LMIXED Procedure

SLICE Statement

SLICE model-effect </ options>;

The SLICE statement is similar to the LSMEANS statement. It provides a general mechanism for performing a partitioned analysis of the LS-means for an interaction. This analysis is also known as an analysis of simple effects (Winer 1971). For the SLICE statement, these effects must be higher-order effects of at least two classification variables. Each effect is then sliced, or partitioned, into subsets that correspond to variables used in forming the effect.

By default, the interaction effect is partitioned by all main effects. For example, the following statements produce simple-effect differences among the A levels for each level of B and simple-effect differences among the B levels for each level of A:

class a b;
model y = a b a*b;
slice a*b / diff;

For example, if the model-effect is a three-way interaction effect, the default output includes comparisons of the two-way interaction means.

Suppose, for example, that the interaction effect A*B is significant in your analysis and that you want to test the effect of A for each level of B. The appropriate statement is

slice A*B / sliceBy = B;

This statement produces an F test for each level of B that compares the equality of the levels of A.

For example, assume that in a balanced design, factors A and B have a = 4 and b = 3 levels, respectively. Consider the following statements:

class a b;
model y = a b a*b;
slice a*b / sliceby=a diff;

The SLICE statement produces four F tests, one for each level of A. The first test is constructed by extracting the three rows that correspond to the first level of A from the coefficient matrix for the A*B interaction. Call this matrix and its rows , , and . The SLICE statement tests the two-degrees-of-freedom hypothesis:

In a balanced design, where denotes the mean response if A is at level i and B is at level j, this hypothesis is equivalent to . The DIFF option considers the three rows of in turn and performs tests of the difference between pairs of rows. By default, all pairwise differences within the subset of are considered; in the example, this corresponds to tests of the form

In the example, where a = 4 and b = 3, this produces four sets of least squares means differences. Within each set, factor A is held fixed at a particular level and each set consists of three comparisons.

Table 16 summarizes the options available in the SLICE statement.

Table 16: SLICE Statement Options

Option	Description
ADJUST=	Determines the method of multiple comparison adjustment of LS-means differences
ALPHA=	Specifies the confidence level
AT	Modifies covariate values in computing LS-means
CL	Constructs t-type confidence limits
CORR	Displays the estimated correlation matrix
COV	Displays the estimated covariance matrix
DF=	Specifies the degrees of freedom
DIFF	Displays the differences of the LS-means
E	Displays the matrix coefficients
MEANS	Displays the LS-means slice
NOF	Suppresses the F test
SINGULAR=	Tunes the estimability checking
SLICEBY	Partitions the interaction effects

You can specify the following options in the SLICE statement after a slash (/):

ADJUST=method

performs a multiple comparison adjustment of the p-values and confidence limits for the differences of LS-means. The adjusted quantities are produced along with the unadjusted quantities. This 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:

BON: performs Bonferroni t tests of differences between LS-means. This method involves correction factors described in Chapter 53, The GLM Procedure (SAS/STAT User's Guide), and Chapter 86, The MULTTEST Procedure (SAS/STAT User's Guide); also see Westfall and Young (1993) and Westfall et al. (1999).
DUNNETT: performs Dunnett’s t test, which determines whether any treatments are significantly different from a single control for the effects in the SLICES statement. If the LS-means are correlated, PROC LMIXED uses the factor-analytic covariance approximation described in Hsu (1992) and identifies the adjustment as "Dunnett-Hsu" in the results. The approximation derives approximate "effective sample sizes" for which exact critical values are computed.
NELSON: performs Nelson’s t test of each LS-mean against an average of the LS-means (Ott 1967; Nelson 1982, 1991, 1993). When the LS-means are correlated, PROC LMIXED uses the factor-analytic covariance approximation described in Hsu (1992) and identifies the adjustment as "Nelson-Hsu" in the results. The approximation derives approximate "effective sample sizes" for which exact critical values are computed.
SCHEFFE: performs Scheffé’s multiple comparison procedure.
SIDAK: performs pairwise t tests on differences between LS-means with levels adjusted according to Šidák’s inequality. This method involves correction factors described in Chapter 53, The GLM Procedure (SAS/STAT User's Guide), and Chapter 86, The MULTTEST Procedure (SAS/STAT User's Guide); also see Westfall and Young (1993) and Westfall et al. (1999).
SIMULATE <(simoptions)>: performs the simulation-based multiple comparison procedure. This method computes adjusted p-values and confidence limits from the simulated distribution of the maximum or maximum absolute value of a multivariate t random vector. All covariance parameters, except the residual scale parameter, are fixed at their estimated values throughout the simulation, potentially resulting in some underdispersion. The simulation estimates q, the true quantile, where is the confidence coefficient. For a description of the simoptions (except for the CVADJUST option, which you cannot use in the SLICE statement), see the ADJUST= option in the LSMEANS statement.
SMM | GT2: performs pairwise comparisons on the basis of the studentized maximum modulus and Šidák’s uncorrelated-t inequality, yielding Hochberg’s GT2 method when sample sizes are unequal.
T | NONE: performs no adjustment for multiple comparisons.
TUKEY: performs Tukey’s studentized range test on LS-means. When your data are unbalanced, PROC LMIXED uses the approximation described in Kramer (1956) and identifies the adjustment as "Tukey-Kramer" in the results.

By default, ADJUST=T.

If you specify ADJUST=DUNNETT, the procedure analyzes differences between each level and the first control level unless you specify a 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 when ADJUST=NELSON.

ALPHA=number

constructs a t-type confidence interval for each LS-means whose confidence level is . The value of number must be between 0 and 1, exclusive; by default, ALPHA=0.05.

AT at-specification

enables you to modify the values of the covariates that are used in computing LS-means. By default, all covariate effects are set equal to their mean values for computation of 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:

MEANS: sets covariates equal to their mean values (as with standard LS-means) and applies this adjustment to crossproducts of covariates.
variable=value: sets the covariate variable equal to value.
(variable-list)=(value-list): sets covariates in the variable-list equal to values in the value-list.

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

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

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

CL

constructs t-type confidence limits 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. By default, the confidence level is 0.95; you can change this by using the ALPHA= option.

CORR

displays the estimated correlation matrix of the LS-means as part of the "Least Squares Means" table.

COV

displays the estimated covariance matrix of the LS-means as part of the "Least Squares Means" table.

DF=number

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

DIFF<=difftype> PDIFF<=difftype>

displays differences of the LS-means. You can specify the following values for the optional difftype:

ALL

displays all pairwise differences; this is the default.

ANOM

displays differences between each LS-mean and the average LS-mean, as in the analysis of means (Ott 1967). The average is computed as a weighted mean of the LS-means, where the weights are inversely proportional to the diagonal entries of the matrix. When you specify a WEIGHT statement, this matrix is replaced by , where is the diagonal matrix that contains the weights. If the LS-means are nonestimable, this design-based weighted mean is replaced by an equally weighted mean. Note that the ANOM procedure in SAS/QC software implements both tables and graphics for the analysis of means with a variety of response types. For one-way designs and normally distributed data, the DIFF=ANOM computations are equivalent to the results of PROC ANOM.

CONTROL

displays differences with a control; by default, the control is the first level of each specified SLICE statement effect. To specify which levels of the effects are the controls, list the quoted formatted values in parentheses after the CONTROL keyword. For example, if the effects A, B, and C are classification variables, and each has two levels (1 and 2), then the following SLICE statement specifies the (1,2) level of A*B and the (2,1) level of B*C as controls:

lsmeans A*B B*C / diff=control('1' '2', '2' '1');

For multiple effects, the results depend on the order of the list, so you should check the output to make sure that the controls are correct.

The CONTROL keyword produces two-tailed tests and confidence limits.

CONTROLL

displays one-tailed test results and performs tests to determine whether the noncontrol levels are significantly smaller than the control. The upper confidence limits for the control minus the noncontrol levels are considered to be infinity and are displayed as missing.

CONTROLU

displays one-tailed test results and performs tests to determine whether the noncontrol levels are significantly larger than the control. The upper confidence limits for the noncontrol levels minus the control are considered to be infinity and are displayed as missing.

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

E

displays the matrix coefficients for all specified SLICE statement effects. The name of this table is "Matrix Coefficients." The ODS table name is Coef.

MEANS

displays the LS-means.

NOF

suppresses the F test for testing the mutual equality of the estimable functions in the partition.

SINGULAR=number

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

SLICEBY sliceby-spec-list SLICE sliceby-spec-list

determines how to construct the partition of the LS-means for the model-effect. The sliceby-spec-list is a list of sliceby-specifications. A sliceby-specification consists of an effect name followed by an optional list of formatted values. The sliceby-spec-list takes either of the following two forms:

<=> sliceby-specification

(sliceby-specification < sliceby-specification < …>>)

If you have only one sliceby-specification, use the first form. If you have one or more sliceby-specifications, you can use the second form.

The following SLICE statement contains one sliceby-specification. It creates partitions of the A*B interaction effect for all levels of variable A.

class a b;
model y = a b a*b;
slice a*b / sliceby=a;

The following SLICE statement contains one sliceby-specification. It creates one partition of the A*B interaction effect for one level, associated with the formatted value 'A1', of variable A.

class a b;
model y = a b a*b;
slice a*b / sliceby a='A1';

The following SLICE statement contains two sliceby-specifications. The first sliceby-specification creates two partitions of the A*B interaction effect for two levels, associated with the formatted values 'B2' and 'B3', of variable B. The second sliceby-specification creates one partition for the level, associated with the formatted values 'A1', of variable A.

class a b;
model y = a b a*b;
slice a*b / sliceby(b=('B2','B3') a='A1') diff;

The following SLICE statement contains one sliceby-specification. It creates two partitions of the A*B*C interaction effect for two levels of the B*C interaction effect. These two levels are associated with the two combinations of the formatted values: the combination of 'B1' and 'C1' and the combination of 'B1' and 'C2'.

class a b c;
model y = a b a*b*c;
slice a*b*c / sliceby b*c=('B1' 'C1', 'B1' 'C2');

The following SLICE statement contains two sliceby-specifications. The first sliceby-specification creates two partitions of the A*B*C interaction effect for two levels that are associated with the two combinations of the formatted values: the combination of 'B1' and 'C1' and the combination of 'B1' and 'C2'. The third sliceby-specification creates one partition for one level, associated with the formatted value 'A1', of variable A.

class a b c;
model y = a b a*b*c;
slice a*b*c / sliceby(b*c=('B1' 'C1', 'B1' 'C2') a='A1');

Notice that an interaction effect of B*C has the internal order of B and C or C and B. The order is determined by the order of these two variables in the CLASS statement. Thus, the order of formatted values in the sliceby-specification must follow the order of variables in the CLASS statement. For example, b*c=('B1' 'C1') is correct if B precedes C in the CLASS statement; otherwise, you have to use b*c=('C1' 'B1').

Last updated: May 14, 2026