SAS Model 2b: Random Linear Time

The Mixed Procedure

Model Information
Data Set WORK.EXAMPLE23
Dependent Variable nm3rt
Covariance Structures Unstructured, Variance Components
Subject Effects ID, ID
Estimation Method REML
Residual Variance Method Parameter
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 4
Columns in X 2
Columns in Z Per Subject 2
Subjects 101
Max Obs Per Subject 6

Number of Observations
Number of Observations Read 606
Number of Observations Used 606
Number of Observations Not Used 0

Estimated R Matrix for ID 101
Row Col1 Col2 Col3 Col4 Col5 Col6
1 27905          
2   27905        
3     27905      
4       27905    
5         27905  
6           27905

Estimated G Matrix
Row Effect ID: Participant ID Col1 Col2
1 Intercept 101 253258 -12701
2 c1sess 101 -12701 2233.83

Estimated V Matrix for ID 101
Row Col1 Col2 Col3 Col4 Col5 Col6
1 281163 240557 227856 215155 202455 189754
2 240557 257995 219623 209156 198689 188222
3 227856 219623 239295 203157 194924 186691
4 215155 209156 203157 225063 191158 185159
5 202455 198689 194924 191158 215298 183627
6 189754 188222 186691 185159 183627 210001

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) ID 253258 37897 6.68 <.0001
UN(2,1) ID -12701 3621.98 -3.51 0.0005
UN(2,2) ID 2233.83 552.92 4.04 <.0001
session ID 27905 1963.42 14.21 <.0001

Fit Statistics
-2 Res Log Likelihood 8372.1
AIC (smaller is better) 8380.1
AICC (smaller is better) 8380.2
BIC (smaller is better) 8390.6

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 830.20 <.0001

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t|
Intercept 1899.63 51.4998 100 36.89 <.0001
c1sess -51.5719 6.1567 100 -8.38 <.0001

Solution for Random Effects
Effect ID: Participant ID Estimate Std Err Pred DF t Value Pr > |t|
Intercept 101 664.70 113.28 440 5.87 <.0001
c1sess 101 -26.7006 29.9792 147 -0.89 0.3746
Intercept 102 564.49 113.28 440 4.98 <.0001
c1sess 102 -28.1081 29.9792 147 -0.94 0.3500
Intercept 105 196.33 113.28 440 1.73 0.0838
c1sess 105 -27.0727 29.9792 147 -0.90 0.3680
Intercept 106 -265.94 113.28 440 -2.35 0.0193
c1sess 106 2.7248 29.9792 147 0.09 0.9277
Intercept 107 -281.82 113.28 440 -2.49 0.0132
c1sess 107 13.4967 29.9792 147 0.45 0.6532
Intercept 108 577.33 113.28 440 5.10 <.0001
c1sess 108 3.7294 29.9792 147 0.12 0.9012
Intercept 109 -542.02 113.28 440 -4.79 <.0001
c1sess 109 24.4079 29.9792 147 0.81 0.4169
Intercept 110 -80.6225 113.28 440 -0.71 0.4770
c1sess 110 14.5905 29.9792 147 0.49 0.6272
Intercept 111 -553.67 113.28 440 -4.89 <.0001
c1sess 111 40.4271 29.9792 147 1.35 0.1796
Intercept 112 -192.75 113.28 440 -1.70 0.0895
c1sess 112 -3.2564 29.9792 147 -0.11 0.9136
Intercept 113 -33.4243 113.28 440 -0.30 0.7681
c1sess 113 -4.3237 29.9792 147 -0.14 0.8855
Intercept 116 -487.19 113.28 440 -4.30 <.0001
c1sess 116 14.4687 29.9792 147 0.48 0.6301
Intercept 117 38.0958 113.28 440 0.34 0.7368
c1sess 117 13.1806 29.9792 147 0.44 0.6608
Intercept 118 -76.2381 113.28 440 -0.67 0.5013
c1sess 118 12.0782 29.9792 147 0.40 0.6876
Intercept 120 -557.71 113.28 440 -4.92 <.0001
c1sess 120 51.9903 29.9792 147 1.73 0.0850
Intercept 121 83.3417 113.28 440 0.74 0.4623
c1sess 121 74.6287 29.9792 147 2.49 0.0139
Intercept 124 244.45 113.28 440 2.16 0.0315
c1sess 124 -4.5897 29.9792 147 -0.15 0.8785
Intercept 125 297.46 113.28 440 2.63 0.0089
c1sess 125 -0.07391 29.9792 147 -0.00 0.9980
Intercept 126 731.69 113.28 440 6.46 <.0001
c1sess 126 -26.4123 29.9792 147 -0.88 0.3797
Intercept 127 399.72 113.28 440 3.53 0.0005
c1sess 127 -4.9108 29.9792 147 -0.16 0.8701
Intercept 128 -280.09 113.28 440 -2.47 0.0138
c1sess 128 26.3539 29.9792 147 0.88 0.3808
Intercept 129 637.87 113.28 440 5.63 <.0001
c1sess 129 -48.7862 29.9792 147 -1.63 0.1058
Intercept 130 -228.39 113.28 440 -2.02 0.0444
c1sess 130 -17.2486 29.9792 147 -0.58 0.5659
Intercept 131 1138.89 113.28 440 10.05 <.0001
c1sess 131 -39.1319 29.9792 147 -1.31 0.1938
Intercept 132 454.85 113.28 440 4.02 <.0001
c1sess 132 11.1322 29.9792 147 0.37 0.7109
Intercept 133 -192.26 113.28 440 -1.70 0.0904
c1sess 133 -12.7246 29.9792 147 -0.42 0.6719
Intercept 136 104.24 113.28 440 0.92 0.3579
c1sess 136 -44.1944 29.9792 147 -1.47 0.1426
Intercept 137 1541.37 113.28 440 13.61 <.0001
c1sess 137 -192.81 29.9792 147 -6.43 <.0001
Intercept 138 335.95 113.28 440 2.97 0.0032
c1sess 138 16.6343 29.9792 147 0.55 0.5798
Intercept 139 1849.27 113.28 440 16.33 <.0001
c1sess 139 -38.1064 29.9792 147 -1.27 0.2057
Intercept 140 1053.84 113.28 440 9.30 <.0001
c1sess 140 -86.6631 29.9792 147 -2.89 0.0044
Intercept 141 -415.93 113.28 440 -3.67 0.0003
c1sess 141 27.0048 29.9792 147 0.90 0.3692
Intercept 145 379.54 113.28 440 3.35 0.0009
c1sess 145 44.5282 29.9792 147 1.49 0.1396
Intercept 147 -400.43 113.28 440 -3.54 0.0005
c1sess 147 36.7693 29.9792 147 1.23 0.2220
Intercept 148 -174.76 113.28 440 -1.54 0.1236
c1sess 148 3.8405 29.9792 147 0.13 0.8982
Intercept 149 561.61 113.28 440 4.96 <.0001
c1sess 149 -54.3153 29.9792 147 -1.81 0.0721
Intercept 150 571.27 113.28 440 5.04 <.0001
c1sess 150 -64.4415 29.9792 147 -2.15 0.0332
Intercept 151 77.9535 113.28 440 0.69 0.4917
c1sess 151 21.0467 29.9792 147 0.70 0.4838
Intercept 153 -694.79 113.28 440 -6.13 <.0001
c1sess 153 24.1020 29.9792 147 0.80 0.4227
Intercept 154 7.9083 113.28 440 0.07 0.9444
c1sess 154 17.8408 29.9792 147 0.60 0.5527
Intercept 501 -423.92 113.28 440 -3.74 0.0002
c1sess 501 4.8303 29.9792 147 0.16 0.8722
Intercept 502 -415.05 113.28 440 -3.66 0.0003
c1sess 502 -40.2521 29.9792 147 -1.34 0.1815
Intercept 504 26.3526 113.28 440 0.23 0.8161
c1sess 504 1.4571 29.9792 147 0.05 0.9613
Intercept 507 801.73 113.28 440 7.08 <.0001
c1sess 507 -42.9666 29.9792 147 -1.43 0.1539
Intercept 508 -402.49 113.28 440 -3.55 0.0004
c1sess 508 18.5660 29.9792 147 0.62 0.5367
Intercept 509 -538.73 113.28 440 -4.76 <.0001
c1sess 509 47.5306 29.9792 147 1.59 0.1150
Intercept 511 438.97 113.28 440 3.88 0.0001
c1sess 511 -29.2888 29.9792 147 -0.98 0.3302
Intercept 512 182.52 113.28 440 1.61 0.1078
c1sess 512 6.2114 29.9792 147 0.21 0.8361
Intercept 513 -429.42 113.28 440 -3.79 0.0002
c1sess 513 -3.7613 29.9792 147 -0.13 0.9003
Intercept 514 8.1290 113.28 440 0.07 0.9428
c1sess 514 -6.7175 29.9792 147 -0.22 0.8230
Intercept 515 -465.23 113.28 440 -4.11 <.0001
c1sess 515 29.7720 29.9792 147 0.99 0.3223
Intercept 516 -420.26 113.28 440 -3.71 0.0002
c1sess 516 -2.2141 29.9792 147 -0.07 0.9412
Intercept 517 -411.38 113.28 440 -3.63 0.0003
c1sess 517 -6.1286 29.9792 147 -0.20 0.8383
Intercept 518 -733.69 113.28 440 -6.48 <.0001
c1sess 518 11.3735 29.9792 147 0.38 0.7050
Intercept 519 -529.64 113.28 440 -4.68 <.0001
c1sess 519 20.2085 29.9792 147 0.67 0.5013
Intercept 520 241.95 113.28 440 2.14 0.0332
c1sess 520 -14.9717 29.9792 147 -0.50 0.6182
Intercept 521 34.2640 113.28 440 0.30 0.7624
c1sess 521 80.3132 29.9792 147 2.68 0.0082
Intercept 522 338.19 113.28 440 2.99 0.0030
c1sess 522 -13.4860 29.9792 147 -0.45 0.6535
Intercept 523 116.23 113.28 440 1.03 0.3054
c1sess 523 3.9536 29.9792 147 0.13 0.8953
Intercept 524 79.7268 113.28 440 0.70 0.4819
c1sess 524 20.1113 29.9792 147 0.67 0.5034
Intercept 525 359.86 113.28 440 3.18 0.0016
c1sess 525 36.3668 29.9792 147 1.21 0.2271
Intercept 526 77.4778 113.28 440 0.68 0.4943
c1sess 526 -17.9443 29.9792 147 -0.60 0.5504
Intercept 527 -348.21 113.28 440 -3.07 0.0022
c1sess 527 6.4270 29.9792 147 0.21 0.8305
Intercept 528 626.46 113.28 440 5.53 <.0001
c1sess 528 37.5502 29.9792 147 1.25 0.2124
Intercept 529 -568.33 113.28 440 -5.02 <.0001
c1sess 529 50.3120 29.9792 147 1.68 0.0954
Intercept 530 -179.97 113.28 440 -1.59 0.1128
c1sess 530 11.3796 29.9792 147 0.38 0.7048
Intercept 531 190.47 113.28 440 1.68 0.0934
c1sess 531 28.0448 29.9792 147 0.94 0.3511
Intercept 532 493.46 113.28 440 4.36 <.0001
c1sess 532 11.6861 29.9792 147 0.39 0.6972
Intercept 533 -7.2608 113.28 440 -0.06 0.9489
c1sess 533 -28.3562 29.9792 147 -0.95 0.3458
Intercept 534 -46.3333 113.28 440 -0.41 0.6827
c1sess 534 1.4683 29.9792 147 0.05 0.9610
Intercept 535 -550.60 113.28 440 -4.86 <.0001
c1sess 535 29.5429 29.9792 147 0.99 0.3260
Intercept 536 -78.8282 113.28 440 -0.70 0.4869
c1sess 536 22.3094 29.9792 147 0.74 0.4580
Intercept 537 -495.58 113.28 440 -4.38 <.0001
c1sess 537 3.9296 29.9792 147 0.13 0.8959
Intercept 538 -156.40 113.28 440 -1.38 0.1681
c1sess 538 3.7038 29.9792 147 0.12 0.9018
Intercept 539 -272.29 113.28 440 -2.40 0.0166
c1sess 539 -31.9593 29.9792 147 -1.07 0.2882
Intercept 540 -417.12 113.28 440 -3.68 0.0003
c1sess 540 35.5456 29.9792 147 1.19 0.2377
Intercept 541 176.81 113.28 440 1.56 0.1193
c1sess 541 -70.0254 29.9792 147 -2.34 0.0209
Intercept 542 -425.01 113.28 440 -3.75 0.0002
c1sess 542 16.5570 29.9792 147 0.55 0.5816
Intercept 543 -515.27 113.28 440 -4.55 <.0001
c1sess 543 12.3561 29.9792 147 0.41 0.6808
Intercept 544 376.41 113.28 440 3.32 0.0010
c1sess 544 -18.9358 29.9792 147 -0.63 0.5286
Intercept 545 -824.63 113.28 440 -7.28 <.0001
c1sess 545 40.8950 29.9792 147 1.36 0.1746
Intercept 546 57.1173 113.28 440 0.50 0.6143
c1sess 546 -14.2554 29.9792 147 -0.48 0.6351
Intercept 547 -387.17 113.28 440 -3.42 0.0007
c1sess 547 14.2645 29.9792 147 0.48 0.6349
Intercept 548 -110.17 113.28 440 -0.97 0.3313
c1sess 548 4.9055 29.9792 147 0.16 0.8702
Intercept 549 41.9679 113.28 440 0.37 0.7112
c1sess 549 -27.1337 29.9792 147 -0.91 0.3669
Intercept 550 -360.20 113.28 440 -3.18 0.0016
c1sess 550 8.9446 29.9792 147 0.30 0.7659
Intercept 551 1201.25 113.28 440 10.60 <.0001
c1sess 551 -21.8869 29.9792 147 -0.73 0.4665
Intercept 552 -427.11 113.28 440 -3.77 0.0002
c1sess 552 -3.3220 29.9792 147 -0.11 0.9119
Intercept 553 311.48 113.28 440 2.75 0.0062
c1sess 553 -15.7823 29.9792 147 -0.53 0.5994
Intercept 554 -441.37 113.28 440 -3.90 0.0001
c1sess 554 30.0933 29.9792 147 1.00 0.3171
Intercept 555 -49.9457 113.28 440 -0.44 0.6595
c1sess 555 -50.0252 29.9792 147 -1.67 0.0973
Intercept 556 282.01 113.28 440 2.49 0.0132
c1sess 556 -6.9185 29.9792 147 -0.23 0.8178
Intercept 557 83.6736 113.28 440 0.74 0.4605
c1sess 557 -88.5578 29.9792 147 -2.95 0.0037
Intercept 558 -57.4848 113.28 440 -0.51 0.6121
c1sess 558 40.1290 29.9792 147 1.34 0.1828
Intercept 559 -767.81 113.28 440 -6.78 <.0001
c1sess 559 26.9457 29.9792 147 0.90 0.3702
Intercept 560 -471.41 113.28 440 -4.16 <.0001
c1sess 560 32.2422 29.9792 147 1.08 0.2839
Intercept 561 57.6257 113.28 440 0.51 0.6112
c1sess 561 -7.6254 29.9792 147 -0.25 0.7996
Intercept 562 -314.94 113.28 440 -2.78 0.0057
c1sess 562 11.0044 29.9792 147 0.37 0.7141
Intercept 563 -229.06 113.28 440 -2.02 0.0438
c1sess 563 33.5516 29.9792 147 1.12 0.2649
Intercept 564 -127.83 113.28 440 -1.13 0.2597
c1sess 564 -33.2313 29.9792 147 -1.11 0.2695
Intercept 565 -258.15 113.28 440 -2.28 0.0231
c1sess 565 30.1600 29.9792 147 1.01 0.3161

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
c1sess 1 100 70.17 <.0001