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 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 LS-mean is computed as , where is the coefficient matrix associated with the least squares mean and is the estimate of the fixed-effects parameter vector. The approximate standard errors for the LS-mean is computed as the square root of .

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 matrix is tested for estimability, and if this test fails, PROC HPMIXED displays "Non-est" for the LS-means entries.

Assuming the LS-mean 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).

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