Here are the same data again, together with the SAS datastep to input the data into a SAS data set named factor01. We then have 4 SAS PROC MIXED analyses, fitting the same fixed effects components (a, b and a*b), but with different combinations of variance components.
Here is the output from the first PROC MIXED run, where we have fitted a model with the main effects factors a and b as well as the interaction a*b with one common residual error variance for all observations.
Factor A has 2 levels (with values 1 and 2). Factor B has 3 levels (with values 1, 2 and 3). The estimate of the (co)variance, the residual error variance is 7.889.
The SAS System
The MIXED Procedure
Class Level Information
Class Levels Values
A 2 1 2
B 3 1 2 3
Covariance Parameter Estimates (REML)
Cov Parm Estimate
Residual 7.88888889
Model Fitting Information for WT
Description Value
Observations 24.0000
Res Log Likelihood -48.2889
Akaike's Information Criterion -49.2889
Schwarz's Bayesian Criterion -49.7341
-2 Res Log Likelihood 96.5777
Tests of Fixed Effects
Source NDF DDF Type III F Pr > F
A 1 18 0.53 0.4767
B 2 18 46.18 0.0001
A*B 2 18 7.93 0.0034
The SAS System
The MIXED Procedure
Class Level Information
Class Levels Values
A 2 1 2
B 3 1 2 3
REML Estimation Iteration History
Iteration Evaluations Objective Criterion
0 1 63.49596156
1 1 60.19416416 0.00000000
Convergence criteria met.
Covariance Parameter Estimates (REML)
Cov Parm Group Estimate
DIAG A*B 1 1 2.25000000
DIAG A*B 1 2 13.33333333
DIAG A*B 1 3 12.91666667
DIAG A*B 2 1 3.58333333
DIAG A*B 2 2 8.25000000
DIAG A*B 2 3 7.00000000
Model Fitting Information for WT
Description Value
Observations 24.0000
Res Log Likelihood -46.6380
Akaike's Information Criterion -52.6380
Schwarz's Bayesian Criterion -55.3091
-2 Res Log Likelihood 93.2760
Null Model LRT Chi-Square 3.3018
Null Model LRT DF 5.0000
Null Model LRT P-Value 0.6536
Tests of Fixed Effects
Source NDF DDF Type III F Pr > F
A 1 18 0.53 0.4767
B 2 18 56.92 0.0001
The SAS System
Tests of Fixed Effects
Source NDF DDF Type III F Pr > F
A*B 2 18 7.73 0.0038
The SAS System
The MIXED Procedure
Class Level Information
Class Levels Values
A 2 1 2
B 3 1 2 3
REML Estimation Iteration History
Iteration Evaluations Objective Criterion
0 1 63.49596156
1 1 60.80351835 0.00000000
Convergence criteria met.
Covariance Parameter Estimates (REML)
Cov Parm Group Estimate
DIAG B 1 2.91666667
DIAG B 2 10.79166667
DIAG B 3 9.95833333
Model Fitting Information for WT
Description Value
Observations 24.0000
Res Log Likelihood -46.9427
Akaike's Information Criterion -49.9427
Schwarz's Bayesian Criterion -51.2782
-2 Res Log Likelihood 93.8853
Null Model LRT Chi-Square 2.6924
Null Model LRT DF 2.0000
Null Model LRT P-Value 0.2602
Tests of Fixed Effects
Source NDF DDF Type III F Pr > F
A 1 18 0.53 0.4767
B 2 18 56.92 0.0001
A*B 2 18 7.73 0.0038
The SAS System
The MIXED Procedure
Class Level Information
Class Levels Values
A 2 1 2
B 3 1 2 3
REML Estimation Iteration History
Iteration Evaluations Objective Criterion
0 1 63.49596156
1 1 63.11253690 0.00000000
Convergence criteria met.
Covariance Parameter Estimates (REML)
Cov Parm Group Estimate
DIAG A 1 9.50000000
DIAG A 2 6.27777778
Model Fitting Information for WT
Description Value
Observations 24.0000
Res Log Likelihood -48.0972
Akaike's Information Criterion -50.0972
Schwarz's Bayesian Criterion -50.9875
-2 Res Log Likelihood 96.1943
Null Model LRT Chi-Square 0.3834
Null Model LRT DF 1.0000
Null Model LRT P-Value 0.5358
Tests of Fixed Effects
Source NDF DDF Type III F Pr > F
A 1 18 0.53 0.4767
B 2 18 46.18 0.0001
A*B 2 18 7.93 0.0034