SAS Model 1.1: Empty Model with Homogeneous Errors

The Mixed Procedure

Model Information
Data Set WORK.EX1
Dependent Variable lg_rt
Covariance Structures Unstructured, Variance Components
Subject Effects Item, ID, ID
Estimation Method ML
Residual Variance Method Parameter
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 3
Columns in X 1
Columns in Z 204
Subjects 1
Max Obs Per Subject 7803

Number of Observations
Number of Observations Read 7803
Number of Observations Used 7646
Number of Observations Not Used 157

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 18819.72618532  
1 2 15178.28226381 0.00002126
2 1 15178.27022752 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) Item 0.1242 0.02514 4.94 <.0001
UN(1,1) ID 0.1798 0.02150 8.36 <.0001
Residual ID 0.3899 0.006391 61.00 <.0001

Fit Statistics
-2 Log Likelihood 15178.3
AIC (smaller is better) 15186.3
AICC (smaller is better) 15186.3
BIC (smaller is better) 15178.3

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
2 3641.46 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
15178.3 4 15186.3 15186.3 15178.3 15178.3 15182.3

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t|
Intercept 1.6226 0.06051 102 26.82 <.0001



SAS Model 1.2a: Main Effects Model with Homogeneous Errors

The Mixed Procedure

Model Information
Data Set WORK.EX1
Dependent Variable lg_rt
Covariance Structures Unstructured, Variance Components
Subject Effects Item, ID, ID
Estimation Method ML
Residual Variance Method Parameter
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 3
Columns in X 5
Columns in Z 204
Subjects 1
Max Obs Per Subject 7803

Number of Observations
Number of Observations Read 7803
Number of Observations Used 7646
Number of Observations Not Used 157

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 16384.48713600  
1 2 14885.27448271 0.00002139
2 1 14885.26544933 0.00000001

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) Item 0.08725 0.01780 4.90 <.0001
UN(1,1) ID 0.02289 0.003523 6.50 <.0001
Residual ID 0.3899 0.006391 61.00 <.0001

Fit Statistics
-2 Log Likelihood 14885.3
AIC (smaller is better) 14901.3
AICC (smaller is better) 14901.3
BIC (smaller is better) 14885.3

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
2 1499.22 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14885.3 8 14901.3 14901.3 14885.3 14885.3 14893.3

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t|
Intercept 1.3067 0.04580 66.3 28.53 <.0001
c_mean -0.05167 0.02277 51 -2.27 0.0275
c_sal -0.1316 0.03931 51 -3.35 0.0015
oldage 0.5899 0.05517 153 10.69 <.0001
yrs65 0.02021 0.004375 154 4.62 <.0001

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
c_mean 1 51 5.15 0.0275
c_sal 1 51 11.21 0.0015
oldage 1 153 114.33 <.0001
yrs65 1 154 21.34 <.0001



SAS Model 1.2b: Main Effects Model with Heterogeneous Errors

The Mixed Procedure

Model Information
Data Set WORK.EX1
Dependent Variable lg_rt
Covariance Structures Unstructured, Variance Components
Subject Effects Item, ID, ID
Group Effects older, older
Estimation Method ML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 5
Columns in Z 357
Subjects 1
Max Obs Per Subject 7803

Number of Observations
Number of Observations Read 7803
Number of Observations Used 7646
Number of Observations Not Used 157

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 16384.48713600  
1 2 14692.20530775 0.00008622
2 1 14692.17702246 0.00000015
3 1 14692.17697430 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Group Estimate Standard Error Z Value Pr > Z
UN(1,1) Item   0.08807 0.01793 4.91 <.0001
UN(1,1) ID older 0 0.01083 0.002499 4.33 <.0001
UN(1,1) ID older 1 0.04318 0.01001 4.31 <.0001
Residual ID older 0 0.3236 0.006719 48.16 <.0001
Residual ID older 1 0.5065 0.01395 36.30 <.0001

Fit Statistics
-2 Log Likelihood 14692.2
AIC (smaller is better) 14712.2
AICC (smaller is better) 14712.2
BIC (smaller is better) 14692.2

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 1692.31 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14692.2 10 14712.2 14712.2 14692.2 14692.2 14702.2

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t|
Intercept 1.3056 0.04444 58.2 29.38 <.0001
c_mean -0.05504 0.02286 51 -2.41 0.0197
c_sal -0.1341 0.03946 51 -3.40 0.0013
oldage 0.5900 0.07007 61.4 8.42 <.0001
yrs65 0.02021 0.005761 57.3 3.51 0.0009

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
c_mean 1 51 5.80 0.0197
c_sal 1 51 11.55 0.0013
oldage 1 61.4 70.90 <.0001
yrs65 1 57.3 12.30 0.0009



SAS Model 1.3a: All Two-Way and Three-Way Interactions

The Mixed Procedure

Model Information
Data Set WORK.EX1
Dependent Variable lg_rt
Covariance Structures Unstructured, Variance Components
Subject Effects Item, ID, ID
Group Effects older, older
Estimation Method ML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 12
Columns in Z 357
Subjects 1
Max Obs Per Subject 7803

Number of Observations
Number of Observations Read 7803
Number of Observations Used 7646
Number of Observations Not Used 157

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 16341.99397839  
1 2 14651.69232490 0.00009102
2 1 14651.66437023 0.00000015
3 1 14651.66432402 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Group Estimate Standard Error Z Value Pr > Z
UN(1,1) Item   0.08778 0.01788 4.91 <.0001
UN(1,1) ID older 0 0.01083 0.002499 4.34 <.0001
UN(1,1) ID older 1 0.04320 0.009995 4.32 <.0001
Residual ID older 0 0.3230 0.006697 48.23 <.0001
Residual ID older 1 0.5007 0.01376 36.39 <.0001

Fit Statistics
-2 Log Likelihood 14651.7
AIC (smaller is better) 14685.7
AICC (smaller is better) 14685.7
BIC (smaller is better) 14651.7

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 1690.33 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14651.7 17 14685.7 14685.7 14651.7 14651.7 14668.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t|
Intercept 1.3038 0.04538 58 28.73 <.0001
c_mean -0.06402 0.02305 52 -2.78 0.0076
c_sal -0.1425 0.04092 52 -3.48 0.0010
oldage 0.6071 0.07065 63.7 8.59 <.0001
yrs65 0.02079 0.005808 59.4 3.58 0.0007
c_mean*c_sal -0.00270 0.01939 52 -0.14 0.8897
c_mean*oldage 0.01413 0.01704 3049 0.83 0.4070
c_mean*yrs65 0.002245 0.001388 2651 1.62 0.1059
c_sal*oldage -0.01542 0.03026 3048 -0.51 0.6103
c_sal*yrs65 0.002619 0.002454 2650 1.07 0.2860
c_mean*c_sal*oldage -0.02520 0.01441 3045 -1.75 0.0804
c_mean*c_sal*yrs65 0.000022 0.001171 2651 0.02 0.9850

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
c_mean 1 52 7.71 0.0076
c_sal 1 52 12.13 0.0010
oldage 1 63.7 73.85 <.0001
yrs65 1 59.4 12.81 0.0007
c_mean*c_sal 1 52 0.02 0.8897
c_mean*oldage 1 3049 0.69 0.4070
c_mean*yrs65 1 2651 2.62 0.1059
c_sal*oldage 1 3048 0.26 0.6103
c_sal*yrs65 1 2650 1.14 0.2860
c_mean*c_sal*oldage 1 3045 3.06 0.0804
c_mean*c_sal*yrs65 1 2651 0.00 0.9850



SAS revised Model 1.3b: Significant Interactions Only

The Mixed Procedure

Model Information
Data Set WORK.EX1
Dependent Variable lg_rt
Covariance Structures Unstructured, Variance Components
Subject Effects Item, ID, ID
Group Effects older, older
Estimation Method ML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 9
Columns in Z 357
Subjects 1
Max Obs Per Subject 7803

Number of Observations
Number of Observations Read 7803
Number of Observations Used 7646
Number of Observations Not Used 157

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 16347.14523223  
1 2 14656.63048340 0.00009025
2 1 14656.60253428 0.00000015
3 1 14656.60248802 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Group Estimate Standard Error Z Value Pr > Z
UN(1,1) Item   0.08779 0.01788 4.91 <.0001
UN(1,1) ID older 0 0.01083 0.002499 4.34 <.0001
UN(1,1) ID older 1 0.04318 0.009996 4.32 <.0001
Residual ID older 0 0.3230 0.006697 48.23 <.0001
Residual ID older 1 0.5016 0.01378 36.39 <.0001

Fit Statistics
-2 Log Likelihood 14656.6
AIC (smaller is better) 14684.6
AICC (smaller is better) 14684.7
BIC (smaller is better) 14656.6

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 1690.54 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14656.6 14 14684.6 14684.7 14656.6 14656.6 14670.6

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t|
Intercept 1.3038 0.04538 58 28.73 <.0001
c_mean -0.06402 0.02306 52 -2.78 0.0076
c_sal -0.1425 0.04092 52 -3.48 0.0010
oldage 0.6140 0.07017 61.9 8.75 <.0001
yrs65 0.02016 0.005756 57.3 3.50 0.0009
c_mean*c_sal -0.00270 0.01939 52 -0.14 0.8897
c_mean*oldage 0.03799 0.008612 4634 4.41 <.0001
c_sal*oldage 0.01265 0.01528 4631 0.83 0.4075
c_mean*c_sal*oldage -0.02489 0.007274 4612 -3.42 0.0006

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
c_mean 1 52 7.71 0.0076
c_sal 1 52 12.13 0.0010
oldage 1 61.9 76.56 <.0001
yrs65 1 57.3 12.27 0.0009
c_mean*c_sal 1 52 0.02 0.8897
c_mean*oldage 1 4634 19.45 <.0001
c_sal*oldage 1 4631 0.69 0.4075
c_mean*c_sal*oldage 1 4612 11.71 0.0006