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Table 7.2 on page 246.
title1 'Table 7.2: Conventional multilevel model for change: Opposite naming data'; title2 'Restricted ML'; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; class id; model opp=time ccog time*ccog / solution ddfm=bw; random intercept time / sub=id type=un; run;
Table 7.2: Conventional multilevel model for change: Opposite naming data Restricted ML
The Mixed Procedure
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) ID 1236.41 332.40 3.72 <.0001
UN(2,1) ID -178.23 85.4298 -2.09 0.0370
UN(2,2) ID 107.25 34.6767 3.09 0.0010
Residual 159.48 26.9566 5.92 <.0001
Fit Statistics -2 Res Log Likelihood 1260.3 AIC (smaller is better) 1268.3 AICC (smaller is better) 1268.6 BIC (smaller is better) 1274.5
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 120.72 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 164.37 6.2061 33 26.49 <.0001
TIME 26.9600 1.9939 103 13.52 <.0001
CCOG -0.1136 0.5040 33 -0.23 0.8231
TIME*CCOG 0.4329 0.1619 103 2.67 0.0087
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F
TIME 1 103 182.83 <.0001
CCOG 1 33 0.05 0.8231
TIME*CCOG 1 103 7.15 0.0087
Table 7.3 on pages 258-259.
title1 'Table 7.3: Conventional multilevel model for change: Opposite naming data'; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; title2 'Comparing alternative error structures at level-1, with none at level-2 (REML)'; title3 'completely unstructured'; class id wave; model opp=time ccog time*ccog / solution ddfm=bw notest; repeated wave / subject=id type=un r; run; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; title3 'compound symmetric'; class id wave; model opp=time ccog time*ccog / solution ddfm=bw notest; repeated wave / subject=id type=cs r; run; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; title3 'compound symmetric heterogeneous CSH'; class id wave; model opp=time ccog time*ccog / solution ddfm=bw notest; repeated wave / subject=id type=csh r; run; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; title3 'ar(1)'; class id wave; model opp=time ccog time*ccog / solution ddfm=bw notest; repeated wave / subject=id type=ar(1) r; run; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; title3 'ar(1)heterogeneous'; class id wave; model opp=time ccog time*ccog / solution ddfm=bw notest; repeated wave / subject=id type=arh(1) r; run; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; title3 'Toeplitz'; class id wave; model opp=time ccog time*ccog / solution ddfm=bw notest; repeated wave / subject=id type=toep r; run; Table 7.3: Conventional multilevel model for change: Opposite naming data Comparing alternative error structures at level-1, with none at level-2 (REML) completely unstructured
The Mixed Procedure
Estimated R Matrix for ID 1
Row Col1 Col2 Col3 Col4
1 1344.84 1005.57 946.05 583.12 2 1005.57 1150.30 1028.43 846.49 3 946.05 1028.43 1235.65 969.24 4 583.12 846.49 969.24 1205.89
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) ID 1344.84 330.16 4.07 <.0001
UN(2,1) ID 1005.57 277.88 3.62 0.0003
UN(2,2) ID 1150.30 282.13 4.08 <.0001
UN(3,1) ID 946.05 276.91 3.42 0.0006
UN(3,2) ID 1028.43 272.75 3.77 0.0002
UN(3,3) ID 1235.65 301.84 4.09 <.0001
UN(4,1) ID 583.12 243.58 2.39 0.0167
UN(4,2) ID 846.49 252.08 3.36 0.0008
UN(4,3) ID 969.24 270.78 3.58 0.0003
UN(4,4) ID 1205.89 296.70 4.06 <.0001
Fit Statistics -2 Res Log Likelihood 1255.8 AIC (smaller is better) 1275.8 AICC (smaller is better) 1277.5 BIC (smaller is better) 1291.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 125.22 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 165.83 5.9523 33 27.86 <.0001
TIME 26.5843 1.9257 33 13.80 <.0001
CCOG -0.07408 0.4834 33 -0.15 0.8791
TIME*CCOG 0.4583 0.1564 33 2.93 0.0061
Table 7.3: Conventional multilevel model for change: Opposite naming data Comparing alternative error structures at level-1, with none at level-2 (REML) compound symmetric
The Mixed Procedure
Estimated R Matrix for ID 1
Row Col1 Col2 Col3 Col4
1 1231.36 900.07 900.07 900.07
2 900.07 1231.36 900.07 900.07
3 900.07 900.07 1231.36 900.07
4 900.07 900.07 900.07 1231.36
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
CS ID 900.07 242.25 3.72 0.0002
Residual 331.28 46.1633 7.18 <.0001
Fit Statistics -2 Res Log Likelihood 1287.0 AIC (smaller is better) 1291.0 AICC (smaller is better) 1291.1 BIC (smaller is better) 1294.2
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 93.96 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 164.37 5.6870 33 28.90 <.0001
TIME 26.9600 1.3759 103 19.59 <.0001
CCOG -0.1136 0.4619 33 -0.25 0.8073
TIME*CCOG 0.4329 0.1117 103 3.87 0.0002
Table 7.3: Conventional multilevel model for change: Opposite naming data Comparing alternative error structures at level-1, with none at level-2 (REML) compound symmetric heterogeneous CSH
The Mixed Procedure
Estimated R Matrix for ID 1
Row Col1 Col2 Col3 Col4
1 1438.04 912.85 946.52 1009.46
2 912.85 1067.67 815.57 869.80
3 946.52 815.57 1147.87 901.88
4 1009.46 869.80 901.88 1305.61
Covariance Parameter Estimates Cov Standard Z Parm Subject Estimate Error Value Pr Z Var(1) ID 1438.04 354.99 4.05 <.0001 Var(2) ID 1067.67 255.23 4.18 <.0001 Var(3) ID 1147.87 273.55 4.20 <.0001 Var(4) ID 1305.61 323.74 4.03 <.0001 CSH ID 0.7367 0.05971 12.34 <.0001
Fit Statistics -2 Res Log Likelihood 1285.0 AIC (smaller is better) 1295.0 AICC (smaller is better) 1295.4 BIC (smaller is better) 1302.7
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 96.06 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 164.32 5.6936 33 28.86 <.0001
TIME 26.9260 1.4192 103 18.97 <.0001
CCOG -0.1937 0.4624 33 -0.42 0.6780
TIME*CCOG 0.4397 0.1153 103 3.81 0.0002
Table 7.3: Conventional multilevel model for change: Opposite naming data Comparing alternative error structures at level-1, with none at level-2 (REML) ar(1)
The Mixed Procedure
Estimated R Matrix for ID 1
Row Col1 Col2 Col3 Col4
1 1256.72 1037.24 856.08 706.57
2 1037.24 1256.72 1037.24 856.08
3 856.08 1037.24 1256.72 1037.24
4 706.57 856.08 1037.24 1256.72
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
AR(1) ID 0.8253 0.03948 20.91 <.0001
Residual 1256.72 248.25 5.06 <.0001
Fit Statistics -2 Res Log Likelihood 1265.9 AIC (smaller is better) 1269.9 AICC (smaller is better) 1270.0 BIC (smaller is better) 1273.0
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 115.13 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 164.34 5.9797 33 27.48 <.0001
TIME 27.1979 1.8689 103 14.55 <.0001
CCOG -0.03324 0.4856 33 -0.07 0.9458
TIME*CCOG 0.4197 0.1518 103 2.77 0.0067
Table 7.3: Conventional multilevel model for change: Opposite naming data Comparing alternative error structures at level-1, with none at level-2 (REML) ar(1)heterogeneous
The Mixed Procedure
Estimated R Matrix for ID 1
Row Col1 Col2 Col3 Col4
1 1340.67 1000.67 857.30 708.87
2 1000.67 1111.10 951.90 787.10
3 857.30 951.90 1213.18 1003.14
4 708.87 787.10 1003.14 1233.93
Covariance Parameter Estimates Cov Standard Z Parm Subject Estimate Error Value Pr Z Var(1) ID 1340.67 316.29 4.24 <.0001 Var(2) ID 1111.10 265.70 4.18 <.0001 Var(3) ID 1213.18 290.11 4.18 <.0001 Var(4) ID 1233.93 293.63 4.20 <.0001 ARH(1) ID 0.8199 0.04105 19.97 <.0001
Fit Statistics -2 Res Log Likelihood 1264.8 AIC (smaller is better) 1274.8 AICC (smaller is better) 1275.3 BIC (smaller is better) 1282.6
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 116.17 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 164.64 6.0588 33 27.17 <.0001
TIME 27.1638 1.9131 103 14.20 <.0001
CCOG -0.1111 0.4920 33 -0.23 0.8228
TIME*CCOG 0.4281 0.1554 103 2.76 0.0069
Table 7.3: Conventional multilevel model for change: Opposite naming data Comparing alternative error structures at level-1, with none at level-2 (REML) Toeplitz
The Mixed Procedure
Estimated R Matrix for ID 1
Row Col1 Col2 Col3 Col4
1 1246.90 1029.33 896.59 624.06
2 1029.33 1246.90 1029.33 896.59
3 896.59 1029.33 1246.90 1029.33
4 624.06 896.59 1029.33 1246.90
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
TOEP(2) ID 1029.33 239.57 4.30 <.0001
TOEP(3) ID 896.59 232.76 3.85 0.0001
TOEP(4) ID 624.06 234.89 2.66 0.0079
Residual 1246.90 242.67 5.14 <.0001
Fit Statistics -2 Res Log Likelihood 1258.1 AIC (smaller is better) 1266.1 AICC (smaller is better) 1266.4 BIC (smaller is better) 1272.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 122.93 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 165.10 5.9225 33 27.88 <.0001
TIME 26.8954 1.9429 103 13.84 <.0001
CCOG -0.00070 0.4810 33 -0.00 0.9988
TIME*CCOG 0.4364 0.1578 103 2.77 0.0067
Table 7.4 on page 265.
title1 'Table 7.4: Comparing fixed effects in models with alternative error structures'; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; title2 'Standard error covariance structure'; class id ; model opp=time ccog time*ccog / solution ddfm=bw notest; random intercept time / subject=id type=un; run; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; title3 'Toeplitz error covariance matrix'; class id wave; model opp=time ccog time*ccog / solution ddfm=bw notest; repeated wave / subject=id type=toep r; run; proc mixed data='c:\alda\opposites_pp' noclprint noinfo covtest noitprint method=reml; title2 'Unstructured error covariance matrix'; class id wave; model opp=time ccog time*ccog / solution ddfm=bw notest; repeated wave / subject=id type=un r; run; Table 7.4: Comparing fixed effects in models with alternative error structures Standard error covariance structure
The Mixed Procedure
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) ID 1236.41 332.40 3.72 <.0001
UN(2,1) ID -178.23 85.4298 -2.09 0.0370
UN(2,2) ID 107.25 34.6767 3.09 0.0010
Residual 159.48 26.9566 5.92 <.0001
Fit Statistics -2 Res Log Likelihood 1260.3 AIC (smaller is better) 1268.3 AICC (smaller is better) 1268.6 BIC (smaller is better) 1274.5
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 120.72 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 164.37 6.2061 33 26.49 <.0001
TIME 26.9600 1.9939 103 13.52 <.0001
CCOG -0.1136 0.5040 33 -0.23 0.8231
TIME*CCOG 0.4329 0.1619 103 2.67 0.0087
Table 7.4: Comparing fixed effects in models with alternative error structures Standard error covariance structure Toeplitz error covariance matrix
The Mixed Procedure
Estimated R Matrix for ID 1
Row Col1 Col2 Col3 Col4
1 1246.90 1029.33 896.59 624.06
2 1029.33 1246.90 1029.33 896.59
3 896.59 1029.33 1246.90 1029.33
4 624.06 896.59 1029.33 1246.90
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
TOEP(2) ID 1029.33 239.57 4.30 <.0001
TOEP(3) ID 896.59 232.76 3.85 0.0001
TOEP(4) ID 624.06 234.89 2.66 0.0079
Residual 1246.90 242.67 5.14 <.0001
Fit Statistics -2 Res Log Likelihood 1258.1 AIC (smaller is better) 1266.1 AICC (smaller is better) 1266.4 BIC (smaller is better) 1272.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 122.93 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 165.10 5.9225 33 27.88 <.0001
TIME 26.8954 1.9429 103 13.84 <.0001
CCOG -0.00070 0.4810 33 -0.00 0.9988
TIME*CCOG 0.4364 0.1578 103 2.77 0.0067
Table 7.4: Comparing fixed effects in models with alternative error structures Unstructured error covariance matrix
The Mixed Procedure
Estimated R Matrix for ID 1
Row Col1 Col2 Col3 Col4
1 1344.84 1005.57 946.05 583.12
2 1005.57 1150.30 1028.43 846.49
3 946.05 1028.43 1235.65 969.24
4 583.12 846.49 969.24 1205.89
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) ID 1344.84 330.16 4.07 <.0001
UN(2,1) ID 1005.57 277.88 3.62 0.0003
UN(2,2) ID 1150.30 282.13 4.08 <.0001
UN(3,1) ID 946.05 276.91 3.42 0.0006
UN(3,2) ID 1028.43 272.75 3.77 0.0002
UN(3,3) ID 1235.65 301.84 4.09 <.0001
UN(4,1) ID 583.12 243.58 2.39 0.0167
UN(4,2) ID 846.49 252.08 3.36 0.0008
UN(4,3) ID 969.24 270.78 3.58 0.0003
UN(4,4) ID 1205.89 296.70 4.06 <.0001
Fit Statistics -2 Res Log Likelihood 1255.8 AIC (smaller is better) 1275.8 AICC (smaller is better) 1277.5 BIC (smaller is better) 1291.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 125.22 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 165.83 5.9523 33 27.86 <.0001
TIME 26.5843 1.9257 33 13.80 <.0001
CCOG -0.07408 0.4834 33 -0.15 0.8791
TIME*CCOG 0.4583 0.1564 33 2.93 0.0061
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