Moser - Repeated Measures Examples - SUGI29
Visual Acuity and Lens Strength

Obs Subject Eye LensStrength ResponseTime
1 1 Left 6/06 116
2 1 Left 6/18 119
3 1 Left 6/36 116
4 1 Left 6/60 124
5 1 Right 6/06 120
6 1 Right 6/18 117
7 1 Right 6/36 114
8 1 Right 6/60 122
9 2 Left 6/06 110
10 2 Left 6/18 110
11 2 Left 6/36 114
12 2 Left 6/60 115
13 2 Right 6/06 106
14 2 Right 6/18 112
15 2 Right 6/36 110
16 2 Right 6/60 110
17 3 Left 6/06 117
18 3 Left 6/18 118
19 3 Left 6/36 120
20 3 Left 6/60 120
21 3 Right 6/06 120
22 3 Right 6/18 120
23 3 Right 6/36 120
24 3 Right 6/60 124
25 4 Left 6/06 112
26 4 Left 6/18 116
27 4 Left 6/36 115
28 4 Left 6/60 113
29 4 Right 6/06 115
30 4 Right 6/18 116
31 4 Right 6/36 116
32 4 Right 6/60 119
33 5 Left 6/06 113
34 5 Left 6/18 114
35 5 Left 6/36 114
36 5 Left 6/60 118
37 5 Right 6/06 114
38 5 Right 6/18 117
39 5 Right 6/36 116
40 5 Right 6/60 112
41 6 Left 6/06 119
42 6 Left 6/18 115
43 6 Left 6/36 94
44 6 Left 6/60 116
45 6 Right 6/06 100
46 6 Right 6/18 99
47 6 Right 6/36 94
48 6 Right 6/60 97
49 7 Left 6/06 110
50 7 Left 6/18 110
51 7 Left 6/36 105
52 7 Left 6/60 118
53 7 Right 6/06 105
54 7 Right 6/18 105
55 7 Right 6/36 115
56 7 Right 6/60 115

 

 

 

 

 

 

 

 

 

 
Moser - Repeated Measures Examples - SUGI29
Visual Acuity and Lens Strength
Paired Comparison of Eyes at 6/06 Lens Strength
Randomized Block Design (RBD) Model

The Mixed Procedure

Model Information
Data Set WORK.VISION
Dependent Variable ResponseTime
Covariance Structure Variance Components
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
 
Class Level Information
Class Levels Values
Subject 7 1 2 3 4 5 6 7
Eye 2 Left Right
 
Dimensions
Covariance Parameters 2
Columns in X 3
Columns in Z 7
Subjects 1
Max Obs Per Subject 14
Observations Used 14
Observations Not Used 0
Total Observations 14
 
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 81.23868776  
1 1 81.17105118 0.00000000
 
Convergence criteria met.
 
Estimated V Matrix for Subject 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8 Col9 Col10 Col11 Col12 Col13 Col14
1 36.8810 3.9048                        
2 3.9048 36.8810                        
3     36.8810 3.9048                    
4     3.9048 36.8810                    
5         36.8810 3.9048                
6         3.9048 36.8810                
7             36.8810 3.9048            
8             3.9048 36.8810            
9                 36.8810 3.9048        
10                 3.9048 36.8810        
11                     36.8810 3.9048    
12                     3.9048 36.8810    
13                         36.8810 3.9048
14                         3.9048 36.8810
 
Estimated V Correlation Matrix for Subject 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8 Col9 Col10 Col11 Col12 Col13 Col14
1 1.0000 0.1059                        
2 0.1059 1.0000                        
3     1.0000 0.1059                    
4     0.1059 1.0000                    
5         1.0000 0.1059                
6         0.1059 1.0000                
7             1.0000 0.1059            
8             0.1059 1.0000            
9                 1.0000 0.1059        
10                 0.1059 1.0000        
11                     1.0000 0.1059    
12                     0.1059 1.0000    
13                         1.0000 0.1059
14                         0.1059 1.0000
 
Covariance Parameter Estimates
Cov Parm Estimate
Subject 3.9048
Residual 32.9762
 
Fit Statistics
-2 Res Log Likelihood 81.2
AIC (smaller is better) 85.2
AICC (smaller is better) 86.5
BIC (smaller is better) 85.1
 
Solution for Fixed Effects
Effect Eye Estimate Standard Error DF t Value Pr > |t|
Intercept   111.43 2.2954 6 48.55 <.0001
Eye Left 2.4286 3.0695 6 0.79 0.4590
Eye Right 0 . . . .
 
Solution for Random Effects
Effect Subject Estimate Std Err Pred DF t Value Pr > |t|
Subject 1 1.0258 1.8066 6 0.57 0.5908
Subject 2 -0.8890 1.8066 6 -0.49 0.6401
Subject 3 1.1215 1.8066 6 0.62 0.5576
Subject 4 0.1641 1.8066 6 0.09 0.9306
Subject 5 0.1641 1.8066 6 0.09 0.9306
Subject 6 -0.6018 1.8066 6 -0.33 0.7504
Subject 7 -0.9847 1.8066 6 -0.55 0.6054
 
Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
Eye 1 6 0.63 0.4590
 
Estimates
Label Estimate Standard Error DF t Value Pr > |t|
Mean Difference 2.4286 3.0695 6 0.79 0.4590
 
Least Squares Means
Effect Eye Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Eye Left 113.86 2.2954 6 49.60 <.0001 0.05 108.24 119.47
Eye Right 111.43 2.2954 6 48.55 <.0001 0.05 105.81 117.05

 

 
Moser - Repeated Measures Examples - SUGI29
Visual Acuity and Lens Strength
Paired Comparison of Eyes at 6/06 Lens Strength
RBD Model But With Heterogeneous Error Variance

The Mixed Procedure

Model Information
Data Set WORK.VISION
Dependent Variable ResponseTime
Covariance Structure Variance Components
Group Effect Eye
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
 
Class Level Information
Class Levels Values
Subject 7 1 2 3 4 5 6 7
Eye 2 Left Right
 
Dimensions
Covariance Parameters 3
Columns in X 3
Columns in Z 7
Subjects 1
Max Obs Per Subject 14
Observations Used 14
Observations Not Used 0
Total Observations 14
 
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 81.23868776  
1 1 77.66170282 0.00000000
 
Convergence criteria met.
 
Estimated V Matrix for Subject 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8 Col9 Col10 Col11 Col12 Col13 Col14
1 12.4762 3.9048                        
2 3.9048 61.2857                        
3     12.4762 3.9048                    
4     3.9048 61.2857                    
5         12.4762 3.9048                
6         3.9048 61.2857                
7             12.4762 3.9048            
8             3.9048 61.2857            
9                 12.4762 3.9048        
10                 3.9048 61.2857        
11                     12.4762 3.9048    
12                     3.9048 61.2857    
13                         12.4762 3.9048
14                         3.9048 61.2857
 
Estimated V Correlation Matrix for Subject 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8 Col9 Col10 Col11 Col12 Col13 Col14
1 1.0000 0.1412                        
2 0.1412 1.0000                        
3     1.0000 0.1412                    
4     0.1412 1.0000                    
5         1.0000 0.1412                
6         0.1412 1.0000                
7             1.0000 0.1412            
8             0.1412 1.0000            
9                 1.0000 0.1412        
10                 0.1412 1.0000        
11                     1.0000 0.1412    
12                     0.1412 1.0000    
13                         1.0000 0.1412
14                         0.1412 1.0000
 
Covariance Parameter Estimates
Cov Parm Group Estimate
Subject   3.9048
Residual Eye Left 8.5714
Residual Eye Right 57.3810
 
Fit Statistics
-2 Res Log Likelihood 77.7
AIC (smaller is better) 83.7
AICC (smaller is better) 86.7
BIC (smaller is better) 83.5
 
Solution for Fixed Effects
Effect Eye Estimate Standard Error DF t Value Pr > |t|
Intercept   111.43 2.9589 6 37.66 <.0001
Eye Left 2.4286 3.0695 6 0.79 0.4590
Eye Right 0 . . . .
 
Solution for Random Effects
Effect Subject Estimate Std Err Pred DF t Value Pr > |t|
Subject 1 1.0235 1.6597 1 0.62 0.6482
Subject 2 -1.3957 1.6597 1 -0.84 0.5549
Subject 3 1.3225 1.6597 1 0.80 0.5717
Subject 4 -0.3958 1.6597 1 -0.24 0.8510
Subject 5 -0.1414 1.6597 1 -0.09 0.9459
Subject 6 1.0273 1.6597 1 0.62 0.6472
Subject 7 -1.4404 1.6597 1 -0.87 0.5450
 
Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
Eye 1 6 0.63 0.4590
 
Estimates
Label Estimate Standard Error DF t Value Pr > |t|
Mean Difference 2.4286 3.0695 6 0.79 0.4590
 
Least Squares Means
Effect Eye Estimate Standard Error DF t Value Pr > |t|
Eye Left 113.86 1.3350 6 85.28 <.0001
Eye Right 111.43 2.9589 6 37.66 <.0001

 

 
Moser - Repeated Measures Examples - SUGI29
Visual Acuity and Lens Strength
Paired Comparison of Eyes at 6/06 Lens Strength
Multivariate Response Model With Unstructured Error Covariance Matrix

The Mixed Procedure

Model Information
Data Set WORK.VISION
Dependent Variable ResponseTime
Covariance Structure Unstructured
Subject Effect Subject
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Between-Within
 
Class Level Information
Class Levels Values
Subject 7 1 2 3 4 5 6 7
Eye 2 Left Right
 
Dimensions
Covariance Parameters 3
Columns in X 3
Columns in Z 0
Subjects 7
Max Obs Per Subject 2
Observations Used 14
Observations Not Used 0
Total Observations 14
 
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 81.23868776  
1 1 77.66170282 0.00000000
 
Convergence criteria met.
 
Estimated R Matrix for Subject 1
Row Col1 Col2
1 12.4762 3.9048
2 3.9048 61.2857
 
Estimated R Correlation Matrix
for Subject 1
Row Col1 Col2
1 1.0000 0.1412
2 0.1412 1.0000
 
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) Subject 12.4762
UN(2,1) Subject 3.9048
UN(2,2) Subject 61.2857
 
Fit Statistics
-2 Res Log Likelihood 77.7
AIC (smaller is better) 83.7
AICC (smaller is better) 86.7
BIC (smaller is better) 83.5
 
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
2 3.58 0.1672
 
Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
Eye 1 6 0.63 0.4590
 
Least Squares Means
Effect Eye Estimate Standard Error DF t Value Pr > |t|
Eye Left 113.86 1.3350 6 85.28 <.0001
Eye Right 111.43 2.9589 6 37.66 <.0001
 
Differences of Least Squares Means
Effect Eye _Eye Estimate Standard Error DF t Value Pr > |t|
Eye Left Right 2.4286 3.0695 6 0.79 0.4590

 

 
Moser - Repeated Measures Examples - SUGI29
Visual Acuity and Lens Strength
Comparison of Lens Strengths For Left Eyes
Randomized Block Design (RBD) Model

The Mixed Procedure

Model Information
Data Set WORK.VISION
Dependent Variable ResponseTime
Covariance Structure Variance Components
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
 
Class Level Information
Class Levels Values
Subject 7 1 2 3 4 5 6 7
LensStrength 4 6/06 6/18 6/36 6/60
 
Dimensions
Covariance Parameters 2
Columns in X 5
Columns in Z 7
Subjects 1
Max Obs Per Subject 28
Observations Used 28
Observations Not Used 0
Total Observations 28
 
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 156.59917030  
1 1 155.54531479 0.00000000
 
Convergence criteria met.
 
Estimated V Matrix for Subject 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8 Col9 Col10 Col11 Col12 Col13 Col14 Col15 Col16 Col17 Col18 Col19 Col20 Col21 Col22 Col23 Col24 Col25 Col26 Col27 Col28
1 28.8690 5.3968 5.3968 5.3968                                                
2 5.3968 28.8690 5.3968 5.3968                                                
3 5.3968 5.3968 28.8690 5.3968                                                
4 5.3968 5.3968 5.3968 28.8690                                                
5         28.8690 5.3968 5.3968 5.3968                                        
6         5.3968 28.8690 5.3968 5.3968                                        
7         5.3968 5.3968 28.8690 5.3968                                        
8         5.3968 5.3968 5.3968 28.8690                                        
9                 28.8690 5.3968 5.3968 5.3968                                
10                 5.3968 28.8690 5.3968 5.3968                                
11                 5.3968 5.3968 28.8690 5.3968                                
12                 5.3968 5.3968 5.3968 28.8690                                
13                         28.8690 5.3968 5.3968 5.3968                        
14                         5.3968 28.8690 5.3968 5.3968                        
15                         5.3968 5.3968 28.8690 5.3968                        
16                         5.3968 5.3968 5.3968 28.8690                        
17                                 28.8690 5.3968 5.3968 5.3968                
18                                 5.3968 28.8690 5.3968 5.3968                
19                                 5.3968 5.3968 28.8690 5.3968                
20                                 5.3968 5.3968 5.3968 28.8690                
21                                         28.8690 5.3968 5.3968 5.3968        
22                                         5.3968 28.8690 5.3968 5.3968        
23                                         5.3968 5.3968 28.8690 5.3968        
24                                         5.3968 5.3968 5.3968 28.8690        
25                                                 28.8690 5.3968 5.3968 5.3968
26                                                 5.3968 28.8690 5.3968 5.3968
27                                                 5.3968 5.3968 28.8690 5.3968
28                                                 5.3968 5.3968 5.3968 28.8690
 
Estimated V Correlation Matrix for Subject 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8 Col9 Col10 Col11 Col12 Col13 Col14 Col15 Col16 Col17 Col18 Col19 Col20 Col21 Col22 Col23 Col24 Col25 Col26 Col27 Col28
1 1.0000 0.1869 0.1869 0.1869                                                
2 0.1869 1.0000 0.1869 0.1869                                                
3 0.1869 0.1869 1.0000 0.1869                                                
4 0.1869 0.1869 0.1869 1.0000                                                
5         1.0000 0.1869 0.1869 0.1869                                        
6         0.1869 1.0000 0.1869 0.1869                                        
7         0.1869 0.1869 1.0000 0.1869                                        
8         0.1869 0.1869 0.1869 1.0000                                        
9                 1.0000 0.1869 0.1869 0.1869                                
10                 0.1869 1.0000 0.1869 0.1869                                
11                 0.1869 0.1869 1.0000 0.1869                                
12                 0.1869 0.1869 0.1869 1.0000                                
13                         1.0000 0.1869 0.1869 0.1869                        
14                         0.1869 1.0000 0.1869 0.1869                        
15                         0.1869 0.1869 1.0000 0.1869                        
16                         0.1869 0.1869 0.1869 1.0000                        
17                                 1.0000 0.1869 0.1869 0.1869                
18                                 0.1869 1.0000 0.1869 0.1869                
19                                 0.1869 0.1869 1.0000 0.1869                
20                                 0.1869 0.1869 0.1869 1.0000                
21                                         1.0000 0.1869 0.1869 0.1869        
22                                         0.1869 1.0000 0.1869 0.1869        
23                                         0.1869 0.1869 1.0000 0.1869        
24                                         0.1869 0.1869 0.1869 1.0000        
25                                                 1.0000 0.1869 0.1869 0.1869
26                                                 0.1869 1.0000 0.1869 0.1869
27                                                 0.1869 0.1869 1.0000 0.1869
28                                                 0.1869 0.1869 0.1869 1.0000
 
Covariance Parameter Estimates
Cov Parm Estimate
Subject 5.3968
Residual 23.4722
 
Fit Statistics
-2 Res Log Likelihood 155.5
AIC (smaller is better) 159.5
AICC (smaller is better) 160.1
BIC (smaller is better) 159.4
 
Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
LensStrength 3 18 2.18 0.1262
 
Least Squares Means
Effect LensStrength Estimate Standard Error DF t Value Pr > |t|
LensStrength 6/06 113.86 2.0308 18 56.07 <.0001
LensStrength 6/18 114.57 2.0308 18 56.42 <.0001
LensStrength 6/36 111.14 2.0308 18 54.73 <.0001
LensStrength 6/60 117.71 2.0308 18 57.96 <.0001
 
Differences of Least Squares Means
Effect LensStrength _LensStrength Estimate Standard Error DF t Value Pr > |t|
LensStrength 6/06 6/18 -0.7143 2.5897 18 -0.28 0.7858
LensStrength 6/06 6/36 2.7143 2.5897 18 1.05 0.3085
LensStrength 6/06 6/60 -3.8571 2.5897 18 -1.49 0.1537
LensStrength 6/18 6/36 3.4286 2.5897 18 1.32 0.2021
LensStrength 6/18 6/60 -3.1429 2.5897 18 -1.21 0.2406
LensStrength 6/36 6/60 -6.5714 2.5897 18 -2.54 0.0206

 

 
Moser - Repeated Measures Examples - SUGI29
Visual Acuity and Lens Strength
Comparison of Lens Strengths For Left Eyes
Randomized Block Design (RBD) Model

The UNIVARIATE Procedure
Variable: Resid

Moments
N 28 Sum Weights 28
Mean 0 Sum Observations 0
Std Deviation 4.28547211 Variance 18.3652712
Skewness -1.6104926 Kurtosis 5.51350052
Uncorrected SS 495.862322 Corrected SS 495.862322
Coeff Variation . Std Error Mean 0.8098781
 
Basic Statistical Measures
Location Variability
Mean 0.000000 Std Deviation 4.28547
Median 0.122224 Variance 18.36527
Mode . Range 22.28710
    Interquartile Range 4.41338
 
Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 0 Pr > |t| 1.0000
Sign M 2 Pr >= |M| 0.5716
Signed Rank S 19 Pr >= |S| 0.6733
 
Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.877977 Pr < W 0.0036
Kolmogorov-Smirnov D 0.109056 Pr > D >0.1500
Cramer-von Mises W-Sq 0.082673 Pr > W-Sq 0.1903
Anderson-Darling A-Sq 0.686878 Pr > A-Sq 0.0685
 
Quantiles (Definition 5)
Quantile Estimate
100% Max 6.735485
99% 6.735485
95% 6.734101
90% 4.164056
75% Q3 2.479367
50% Median 0.122224
25% Q1 -1.934013
10% -4.431842
5% -4.560294
1% -15.551614
0% Min -15.551614
 
Extreme Observations
Lowest Highest
Value Obs Value Obs
-15.55161 23 3.84953 7
-4.56029 16 4.01113 15
-4.43184 27 4.16406 4
-3.57904 6 6.73410 21
-2.86475 5 6.73548 11

 

 

The UNIVARIATE Procedure
Variable: Resid

 

 

 

 
Moser - Repeated Measures Examples - SUGI29
Visual Acuity and Lens Strength
Comparison of Lens Strengths For Left Eyes
Randomized Block Design (RBD) Heterogeneous Errors Model

The Mixed Procedure

Model Information
Data Set WORK.VISION
Dependent Variable ResponseTime
Covariance Structure Variance Components
Group Effect LensStrength
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Prasad-Rao-Jeske-Kackar-Harville
Degrees of Freedom Method Kenward-Roger
 
Class Level Information
Class Levels Values
Subject 7 1 2 3 4 5 6 7
LensStrength 4 6/06 6/18 6/36 6/60
 
Dimensions
Covariance Parameters 5
Columns in X 5
Columns in Z 7
Subjects 1
Max Obs Per Subject 28
Observations Used 28
Observations Not Used 0
Total Observations 28
 
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 156.59917030  
1 2 142.05883181 0.00379524
2 1 141.90196732 0.00056138
3 1 141.87241324 0.00000976
4 1 141.87192911 0.00000001
 
Convergence criteria met.
 
Estimated V Matrix for Subject 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8 Col9 Col10 Col11 Col12 Col13 Col14 Col15 Col16 Col17 Col18 Col19 Col20 Col21 Col22 Col23 Col24 Col25 Col26 Col27 Col28
1 13.2476 8.1921 8.1921 8.1921                                                
2 8.1921 10.7999 8.1921 8.1921                                                
3 8.1921 8.1921 82.9017 8.1921                                                
4 8.1921 8.1921 8.1921 17.1109                                                
5         13.2476 8.1921 8.1921 8.1921