LMIXED Procedure

requests a multiple comparison adjustment for the p-values and confidence limits for the differences of LS-means. The adjusted quantities are produced along with the unadjusted quantities. The ADJUST= option works together with the DIFF option. If you omit the DIFF option, then the ADJUST= option implies the DIFF option except for ADJUST=T.

You can specify the following methods for the ADJUST= option:

By default, ADJUST=T | NONE.

If you specify ADJUST=DUNNETT, the procedure analyzes all differences with the first control level unless you have specified different control level. If you specify ADJUST=NELSON, then DIFF=ANOM is assumed.

If you specify ADJUST=TUKEY, then DIFF=ALL is assumed. If you specify other methods, then the procedure performs all pairwise differences unless you specify the DIFF option.

Note that computing the exact adjusted p-values and critical values for unbalanced designs can be computationally intensive, especially for ADJUST=NELSON.

requests that a t-type confidence interval be constructed for each of the LS-means with confidence level . The value of number must be between 0 and 1; the default is 0.05.

enables you to modify the values of the covariates that are used in computing LS-means. By default, all covariates are set equal to their mean values for computing standard LS-means. The AT option enables you to assign arbitrary values to the covariates. Additional columns in the output table indicate the values of the covariates.

You can specify the following at-specifications:

As an example, consider the following invocation of PROC LMIXED:

proc lmixed;
   class A B;
   model Y = A*B x1 x2 x1*x2;
   LSMEANS A*B;
   LSMEANS A*B / at means;
   LSMEANS A*B / at x1=1.2;
   LSMEANS A*B / at (x1 x2)=(1.2 0.3);
run;

For the first two LSMEANS statements, the LS-means coefficient of x1 is (the mean of x1) and of x2 is (the mean of x2). For the first LSMEANS statement, the coefficient of x1*x2 is . However, for the second LSMEANS statement, the coefficient is . The third LSMEANS statement sets the coefficient of x1 equal to 1.2 and leaves it at for x2, and the final LSMEANS statement sets these values to 1.2 and 0.3, respectively.

Even if you specify a WEIGHT variable, the unweighted covariate means are used for the covariate coefficients if you omit the AT option. If you specify the AT option, then WEIGHT or FREQ variables are taken into account as follows. The weighted covariate means are used for the covariate coefficients for which no explicit AT option values are given, or if you specify the AT MEANS option. Observations that do not contribute to the analysis because of a missing dependent variable are used in computing the covariate means. You should use the E option in conjunction with the AT option to verify that the modified LS-means coefficients are the ones that you want.

requests that t-type confidence limits be constructed for each of the LS-means. If DDFM=NONE, then PROC LMIXED uses infinite degrees of freedom for this test, essentially computing a z interval. The confidence level is 0.95 by default; this can be changed with the ALPHA= option. If you specify an ADJUST= option, then the confidence limits are adjusted for multiplicity. If you also specify the STEPDOWN option, then only p-values, not the confidence limits, are step-down-adjusted.

displays the estimated correlation matrix of the least squares means as part of the "Least Squares Means" table.

displays the estimated covariance matrix of the least squares means as part of the "Least Squares Means" table.

specifies the degrees of freedom for the t test and confidence limits. The default is the residual degrees of freedom that you define by specifying the DDFM=RESIDUAL option.

requests that differences of the LS-means be displayed. You can specify the following values for the optional difftype.

The differences of the LS-means are displayed in a table titled "Differences of Least Squares Means." The table name is "Diffs."

requests that the matrix coefficients for all LSMEANS effects be displayed. The name of this "Matrix Coefficients" table is "Coef."

is the same as the DIFF option.

tunes the estimability checking as documented for the SINGULAR= in the CONTRAST statement.

specifies effects by which to partition interaction LSMEANS effects. This can produce what are known as tests of simple effects (Winer 1971). For example, suppose that A*B is significant, and you want to test the effect of A for each level of B. The appropriate LSMEANS statement is

lsmeans A*B / slice=B;

This statement tests for the simple main effects of A for B, which are calculated by extracting the appropriate rows from the coefficient matrix for the A*B LS-means and by using them to form an F test.

The SLICE= option produces F tests that test the simultaneous equality of cell means at a fixed level of the slice effect (Schabenberger, Gregoire, and Kong 2000).

The SLICE= option produces a table titled "Tests of Effect Slices." The table name is "Slices."

performs a further step-down adjustment to the multiple-comparison-adjusted p-values for differences of LS-means. Specifically, the ADJUST= option in the LSMEANS statement performs a multiple comparison adjustment for the p-values and confidence limits that are associated with differences of LS-means. When you specify the STEPDOWN option, PROC LMIXED applies an additional adjustment to these multiple-comparison-adjusted p-values. Step-down methods increase the power of multiple comparisons by taking advantage of the fact that a p-value will never be declared significant unless all smaller p-values are also declared significant.

You must specify the ADJUST= option when you specify the STEPDOWN option in the LSMEANS statement.

The STEPDOWN option affects only p-values, not confidence limits.

You can specify the following step-down-options in parentheses: