SAS/STAT 9.2 User's Guide: The MIXED Procedure (Book Excerpt)

Output 56.4.9 Solutions of the Mixed Model Equations with Y Border
Mixed Model Equations Solution
Example 56.4: Known G and R ✦ 4039
Row Effect Trait Animal Col1 Col2 Col3 Col4
1 Trait 1 2.5508 1.5685 -1.3047 -1.1775
2 Trait 2 1.5685 4.5539 -1.4112 -1.3534
3 Trait*Animal 1 1 -1.3047 -1.4112 1.8282 1.0652
4 Trait*Animal 1 2 -1.1775 -1.3534 1.0652 1.7589
5 Trait*Animal 1 3 -1.1701 -0.9410 1.0206 0.7085
6 Trait*Animal 2 1 -1.3002 -2.1592 1.8010 1.0900
7 Trait*Animal 2 2 -1.1821 -2.1055 1.0925 1.7341
8 Trait*Animal 2 3 -1.1678 -1.3149 1.0070 0.7209
Mixed Model Equations Solution
Row Col5 Col6 Col7 Col8 Col9
1 -1.1701 -1.3002 -1.1821 -1.1678 6.9909
2 -0.9410 -2.1592 -2.1055 -1.3149 6.9959
3 1.0206 1.8010 1.0925 1.0070 0.05450
4 0.7085 1.0900 1.7341 0.7209 -0.04955
5 1.7812 1.0095 0.7197 1.7756 0.02230
6 1.0095 2.7518 1.6392 1.4849 0.2651
7 0.7197 1.6392 2.6874 0.9930 -0.2601
8 1.7756 1.4849 0.9930 2.7645 0.1276
The solutions for the fixed and random effects in Output 56.4.10 correspond to the last column in
Output 56.4.9. Note that the standard errors for the fixed effects and the prediction standard errors
for the random effects are the square root values of the diagonal entries in the solution of the mixed
model equations (Output 56.4.9).
Output 56.4.10 Solutions for Fixed and Random Effects
Solution for Fixed Effects
Standard
Effect Trait Estimate Error DF t Value Pr > |t|
Trait 1 6.9909 1.5971 3 4.38 0.0221
Trait 2 6.9959 2.1340 3 3.28 0.0465
Solution for Random Effects
Std Err
Effect Trait Animal Estimate Pred DF t Value Pr > |t|
Trait*Animal 1 1 0.05450 1.3521 0 0.04 .
Trait*Animal 1 2 -0.04955 1.3262 0 -0.04 .
Trait*Animal 1 3 0.02230 1.3346 0 0.02 .
Trait*Animal 2 1 0.2651 1.6589 0 0.16 .
Trait*Animal 2 2 -0.2601 1.6393 0 -0.16 .
Trait*Animal 2 3 0.1276 1.6627 0 0.08 .