Results: classicalmixed.sas

Default proc glm: Both Fixed

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
A 3 1 2 3
B 4 1 2 3 4

Number of Observations

Number of Observations Read 36
Number of Observations Used 36

Default proc glm: Both Fixed

The GLM Procedure

Dependent Variable: Y

Analysis of Variance

Y

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 11 723.6220996 65.7838272 6.69 <.0001
Error 24 236.0284247 9.8345177    
Corrected Total 35 959.6505243      

Fit Statistics

R-Square Coeff Var Root MSE Y Mean
0.754048 29.78261 3.136003 10.52964

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B 3 146.2572697 48.7524232 4.96 0.0081
A*B 6 129.2085173 21.5347529 2.19 0.0796

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B 3 146.2572697 48.7524232 4.96 0.0081
A*B 6 129.2085173 21.5347529 2.19 0.0796

Default proc glm: Both Fixed

The GLM Procedure

Means

A*B

Means

Level of
A		 Level of
B		 N Y
Mean Std Dev
1 1 3 2.4164667 1.09897696
1 2 3 6.8333000 1.16655871
1 3 3 7.9240333 1.38364568
1 4 3 7.7945333 1.04795282
2 1 3 10.6492333 1.77785766
2 2 3 8.8264667 1.54613910
2 3 3 10.7444667 3.11568343
2 4 3 11.6320000 3.12081192
3 1 3 12.2519333 6.20695971
3 2 3 12.7310000 5.46750012
3 3 3 12.5628000 3.52730444
3 4 3 21.9895000 2.56375992

Both Random with proc glm

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
A 3 1 2 3
B 4 1 2 3 4

Number of Observations

Number of Observations Read 36
Number of Observations Used 36

Both Random with proc glm

The GLM Procedure

Dependent Variable: Y

Analysis of Variance

Y

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 11 723.6220996 65.7838272 6.69 <.0001
Error 24 236.0284247 9.8345177    
Corrected Total 35 959.6505243      

Fit Statistics

R-Square Coeff Var Root MSE Y Mean
0.754048 29.78261 3.136003 10.52964

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B 3 146.2572697 48.7524232 4.96 0.0081
A*B 6 129.2085173 21.5347529 2.19 0.0796

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B 3 146.2572697 48.7524232 4.96 0.0081
A*B 6 129.2085173 21.5347529 2.19 0.0796

Both Random with proc glm

The GLM Procedure

Random Effects Analysis

Model Expected Mean Squares

Source Type III Expected Mean Square
A Var(Error) + 3 Var(A*B) + 12 Var(A)
B Var(Error) + 3 Var(A*B) + 9 Var(B)
A*B Var(Error) + 3 Var(A*B)

Both Random with proc glm

The GLM Procedure

Tests of Hypotheses for Random Model Analysis of Variance

Dependent Variable: Y

Y

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 448.156313 224.078156 10.41 0.0112
B 3 146.257270 48.752423 2.26 0.1813
Error: MS(A*B) 6 129.208517 21.534753    

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A*B 6 129.208517 21.534753 2.19 0.0796
Error: MS(Error) 24 236.028425 9.834518    

A Fixed, B Random

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
A 3 1 2 3
B 4 1 2 3 4

Number of Observations

Number of Observations Read 36
Number of Observations Used 36

A Fixed, B Random

The GLM Procedure

Dependent Variable: Y

Analysis of Variance

Y

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 11 723.6220996 65.7838272 6.69 <.0001
Error 24 236.0284247 9.8345177    
Corrected Total 35 959.6505243      

Fit Statistics

R-Square Coeff Var Root MSE Y Mean
0.754048 29.78261 3.136003 10.52964

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B 3 146.2572697 48.7524232 4.96 0.0081
A*B 6 129.2085173 21.5347529 2.19 0.0796

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B 3 146.2572697 48.7524232 4.96 0.0081
A*B 6 129.2085173 21.5347529 2.19 0.0796

A Fixed, B Random

The GLM Procedure

Random Effects Analysis

Model Expected Mean Squares

Source Type III Expected Mean Square
A Var(Error) + 3 Var(A*B) + Q(A)
B Var(Error) + 3 Var(A*B) + 9 Var(B)
A*B Var(Error) + 3 Var(A*B)

A Fixed, B Random

The GLM Procedure

Tests of Hypotheses for Mixed Model Analysis of Variance

Dependent Variable: Y

Y

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 448.156313 224.078156 10.41 0.0112
B 3 146.257270 48.752423 2.26 0.1813
Error: MS(A*B) 6 129.208517 21.534753    

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A*B 6 129.208517 21.534753 2.19 0.0796
Error: MS(Error) 24 236.028425 9.834518    

A fixed, B random and nested within A

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
A 3 1 2 3
B 4 1 2 3 4

Number of Observations

Number of Observations Read 36
Number of Observations Used 36

A fixed, B random and nested within A

The GLM Procedure

Dependent Variable: Y

Analysis of Variance

Y

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 11 723.6220996 65.7838272 6.69 <.0001
Error 24 236.0284247 9.8345177    
Corrected Total 35 959.6505243      

Fit Statistics

R-Square Coeff Var Root MSE Y Mean
0.754048 29.78261 3.136003 10.52964

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B(A) 9 275.4657870 30.6073097 3.11 0.0126

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B(A) 9 275.4657870 30.6073097 3.11 0.0126

A fixed, B random and nested within A

The GLM Procedure

Random Effects Analysis

Model Expected Mean Squares

Source Type III Expected Mean Square
A Var(Error) + 3 Var(B(A)) + Q(A)
B(A) Var(Error) + 3 Var(B(A))

A fixed, B random and nested within A

The GLM Procedure

Tests of Hypotheses for Mixed Model Analysis of Variance

Dependent Variable: Y

Y

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 448.156313 224.078156 7.32 0.0130
Error: MS(B(A)) 9 275.465787 30.607310    

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
B(A) 9 275.465787 30.607310 3.11 0.0126
Error: MS(Error) 24 236.028425 9.834518    

A fixed, B random and nested within A

Using proc mixed

Compare F for A = 7.32, F for B(A) = 3.11, p = 0.0126

The Mixed Procedure

The MIXED Procedure

Model Information

Model Information
Data Set WORK.MIXEDUP
Dependent Variable Y
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 Level Information
Class Levels Values
A 3 1 2 3
B 4 1 2 3 4

Dimensions

Dimensions
Covariance Parameters 2
Columns in X 4
Columns in Z 12
Subjects 1
Max Obs per Subject 36

Number of Observations

Number of Observations
Number of Observations Read 36
Number of Observations Used 36
Number of Observations Not Used 0

Iteration History

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 191.55201049  
1 1 186.75737473 0.00000000

Convergence Status

Convergence criteria met.

Covariance Parameter Estimates

Covariance Parameter Estimates
Cov Parm Estimate Alpha Lower Upper
B(A) 6.9243 0.05 2.4834 57.3781
Residual 9.8345 0.05 5.9960 19.0328

Fit Statistics

Fit Statistics
-2 Res Log Likelihood 186.8
AIC (Smaller is Better) 190.8
AICC (Smaller is Better) 191.2
BIC (Smaller is Better) 191.7

Type 3 Tests of Fixed Effects

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
A 2 9 7.32 0.0130

Both random, B nested within A

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
A 3 1 2 3
B 4 1 2 3 4

Number of Observations

Number of Observations Read 36
Number of Observations Used 36

Both random, B nested within A

The GLM Procedure

Dependent Variable: Y

Analysis of Variance

Y

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 11 723.6220996 65.7838272 6.69 <.0001
Error 24 236.0284247 9.8345177    
Corrected Total 35 959.6505243      

Fit Statistics

R-Square Coeff Var Root MSE Y Mean
0.754048 29.78261 3.136003 10.52964

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B(A) 9 275.4657870 30.6073097 3.11 0.0126

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 448.1563126 224.0781563 22.78 <.0001
B(A) 9 275.4657870 30.6073097 3.11 0.0126

Both random, B nested within A

The GLM Procedure

Random Effects Analysis

Model Expected Mean Squares

Source Type III Expected Mean Square
A Var(Error) + 3 Var(B(A)) + 12 Var(A)
B(A) Var(Error) + 3 Var(B(A))

Both random, B nested within A

The GLM Procedure

Tests of Hypotheses for Random Model Analysis of Variance

Dependent Variable: Y

Y

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 448.156313 224.078156 7.32 0.0130
Error: MS(B(A)) 9 275.465787 30.607310    

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
B(A) 9 275.465787 30.607310 3.11 0.0126
Error: MS(Error) 24 236.028425 9.834518    

Nested random effects with proc nested

Compare F for A = 7.32, F for B(A) = 3.11

The NESTED Procedure

The NESTED Procedure

EMS Coefficients

Coefficients of Expected Mean Squares
Source A B Error
A 12 3 1
B 0 3 1
Error 0 0 1

Y

ANOVA

Nested Random Effects Analysis of Variance for Variable Y
Variance Source DF Sum of Squares F Value Pr > F Error Term Mean Square Variance Component Percent of Total
Total 35 959.650524       27.418586 32.881352 100.0000
A 2 448.156313 7.32 0.0130 B 224.078156 16.122571 49.0326
B 9 275.465787 3.11 0.0126 Error 30.607310 6.924264 21.0583
Error 24 236.028425       9.834518 9.834518 29.9091

Statistics

Y Mean 10.52964444
Standard Error of Y Mean 2.49487339

Pure nested with proc mixed

The Mixed Procedure

The MIXED Procedure

Model Information

Model Information
Data Set WORK.MIXEDUP
Dependent Variable Y
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 Level Information
Class Levels Values
A 3 1 2 3
B 4 1 2 3 4

Dimensions

Dimensions
Covariance Parameters 3
Columns in X 1
Columns in Z 15
Subjects 1
Max Obs per Subject 36

Number of Observations

Number of Observations
Number of Observations Read 36
Number of Observations Used 36
Number of Observations Not Used 0

Iteration History

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 218.80195545  
1 1 199.38591766 0.00000000

Convergence Status

Convergence criteria met.

Covariance Parameter Estimates

Covariance Parameter Estimates
Cov Parm Estimate Alpha Lower Upper
A 16.1226 0.05 3.8361 1927.28
B(A) 6.9243 0.05 2.4834 57.3781
Residual 9.8345 0.05 5.9960 19.0328

Fit Statistics

Fit Statistics
-2 Res Log Likelihood 199.4
AIC (Smaller is Better) 205.4
AICC (Smaller is Better) 206.2
BIC (Smaller is Better) 202.7

UNBALANCED: Both random, B nested within A

Using proc glm

Compare F for A = 7.32, F for B(A) = 3.11

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
A 3 1 2 3
B 4 1 2 3 4

Number of Observations

Number of Observations Read 35
Number of Observations Used 35

UNBALANCED: Both random, B nested within A

Using proc glm

Compare F for A = 7.32, F for B(A) = 3.11

The GLM Procedure

Dependent Variable: Y

Analysis of Variance

Y

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 11 648.4089667 58.9462697 5.75 0.0002
Error 23 235.7168398 10.2485583    
Corrected Total 34 884.1258066      

Fit Statistics

R-Square Coeff Var Root MSE Y Mean
0.733390 29.71224 3.201337 10.77447

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
A 2 392.6282239 196.3141119 19.16 <.0001
B(A) 9 255.7807429 28.4200825 2.77 0.0233

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
A 2 417.3152166 208.6576083 20.36 <.0001
B(A) 9 255.7807429 28.4200825 2.77 0.0233

UNBALANCED: Both random, B nested within A

Using proc glm

Compare F for A = 7.32, F for B(A) = 3.11

The GLM Procedure

Random Effects Analysis

Model Expected Mean Squares

Source Type III Expected Mean Square
A Var(Error) + 2.8846 Var(B(A)) + 11.538 Var(A)
B(A) Var(Error) + 2.9091 Var(B(A))

UNBALANCED: Both random, B nested within A

Using proc glm

Compare F for A = 7.32, F for B(A) = 3.11

The GLM Procedure

Tests of Hypotheses for Random Model Analysis of Variance

Dependent Variable: Y

Y

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
Error: 0.9916*MS(B(A)) + 0.0084*MS(Error)
A 2 417.315217 208.657608 7.38 0.0125
Error 9.0551 255.963032 28.267197    

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
B(A) 9 255.780743 28.420083 2.77 0.0233
Error: MS(Error) 23 235.716840 10.248558    

UNBALANCED: Nested random effects with proc nested

Proc glm gave F for A = 7.38, F for B(A) = 2.77

The NESTED Procedure

The NESTED Procedure

EMS Coefficients

Coefficients of Expected Mean Squares
Source A B Error
A 11.65714286 2.93766234 1.00000000
B 0.00000000 2.90909091 1.00000000
Error 0.00000000 0.00000000 1.00000000

Y

ANOVA

Nested Random Effects Analysis of Variance for Variable Y
Variance Source DF Sum of Squares F Value Pr > F Error Term Mean Square Variance Component Percent of Total
Total 34 884.125807       26.003700 30.882384 100.0000
A 2 392.628224       196.314112 14.387364 46.5876
B 9 255.780743       28.420083 6.246461 20.2266
Error 23 235.716840       10.248558 10.248558 33.1858

Statistics

Y Mean 10.77447143
Standard Error of Y Mean 2.37100117

UNBALANCED: Pure nested with proc mixed

Proc nested estimated Var[A]=14.39, Var[B(A)]=6.25

The Mixed Procedure

The MIXED Procedure

Model Information

Model Information
Data Set WORK.MIXEDUP
Dependent Variable Y
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 Level Information
Class Levels Values
A 3 1 2 3
B 4 1 2 3 4

Dimensions

Dimensions
Covariance Parameters 3
Columns in X 1
Columns in Z 15
Subjects 1
Max Obs per Subject 35

Number of Observations

Number of Observations
Number of Observations Read 35
Number of Observations Used 35
Number of Observations Not Used 0

Iteration History

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 210.82328898  
1 2 194.46763052 0.00015605
2 1 194.45677654 0.00000119
3 1 194.45669786 0.00000000

Convergence Status

Convergence criteria met.

Covariance Parameter Estimates

Covariance Parameter Estimates
Cov Parm Estimate Alpha Lower Upper
A 15.3570 0.05 3.6517 1846.90
B(A) 6.2004 0.05 2.0886 67.8487
Residual 10.3091 0.05 6.2133 20.3680

Fit Statistics

Fit Statistics
-2 Res Log Likelihood 194.5
AIC (Smaller is Better) 200.5
AICC (Smaller is Better) 201.3
BIC (Smaller is Better) 197.8