625 M2b: Poisson GLMM with random intercept 10 Same model as M2a, but fit with ML The NLMIXED Procedure Iteration History Iter Calls NegLogLike Diff MaxGrad Slope 8 21 281.634577 0.008615 2.632247 -0.03949 9 23 281.631332 0.003245 1.221163 -0.00665 10 25 281.630397 0.000935 1.158258 -0.00249 11 26 281.629882 0.000515 0.582208 -0.00116 12 27 281.629746 0.000137 0.448727 -0.00063 13 28 281.629522 0.000224 0.113151 -0.00048 14 30 281.629493 0.000028 0.083158 -0.00005 15 32 281.629493 7.845E-7 0.037081 -9.19E-7 NOTE: GCONV convergence criterion satisfied. Fit Statistics -2 Log Likelihood 563.3 AIC (smaller is better) 579.3 AICC (smaller is better) 580.0 BIC (smaller is better) 595.0 Parameter Estimates Standard Parameter Estimate Error DF t Value Pr > |t| Alpha Lower Upper Gradient bIntercept -0.9748 0.2345 52 -4.16 0.0001 0.05 -1.4454 -0.5041 -0.00013 bquarter1 1.1394 0.2345 52 4.86 <.0001 0.05 0.6688 1.6100 -0.00005 bquarter2 0.7340 0.2483 52 2.96 0.0047 0.05 0.2357 1.2323 0.000119 bquarter3 0.8995 0.2421 52 3.72 0.0005 0.05 0.4137 1.3853 -0.00003 bsexF -0.04461 0.2528 52 -0.18 0.8606 0.05 -0.5519 0.4627 -0.00043 bagecent 0.000094 0.007364 52 0.01 0.9899 0.05 -0.01468 0.01487 -0.03708 bagecentsexF 0.03263 0.01645 52 1.98 0.0525 0.05 -0.00037 0.06563 -0.0112 sigb 0.5625 0.1083 52 5.19 <.0001 0.05 0.3452 0.7798 -0.0006 Contrasts Num Den Label DF DF F Value Pr > F sex*agecent 1 52 3.94 0.0525 sex 1 52 0.03 0.8606 agecent 1 52 3.96 0.0518 quarter 3 52 8.14 0.0002 M3a: Neg Bin GLMM with random intercept 11 Fit with PROC GLIMMIX, PQL The GLIMMIX Procedure Model Information Data Set WORK.TWO Response Variable y Response Distribution Negative Binomial 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 53 1 2 3 4 5 6 7 8 9 10 11 12 13 17 18 20 21 22 24 25 27 28 29 30 36 39 40 41 42 43 45 46 47 48 49 50 51 52 53 54 55 58 59 60 62 63 64 67 69 70 71 72 73 sex 2 F M msmoke 1 Yes quarter 4 1 2 3 4 Number of Observations Read 212 Number of Observations Used 212 Dimensions G-side Cov. Parameters 1 R-side Cov. Parameters 1 Columns in X 10 Columns in Z per Subject 1 Subjects (Blocks in V) 53 Max Obs per Subject 4 Optimization Information Optimization Technique Dual Quasi-Newton Parameters in Optimization 2 Lower Boundaries 2 Upper Boundaries 0 Fixed Effects Profiled Starting From Data M3a: Neg Bin GLMM with random intercept 12 Fit with PROC GLIMMIX, PQL The GLIMMIX Procedure Iteration History Objective Max Iteration Restarts Subiterations Function Change Gradient 0 0 5 640.89607964 1.61154849 4.085E-6 1 0 6 691.34429235 0.52240774 0.001672 2 0 4 700.4646253 0.09937093 0.000683 3 0 3 701.05128976 0.01042381 3.159E-6 4 0 3 701.01291093 0.00065183 2.868E-6 5 0 3 701.00304931 0.00013404 1.758E-7 6 0 2 701.00209084 0.00001766 0.000257 7 0 2 701.0020472 0.00000534 1.553E-9 8 0 0 701.00207759 0.00000098 8.259E-6 Convergence criterion (PCONV=1E-6) satisfied. Fit Statistics -2 Log Pseudo-Likelihood 701.00 Generalized Chi-Square 190.20 Gener. Chi-Square / DF 0.90 Covariance Parameter Estimates Standard Cov Parm Subject Estimate Error Intercept id 0.1990 0.1126 Scale 0.3402 0.1407 Solutions for Fixed Effects Standard Effect sex quarter Estimate Error DF t Value Pr > |t| Intercept -0.8690 0.2408 212 -3.61 0.0004 quarter 1 1.1238 0.2657 212 4.23 <.0001 quarter 2 0.7396 0.2777 212 2.66 0.0083 quarter 3 0.8705 0.2731 212 3.19 0.0017 quarter 4 0 . . . . sex F -0.07402 0.2460 64.38 -0.30 0.7645 sex M 0 . . . . agecent -0.00076 0.007124 55.49 -0.11 0.9153 agecent*sex F 0.03235 0.01583 52.72 2.04 0.0460 agecent*sex M 0 . . . . M3a: Neg Bin GLMM with random intercept 13 Fit with PROC GLIMMIX, PQL The GLIMMIX Procedure Type III Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F quarter 3 193.8 6.07 0.0006 sex 1 64.38 0.09 0.7645 agecent 1 52.72 3.79 0.0569 agecent*sex 1 52.72 4.17 0.0460 M3b: Neg Bin GLMM with random intercept 14 Same model as M3a, but fit with ML The NLMIXED Procedure Specifications Data Set WORK.TWO Dependent Variable y Distribution for Dependent Variable General Random Effects b Distribution for Random Effects Normal Subject Variable id Optimization Technique Dual Quasi-Newton Integration Method Adaptive Gaussian Quadrature Dimensions Observations Used 212 Observations Not Used 0 Total Observations 212 Subjects 53 Max Obs Per Subject 4 Parameters 9 Quadrature Points 1 Parameters b bagecentsex Intercept bquarter1 bquarter2 bquarter3 bsexF bagecent F sigb alpha -0.8947 1.1394 0.734 0.8995 -0.04466 0.000048 0.03136 0.1 1 Parameters NegLogLike 281.126401 Iteration History Iter Calls NegLogLike Diff MaxGrad Slope 1 5 281.038815 0.087585 16.02592 -339.213 2 8 280.980774 0.058041 6.637507 -27.9624 3 9 280.344659 0.636115 5.349551 -9.97608 4 11 278.621655 1.723004 11.01713 -4.49414 5 13 278.027239 0.594416 14.83831 -3.60627 6 15 277.721079 0.30616 1.540772 -0.5399 7 17 277.650258 0.070821 4.070567 -0.14885 M3b: Neg Bin GLMM with random intercept 15 Same model as M3a, but fit with ML The NLMIXED Procedure Iteration History Iter Calls NegLogLike Diff MaxGrad Slope 8 18 277.546245 0.104013 8.241055 -0.14297 9 20 277.506691 0.039554 2.006321 -0.10034 10 22 277.495202 0.011489 0.503888 -0.03337 11 24 277.490197 0.005005 0.953407 -0.01133 12 26 277.489589 0.000608 0.3449 -0.00078 13 28 277.489464 0.000125 0.027303 -0.00014 14 30 277.489454 9.831E-6 0.011249 -0.00002 15 32 277.489454 4.386E-8 0.000631 -8.26E-8 NOTE: GCONV convergence criterion satisfied. Fit Statistics -2 Log Likelihood 555.0 AIC (smaller is better) 573.0 AICC (smaller is better) 573.9 BIC (smaller is better) 590.7 Parameter Estimates Standard Parameter Estimate Error DF t Value Pr > |t| Alpha Lower Upper Gradient bIntercept -0.9202 0.2495 52 -3.69 0.0005 0.05 -1.4208 -0.4196 0.000231 bquarter1 1.1489 0.2690 52 4.27 <.0001 0.05 0.6091 1.6888 0.000093 bquarter2 0.7550 0.2813 52 2.68 0.0097 0.05 0.1906 1.3195 0.000016 bquarter3 0.8872 0.2755 52 3.22 0.0022 0.05 0.3344 1.4401 0.000103 bsexF -0.07746 0.2521 52 -0.31 0.7599 0.05 -0.5834 0.4285 0.000088 bagecent -0.00080 0.007339 52 -0.11 0.9131 0.05 -0.01553 0.01392 -0.00063 bagecentsexF 0.03356 0.01645 52 2.04 0.0464 0.05 0.000556 0.06656 0.000175 sigb 0.4577 0.1423 52 3.22 0.0022 0.05 0.1722 0.7433 0.000159 alpha 2.6904 1.3324 52 2.02 0.0486 0.05 0.01681 5.3639 -5.47E-6 Contrasts Num Den Label DF DF F Value Pr > F sex*agecent 1 52 4.16 0.0464 sex 1 52 0.09 0.7599 agecent 1 52 3.75 0.0582 quarter 3 52 6.20 0.0011 M4: Poisson GLMM with random subject-specific and obs-specific intercepts 16 Fit with PROC GLIMMIX, PQL The GLIMMIX Procedure Model Information Data Set WORK.THREE Response Variable y 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 53 1 2 3 4 5 6 7 8 9 10 11 12 13 17 18 20 21 22 24 25 27 28 29 30 36 39 40 41 42 43 45 46 47 48 49 50 51 52 53 54 55 58 59 60 62 63 64 67 69 70 71 72 73 sex 2 F M msmoke 1 Yes quarter 4 1 2 3 4 obsno 212 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 65 66 67 68 69 70 71 72 77 78 79 80 81 82 83 84 85 86 87 88 93 94 95 96 97 98 99 100 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 141 142 143 144 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 229 230 231 232 233 234 235 236 237 238 239 240 245 246 247 248 249 250 251 252 253 254 255 256 265 266 267 268 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 Number of Observations Read 212 Number of Observations Used 212 M4: Poisson GLMM with random subject-specific and obs-specific intercepts 17 Fit with PROC GLIMMIX, PQL The GLIMMIX Procedure Dimensions G-side Cov. Parameters 2 Columns in X 10 Columns in Z per Subject 5 Subjects (Blocks in V) 53 Max Obs per Subject 4 Optimization Information Optimization Technique Dual Quasi-Newton Parameters in Optimization 2 Lower Boundaries 2 Upper Boundaries 0 Fixed Effects Profiled Starting From Data Iteration History Objective Max Iteration Restarts Subiterations Function Change Gradient 0 0 5 625.01916928 1.63073992 0.000084 1 0 6 671.75879911 0.31950742 0.003377 2 0 4 680.08068527 0.06728726 0.000014 3 0 4 681.10579593 0.00896864 5.067E-7 4 0 3 681.21222354 0.00093520 3.869E-7 5 0 3 681.22198259 0.00008573 3.071E-9 6 0 2 681.22286818 0.00000803 0.000013 7 0 1 681.22294427 0.00000142 0.000039 8 0 1 681.22297073 0.00000175 0.000046 9 0 1 681.22293957 0.00000202 0.000053 10 0 1 681.22297555 0.00000233 0.000061 11 0 1 681.22293402 0.00000269 0.00007 12 0 1 681.22298196 0.00000131 1.831E-6 13 0 0 681.22295856 0.00000000 5.496E-6 Convergence criterion (PCONV=1E-6) satisfied. Fit Statistics -2 Log Pseudo-Likelihood 681.22 Generalized Chi-Square 174.72 Gener. Chi-Square / DF 0.82 M4: Poisson GLMM with random subject-specific and obs-specific intercepts 18 Fit with PROC GLIMMIX, PQL The GLIMMIX Procedure Covariance Parameter Estimates Standard Cov Parm Subject Estimate Error Intercept id 0.1989 0.1111 Intercept quarter(id) 0.2670 0.1226 Solutions for Fixed Effects Standard Effect sex quarter Estimate Error DF t Value Pr > |t| Intercept -0.8807 0.2360 212 -3.73 0.0002 quarter 1 1.0969 0.2597 212 4.22 <.0001 quarter 2 0.7223 0.2718 212 2.66 0.0085 quarter 3 0.8532 0.2667 212 3.20 0.0016 quarter 4 0 . . . . sex F -0.05892 0.2421 61.75 -0.24 0.8085 sex M 0 . . . . agecent -0.00045 0.007046 53.47 -0.06 0.9498 agecent*sex F 0.03130 0.01569 52.38 2.00 0.0512 agecent*sex M 0 . . . . Type III Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F quarter 3 203.6 18.20 6.06 0.0004 0.0006 sex 1 61.75 0.06 0.06 0.8077 0.8085 agecent 1 52.35 3.76 3.76 0.0525 0.0579 agecent*sex 1 52.38 3.98 3.98 0.0460 0.0512 M4a: Poisson GLMM with random subject-specific and obs-specific intercepts 19 Fit with PROC GLIMMIX, ML estimation via AGQ The GLIMMIX Procedure Model Information Data Set WORK.THREE Response Variable y 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 53 1 2 3 4 5 6 7 8 9 10 11 12 13 17 18 20 21 22 24 25 27 28 29 30 36 39 40 41 42 43 45 46 47 48 49 50 51 52 53 54 55 58 59 60 62 63 64 67 69 70 71 72 73 sex 2 F M msmoke 1 Yes quarter 4 1 2 3 4 obsno 212 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 65 66 67 68 69 70 71 72 77 78 79 80 81 82 83 84 85 86 87 88 93 94 95 96 97 98 99 100 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 141 142 143 144 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 229 230 231 232 233 234 235 236 237 238 239 240 245 246 247 248 249 250 251 252 253 254 255 256 265 266 267 268 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 Number of Observations Read 212 Number of Observations Used 212 M4a: Poisson GLMM with random subject-specific and obs-specific intercepts 20 Fit with PROC GLIMMIX, ML estimation via AGQ The GLIMMIX Procedure Dimensions G-side Cov. Parameters 2 Columns in X 10 Columns in Z per Subject 5 Subjects (Blocks in V) 53 Max Obs per Subject 4 Optimization Information Optimization Technique Dual Quasi-Newton Parameters in Optimization 9 Lower Boundaries 2 Upper Boundaries 0 Fixed Effects Not Profiled Starting From GLM estimates Quadrature Points 7 Iteration History Objective Max Iteration Restarts Evaluations Function Change Gradient 0 0 4 589.54885947 . 140.6836 1 0 4 589.02607909 0.52278038 66.40203 2 0 3 584.52986298 4.49621611 169.9184 3 0 3 566.79279785 17.73706513 33.96369 4 0 3 561.71330175 5.07949611 34.96838 5 0 2 560.2929777 1.42032405 47.29788 6 0 4 555.72617205 4.56680565 13.10278 7 0 3 555.24824601 0.47792603 4.634986 8 0 3 555.16298823 0.08525778 3.311806 9 0 3 555.156837 0.00615123 1.584666 10 0 3 555.15584456 0.00099244 0.901384 11 0 3 555.15549781 0.00034675 0.395562 12 0 3 555.15547916 0.00001865 0.056503 13 0 3 555.15547769 0.00000148 0.02508 Convergence criterion (GCONV=1E-8) satisfied. Fit Statistics -2 Log Likelihood 555.16 AIC (smaller is better) 573.16 AICC (smaller is better) 574.05 BIC (smaller is better) 590.89 CAIC (smaller is better) 599.89 M4a: Poisson GLMM with random subject-specific and obs-specific intercepts 21 Fit with PROC GLIMMIX, ML estimation via AGQ The GLIMMIX Procedure Fit Statistics HQIC (smaller is better) 579.97 Fit Statistics for Conditional Distribution -2 log L(y | r. effects) 415.53 Pearson Chi-Square 114.99 Pearson Chi-Square / DF 0.54 Covariance Parameter Estimates Standard Cov Parm Subject Estimate Error Intercept id 0.2295 0.1310 Intercept quarter(id) 0.3242 0.1527 Solutions for Fixed Effects Standard Effect sex quarter Estimate Error DF t Value Pr > |t| Intercept -1.0867 0.2549 50 -4.26 <.0001 quarter 1 1.1394 0.2687 156 4.24 <.0001 quarter 2 0.7491 0.2809 156 2.67 0.0085 quarter 3 0.8825 0.2758 156 3.20 0.0017 quarter 4 0 . . . . sex F -0.05944 0.2555 0 -0.23 . sex M 0 . . . . agecent -0.00044 0.007448 0 -0.06 . agecent*sex F 0.03325 0.01662 0 2.00 . agecent*sex M 0 . . . . Type III Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F quarter 3 156 18.33 6.11 0.0004 0.0006 sex 1 0 0.05 0.05 0.8160 . agecent 1 0 3.78 3.78 0.0520 . agecent*sex 1 0 4.00 4.00 0.0455 . M5: Plain Poisson GLM (for comparison) 22 Same model as M2b but without random intercept The NLMIXED Procedure Specifications Data Set WORK.TWO Dependent Variable y Distribution for Dependent Variable Poisson Optimization Technique Dual Quasi-Newton Integration Method None Dimensions Observations Used 212 Observations Not Used 0 Total Observations 212 Parameters 7 Parameters b bagecentsex Intercept bquarter1 bquarter2 bquarter3 bsexF bagecent F NegLogLike -0.8947 1.1394 0.734 0.8995 -0.04466 0.000048 0.03136 293.679263 Iteration History Iter Calls NegLogLike Diff MaxGrad Slope 1 5 293.555293 0.123971 15.00447 -653.37 2 7 293.273518 0.281775 50.27322 -13.0513 3 10 292.960532 0.312986 4.264847 -134.037 4 11 292.945162 0.01537 1.090964 -0.061 5 12 292.939918 0.005244 0.499813 -0.01455 6 14 292.937911 0.002006 0.154135 -0.00616 7 16 292.936981 0.00093 0.1429 -0.00113 8 18 292.936625 0.000356 0.081492 -0.00079 9 20 292.936497 0.000128 0.000873 -0.0003 10 22 292.936497 3.572E-9 0.000163 -7.32E-9 NOTE: GCONV convergence criterion satisfied. Fit Statistics -2 Log Likelihood 585.9 AIC (smaller is better) 599.9 AICC (smaller is better) 600.4 BIC (smaller is better) 623.4 M5: Plain Poisson GLM (for comparison) 23 Same model as M2b but without random intercept The NLMIXED Procedure Parameter Estimates Standard Parameter Estimate Error DF t Value Pr > |t| Alpha Lower Upper Gradient bIntercept -0.8085 0.2090 212 -3.87 0.0001 0.05 -1.2204 -0.3966 -0.00003 bquarter1 1.1394 0.2345 212 4.86 <.0001 0.05 0.6771 1.6017 -0.00001 bquarter2 0.7340 0.2483 212 2.96 0.0035 0.05 0.2445 1.2235 -7.67E-6 bquarter3 0.8995 0.2421 212 3.72 0.0003 0.05 0.4222 1.3767 -9.49E-6 bsexF -0.06630 0.1691 212 -0.39 0.6953 0.05 -0.3996 0.2670 -0.00001 bagecent -0.00102 0.004800 212 -0.21 0.8316 0.05 -0.01048 0.008439 -0.00016 bagecentsexF 0.02838 0.01001 212 2.84 0.0050 0.05 0.008654 0.04811 -0.00002