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

3916 ✦ Chapter 56: The MIXED Procedure
UPPER
UPPERTAILED
requests that the p-value for the t test be based only on values greater than the t statistic. A
two-tailed test is the default. An upper-tailed confidence limit is also produced if you specify
the CL option.
ID Statement
ID variables ;
The ID statement specifies which variables from the input data set are to be included in the OUTP=
and OUTPM= data sets from the MODEL statement. If you do not specify an ID statement, then
all variables are included in these data sets. Otherwise, only the variables you list in the ID statement
are included. Specifying an ID statement with no variables prevents any variables from being
included in these data sets.
LSMEANS Statement
LSMEANS fixed-effects < / options > ;
The LSMEANS statement computes least squares means (LS-means) of fixed effects. As in the
GLM procedure, LS-means are predicted population margins—that is, they estimate the marginal
means over a balanced population. In a sense, LS-means are to unbalanced designs as class and
subclass arithmetic means are to balanced designs. The L matrix constructed to compute them is
the same as the L matrix formed in PROC GLM; however, the standard errors are adjusted for the
covariance parameters in the model.
Each LS-mean is computed as Lbˇ, where L is the coefficient matrix associated with the least squares
mean and bˇ is the estimate of the fixed-effects parameter vector (see the section “Estimating Fixed
and Random Effects in the Mixed Model” on page 3970). The approximate standard errors for the
LS-mean is computed as the square root of L.X 0bV 1 X/ L 0 .
LS-means can be computed for any effect in the MODEL statement that involves CLASS variables.
You can specify multiple effects in one LSMEANS statement or in multiple LSMEANS statements,
and all LSMEANS statements must appear after the MODEL statement. As in the ESTIMATE
statement, the L matrix is tested for estimability, and if this test fails, PROC MIXED displays
“Non-est” for the LS-means entries.
Assuming the LS-mean is estimable, PROC MIXED constructs an approximate t test to test the null
hypothesis that the associated population quantity equals zero. By default, the denominator degrees
of freedom for this test are the same as those displayed for the effect in the “Tests of Fixed Effects”
table (see the section “Default Output” on page 3989).
Table 56.5 summarizes important options in the LSMEANS statement. All LSMEANS options are
subsequently discussed in alphabetical order.