OPTIONS LS=80; DATA ONE; INPUT ID Depress Intcpt Linear LinChang Order OrdLin OrdLCha; WEEK = LINEAR + 3.5; CARDS; 1 1 1 -2.5 -0.5 0 0 0 1 1 1 -1.5 0.0 0 0 0 1 1 1 -0.5 0.5 0 0 0 1 1 1 0.5 0.5 0 0 0 1 1 1 1.5 0.0 0 0 0 1 1 1 2.5 -0.5 0 0 0 ...... more data ..... 75 5 1 -2.5 -0.5 1 -2.5 -0.5 75 5 1 -1.5 0 1 -1.5 0 75 5 1 -0.5 0.5 1 -0.5 0.5 75 5 1 0.5 0.5 1 0.5 0.5 75 5 1 1.5 0 1 1.5 0 75 4 1 2.5 -0.5 1 2.5 -0.5 ; PROC MIXED METHOD=ML COVTEST; CLASS ID; MODEL Depress = Linear LinChang Order OrdLin OrdLCha/SOLUTION; RANDOM INTERCEPT LINEAR LINCHANG /SUB=ID TYPE=UN G; PROC MIXED METHOD=ML COVTEST; CLASS ID WEEK; MODEL Depress = Linear LinChang Order OrdLin OrdLCha/SOLUTION; REPEATED WEEK /SUB=ID TYPE=UN R; RUN; PROC GENMOD; CLASS ID WEEK; MODEL Depress = Linear LinChang Order OrdLin OrdLCha / DIST=NORMAL LINK=IDENTITY; REPEATED SUBJECT=ID / WITHIN=WEEK CORRW TYPE=EXCH MODELSE; PROC GENMOD; CLASS ID WEEK; MODEL Depress = Linear LinChang Order OrdLin OrdLCha / DIST=NORMAL LINK=IDENTITY; REPEATED SUBJECT=ID / WITHIN=WEEK CORRW TYPE=AR(1); PROC GENMOD; CLASS ID WEEK; MODEL Depress = Linear LinChang Order OrdLin OrdLCha / DIST=NORMAL LINK=IDENTITY; REPEATED SUBJECT=ID / WITHIN=WEEK CORRW TYPE=MDEP(5); PROC GENMOD; CLASS ID WEEK; MODEL Depress = Linear LinChang Order OrdLin OrdLCha / DIST=NORMAL LINK=IDENTITY; REPEATED SUBJECT=ID / WITHIN=WEEK CORRW TYPE=UN; RUN; The MIXED Procedure G Matrix Effect ID Row COL1 COL2 COL3 INTERCEPT 1 1 1.46321661 0.09931220 0.14285441 LINEAR 1 2 0.09931220 0.07856944 -0.00136946 LINCHANG 1 3 0.14285441 -0.00136946 0.41252053 Covariance Parameter Estimates (MLE) Cov Parm Subject Estimate Std Error Z Pr > |Z| UN(1,1) ID 1.46321661 0.24299709 6.02 0.0001 UN(2,1) ID 0.09931220 0.04311306 2.30 0.0212 UN(2,2) ID 0.07856944 0.01423923 5.52 0.0001 UN(3,1) ID 0.14285441 0.10678952 1.34 0.1810 UN(3,2) ID -0.00136946 0.02552126 -0.05 0.9572 UN(3,3) ID 0.41252053 0.09269045 4.45 0.0001 Residual 0.14857143 0.01400745 10.61 0.0001 Model Fitting Information for DEPRESS Description Value Observations 450.0000 Log Likelihood -496.234 Akaike's Information Criterion -503.234 Schwarz's Bayesian Criterion -517.616 -2 Log Likelihood 992.4670 Null Model LRT Chi-Square 575.7040 Null Model LRT DF 6.0000 Null Model LRT P-Value 0.0000 Solution for Fixed Effects Effect Estimate Std Error DF t Pr > |t| INTERCEPT 3.12681159 0.17985372 73 17.39 0.0001 LINEAR -0.20807453 0.04350393 73 -4.78 0.0001 LINCHANG -0.25000000 0.11044298 73 -2.26 0.0266 ORDER 1.28123438 0.28923513 225 4.43 0.0001 ORDLIN 0.05142429 0.06996167 225 0.74 0.4631 ORDLCHA 0.43965517 0.17761095 225 2.48 0.0140 Tests of Fixed Effects Source NDF DDF Type III F Pr > F LINEAR 1 73 22.88 0.0001 LINCHANG 1 73 5.12 0.0266 ORDER 1 225 19.62 0.0001 ORDLIN 1 225 0.54 0.4631 ORDLCHA 1 225 6.13 0.0140 The MIXED Procedure Covariance Parameter Estimates (MLE) Cov Parm Subject Estimate Std Error Z Pr > |Z| UN(1,1) ID 1.44262923 0.23565295 6.12 0.0001 UN(2,1) ID 1.36083960 0.23591392 5.77 0.0001 UN(2,2) ID 1.60543066 0.26246412 6.12 0.0001 UN(3,1) ID 1.12889629 0.22773350 4.96 0.0001 UN(3,2) ID 1.42547673 0.25684413 5.55 0.0001 UN(3,3) ID 1.80978752 0.29574897 6.12 0.0001 UN(4,1) ID 1.05826378 0.23090731 4.58 0.0001 UN(4,2) ID 1.38891952 0.26166463 5.31 0.0001 UN(4,3) ID 1.68444160 0.29324616 5.74 0.0001 UN(4,4) ID 1.99523511 0.32584913 6.12 0.0001 UN(5,1) ID 0.93905531 0.23433310 4.01 0.0001 UN(5,2) ID 1.21633329 0.26027272 4.67 0.0001 UN(5,3) ID 1.46047427 0.28732084 5.08 0.0001 UN(5,4) ID 1.79173091 0.32022879 5.60 0.0001 UN(5,5) ID 2.24219747 0.36646428 6.12 0.0001 UN(6,1) ID 1.00331361 0.24289713 4.13 0.0001 UN(6,2) ID 1.21630669 0.26544765 4.58 0.0001 UN(6,3) ID 1.39815941 0.28850923 4.85 0.0001 UN(6,4) ID 1.78767565 0.32508953 5.50 0.0001 UN(6,5) ID 2.19194630 0.36750938 5.96 0.0001 UN(6,6) ID 2.36866592 0.38699122 6.12 0.0001 Model Fitting Information for DEPRESS Description Value Observations 450.0000 Log Likelihood -472.968 Akaike's Information Criterion -493.968 Schwarz's Bayesian Criterion -537.115 -2 Log Likelihood 945.9351 Null Model LRT Chi-Square 622.2359 Null Model LRT DF 20.0000 Null Model LRT P-Value 0.0000 Solution for Fixed Effects Effect Estimate Std Error DF t Pr > |t| INTERCEPT 3.12264069 0.17907625 73 17.44 0.0001 LINEAR -0.19828939 0.03621366 73 -5.48 0.0001 LINCHANG -0.25457833 0.10223648 73 -2.49 0.0150 ORDER 1.28571545 0.28798484 73 4.46 0.0001 ORDLIN 0.01651129 0.05823768 73 0.28 0.7776 ORDLCHA 0.47452000 0.16441352 73 2.89 0.0051 Tests of Fixed Effects Source NDF DDF Type III F Pr > F LINEAR 1 73 29.98 0.0001 LINCHANG 1 73 6.20 0.0150 ORDER 1 73 19.93 0.0001 ORDLIN 1 73 0.08 0.7776 ORDLCHA 1 73 8.33 0.0051 The GENMOD Procedure Model Information Description Value Data Set WORK.ONE Distribution NORMAL Link Function IDENTITY Dependent Variable DEPRESS Observations Used 450 Class Level Information Class Levels Values ID 75 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 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 WEEK 6 1 2 3 4 5 6 Parameter Information Parameter Effect PRM1 INTERCEPT PRM2 LINEAR PRM3 LINCHANG PRM4 ORDER PRM5 ORDLIN PRM6 ORDLCHA Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 444 859.3660 1.9355 Scaled Deviance 444 450.0000 1.0135 Pearson Chi-Square 444 859.3660 1.9355 Scaled Pearson X2 444 450.0000 1.0135 Log Likelihood . -784.0855 . Analysis Of Initial Parameter Estimates Parameter DF Estimate Std Err ChiSquare Pr>Chi INTERCEPT 1 3.1268 0.0832 1413.0152 0.0001 LINEAR 1 -0.2081 0.0487 18.2502 0.0001 LINCHANG 1 -0.2500 0.2038 1.5055 0.2198 ORDER 1 1.2812 0.1338 91.7355 0.0001 ORDLIN 1 0.0514 0.0783 0.4310 0.5115 ORDLCHA 1 0.4397 0.3277 1.8003 0.1797 SCALE 1 1.3819 0.0461 . . NOTE: The scale parameter was estimated by maximum likelihood. GEE Model Information Description Value Correlation Structure Exchangeable Within-Subject Effect WEEK (6 levels) Subject Effect ID (75 levels) Number of Clusters 75 Correlation Matrix Dimension 6 Maximum Cluster Size 6 Minimum Cluster Size 6 Working Correlation Matrix COL1 COL2 COL3 COL4 COL5 COL6 ROW1 1.0000 0.7350 0.7350 0.7350 0.7350 0.7350 ROW2 0.7350 1.0000 0.7350 0.7350 0.7350 0.7350 ROW3 0.7350 0.7350 1.0000 0.7350 0.7350 0.7350 ROW4 0.7350 0.7350 0.7350 1.0000 0.7350 0.7350 ROW5 0.7350 0.7350 0.7350 0.7350 1.0000 0.7350 ROW6 0.7350 0.7350 0.7350 0.7350 0.7350 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Empirical 95% Confidence Limits Parameter Estimate Std Err Lower Upper Z Pr>|Z| INTERCEPT 3.1268 0.1939 2.7468 3.5069 16.125 0.0000 LINEAR -0.2081 0.0467 -0.2996 -0.1166 -4.456 0.0000 LINCHANG -0.2500 0.1227 -0.4906 -0.0094 -2.037 0.0417 ORDER 1.2812 0.2751 0.7420 1.8205 4.6570 0.0000 ORDLIN 0.0514 0.0668 -0.0794 0.1823 0.7701 0.4412 ORDLCHA 0.4397 0.1649 0.1164 0.7629 2.6658 0.0077 Scale 1.3819 . . . . . NOTE: The scale parameter for GEE estimation was computed as the square root of the normalized Pearson's chi-square. Analysis Of GEE Parameter Estimates Model-Based Standard Error Estimates Model 95% Confidence Limits Parameter Estimate Std Err Lower Upper Z Pr>|Z| INTERCEPT 3.1268 0.1799 2.7743 3.4793 17.385 0.0000 LINEAR -0.2081 0.0251 -0.2572 -0.1589 -8.299 0.0000 LINCHANG -0.2500 0.1049 -0.4556 -0.0444 -2.383 0.0171 ORDER 1.2812 0.2892 0.7143 1.8481 4.4297 0.0000 ORDLIN 0.0514 0.0403 -0.0276 0.1305 1.2754 0.2022 ORDLCHA 0.4397 0.1687 0.1091 0.7703 2.6065 0.0091 Scale 1.3819 . . . . . The GENMOD Procedure GEE Model Information Description Value Correlation Structure AR(1) Within-Subject Effect WEEK (6 levels) Subject Effect ID (75 levels) Number of Clusters 75 Correlation Matrix Dimension 6 Maximum Cluster Size 6 Minimum Cluster Size 6 Working Correlation Matrix COL1 COL2 COL3 COL4 COL5 COL6 ROW1 1.0000 0.8850 0.7832 0.6931 0.6134 0.5428 ROW2 0.8850 1.0000 0.8850 0.7832 0.6931 0.6134 ROW3 0.7832 0.8850 1.0000 0.8850 0.7832 0.6931 ROW4 0.6931 0.7832 0.8850 1.0000 0.8850 0.7832 ROW5 0.6134 0.6931 0.7832 0.8850 1.0000 0.8850 ROW6 0.5428 0.6134 0.6931 0.7832 0.8850 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Empirical 95% Confidence Limits Parameter Estimate Std Err Lower Upper Z Pr>|Z| INTERCEPT 3.1255 0.1943 2.7447 3.5064 16.085 0.0000 LINEAR -0.2045 0.0421 -0.2870 -0.1220 -4.859 0.0000 LINCHANG -0.2499 0.1225 -0.4900 -0.0099 -2.041 0.0413 ORDER 1.2805 0.2738 0.7439 1.8171 4.6770 0.0000 ORDLIN 0.0393 0.0615 -0.0812 0.1599 0.6394 0.5226 ORDLCHA 0.4397 0.1648 0.1168 0.7626 2.6686 0.0076 Scale 1.3820 . . . . . NOTE: The scale parameter for GEE estimation was computed as the square root of the normalized Pearson's chi-square. The GENMOD Procedure GEE Model Information Description Value Correlation Structure 5-Dependent Within-Subject Effect WEEK (6 levels) Subject Effect ID (75 levels) Number of Clusters 75 Correlation Matrix Dimension 6 Maximum Cluster Size 6 Minimum Cluster Size 6 Working Correlation Matrix COL1 COL2 COL3 COL4 COL5 COL6 ROW1 1.0000 0.8850 0.7547 0.6414 0.5648 0.5257 ROW2 0.8850 1.0000 0.8850 0.7547 0.6414 0.5648 ROW3 0.7547 0.8850 1.0000 0.8850 0.7547 0.6414 ROW4 0.6414 0.7547 0.8850 1.0000 0.8850 0.7547 ROW5 0.5648 0.6414 0.7547 0.8850 1.0000 0.8850 ROW6 0.5257 0.5648 0.6414 0.7547 0.8850 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Empirical 95% Confidence Limits Parameter Estimate Std Err Lower Upper Z Pr>|Z| INTERCEPT 3.1253 0.1945 2.7442 3.5064 16.072 0.0000 LINEAR -0.2025 0.0400 -0.2808 -0.1241 -5.064 0.0000 LINCHANG -0.2505 0.1253 -0.4961 -0.0050 -2.000 0.0455 ORDER 1.2804 0.2737 0.7440 1.8167 4.6785 0.0000 ORDLIN 0.0324 0.0595 -0.0842 0.1491 0.5447 0.5860 ORDLCHA 0.4393 0.1667 0.1127 0.7660 2.6361 0.0084 Scale 1.3820 . . . . . NOTE: The scale parameter for GEE estimation was computed as the square root of the normalized Pearson's chi-square. The GENMOD Procedure GEE Model Information Description Value Correlation Structure Unstructured Within-Subject Effect WEEK (6 levels) Subject Effect ID (75 levels) Number of Clusters 75 Correlation Matrix Dimension 6 Maximum Cluster Size 6 Minimum Cluster Size 6 Working Correlation Matrix COL1 COL2 COL3 COL4 COL5 COL6 ROW1 1.0000 0.5435 0.4509 0.4233 0.3759 0.4014 ROW2 0.5435 1.0000 0.4347 0.4240 0.3717 0.3718 ROW3 0.4509 0.4347 1.0000 0.5142 0.4462 0.4272 ROW4 0.4233 0.4240 0.5142 1.0000 0.5469 0.5455 ROW5 0.3759 0.3717 0.4462 0.5469 1.0000 0.6685 ROW6 0.4014 0.3718 0.4272 0.5455 0.6685 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Empirical 95% Confidence Limits Parameter Estimate Std Err Lower Upper Z Pr>|Z| INTERCEPT 3.1279 0.1938 2.7480 3.5077 16.138 0.0000 LINEAR -0.2063 0.0441 -0.2928 -0.1198 -4.674 0.0000 LINCHANG -0.2511 0.1174 -0.4812 -0.0210 -2.139 0.0325 ORDER 1.2777 0.2754 0.7379 1.8174 4.6391 0.0000 ORDLIN 0.0453 0.0637 -0.0795 0.1700 0.7111 0.4770 ORDLCHA 0.4483 0.1611 0.1324 0.7641 2.7819 0.0054 Scale 1.3819 . . . . . NOTE: The scale parameter for GEE estimation was computed as the square root of the normalized Pearson's chi-square.