The LSMEANS statement computes least squares means (LSmeans) of fixed effects. As in the GLM procedure, LSmeans are predicted population margins—that is, they estimate the marginal means over a balanced population. In a sense, LSmeans are to unbalanced designs as classification and subclassification arithmetic means are to balanced designs. The matrix constructed to compute them is the same as the matrix formed in PROC GLM; however, the standard errors are adjusted for the covariance parameters in the model.
Each LSmean is computed as , where is the coefficient matrix associated with the least squares mean and is the estimate of the fixedeffects parameter vector. The approximate standard errors for the LSmean is computed as the square root of .
LSmeans 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 matrix is tested for estimability, and if this test fails, PROC HPMIXED displays "Nonest" for the LSmeans entries.
Assuming the LSmean is estimable, PROC HPMIXED 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 "Type III Tests of Fixed Effects" table (see the section TEST Statement).
Table 49.6 summarizes the options available in the LSMEANS statement.
Table 49.6: LSMEANS Statement Options
Option 
Description 

Specifies the confidence level 

Constructs ttype confidence limits 

Displays the estimated correlation matrix 

Displays the estimated covariance matrix 

Specifies the degrees of freedom 

Displays the differences of the LSmeans 

Displays the matrix coefficients for LSMEANS effects 

Tunes the estimability checking 

Partitions interaction LSMEANS effects 
You can specify the following options in the LSMEANS statement after a slash (/).