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

3912 ✦ Chapter 56: The MIXED Procedure
If PROC MIXED finds the fixed-effects portion of the specified contrast to be nonestimable (see the
SINGULAR= option), then it displays a message in the log.
The following CONTRAST statement reproduces the F test for the effect A in the split-plot example
(see Example 56.1):
contrast ’A broad’
A 1 -1 0 A*B .5 .5 -.5 -.5 0 0 ,
A 1 0 -1 A*B .5 .5 0 0 -.5 -.5 / df=6;
Note that no random effects are specified in the preceding contrast; thus, the inference space is
broad. The resulting F test has two numerator degrees of freedom because L 0 has two rows. The
denominator degrees of freedom is, by default, the residual degrees of freedom (9), but the DF=
option changes the denominator degrees of freedom to 6.
The following CONTRAST statement reproduces the F test for A when Block and A*Block are considered
fixed effects (the narrow inference space):
contrast ’A narrow’
A 1 -1 0
A*B .5 .5 -.5 -.5 0 0 |
A*Block .25 .25 .25 .25
-.25 -.25 -.25 -.25
0 0 0 0 ,
A 1 0 -1
A*B .5 .5 0 0 -.5 -.5 |
A*Block .25 .25 .25 .25
0 0 0 0
-.25 -.25 -.25 -.25 ;
The preceding contrast does not contain coefficients for B and Block, because they cancel out in
estimated differences between levels of A. Coefficients for B and Block are necessary to estimate the
mean of one of the levels of A in the narrow inference space (see Example 56.1).
If the elements of L are not specified for an effect that contains a specified effect, then the elements
of the specified effect are automatically “filled in” over the levels of the higher-order effect. This
feature is designed to preserve estimability for cases where there are complex higher-order effects.
The coefficients for the higher-order effect are determined by equitably distributing the coefficients
of the lower-level effect, as in the construction of least squares means. In addition, if the intercept
is specified, it is distributed over all classification effects that are not contained by any other
specified effect. If an effect is not specified and does not contain any specified effects, then all of
its coefficients in L are set to 0. You can override this behavior by specifying coefficients for the
higher-order effect.
If too many values are specified for an effect, the extra ones are ignored; if too few are specified,
the remaining ones are set to 0. If no random effects are specified, the vertical bar can be omitted;
otherwise, it must be present. If a SUBJECT effect is used in the RANDOM statement, then the
coefficients specified for the effects in the RANDOM statement are equitably distributed across the
levels of the SUBJECT effect. You can use the E option to see exactly which L matrix is used.
The SUBJECT and GROUP options in the CONTRAST statement are useful for the case when a
SUBJECT= or GROUP= variable appears in the RANDOM statement, and you want to contrast