- 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
Each LS-mean is computed as where L is
the coefficient matrix associated with the least-squares mean and
is the estimate of the fixed-effects parameter
vector (see the "Estimating and in the Mixed Model" section). 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 L matrix is tested for estimability, and
if this test fails, PROC MIXED displays "Non-est" for the LS-means
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 "Default Output" section).
You can specify the following options in the LSMEANS statement after a
- ADJUST=SMM | GT2
requests a multiple comparison adjustment for the p-values and
confidence limits for the differences of LS-means. By
default, PROC MIXED adjusts all pairwise differences unless you
specify ADJUST=DUNNETT, in which case PROC MIXED analyzes
all differences with a control level. The ADJUST= option implies
the DIFF option.
The BON (Bonferroni) and SIDAK adjustments involve correction
factors described in Chapter 30, "The GLM Procedure," and
Chapter 43, "The MULTTEST Procedure"; also refer to
Westfall and Young (1993).
When you specify ADJUST=TUKEY and your
data are unbalanced, PROC MIXED uses the approximation described in
Kramer (1956). Similarly, when you specify ADJUST=DUNNETT and the
LS-means are correlated, PROC MIXED uses the factor-analytic
covariance approximation described in Hsu (1992). The preceding
references also describe the SCHEFFE and SMM adjustments.
The SIMULATE adjustment 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 variance are fixed at
their estimated values throughout the simulation, potentially
resulting in some underdispersion. The simulation estimates q,
the true th quantile, where is the
confidence coefficient. The default is 0.05, and you can
change this value with the ALPHA= option in the LSMEANS statement.
The number of samples is set so that the tail area
for the simulated q is within of with
% confidence. In equation form,
where is the simulated q and F is the true
distribution function of the maximum; refer to Edwards and Berry
(1987) for details. By default, = 0.005 and =
0.01, placing the tail area of within 0.005 of 0.95
with 99% confidence. The ACC= and EPS= simoptions reset
and , respectively; the NSAMP= simoption
sets the sample size directly; and the SEED= simoption enables
you to control the beginning of the random number sequence (the
clock time is used by default). For additional description of
these and other simulation options, see
the "LSMEANS Statement" section in Chapter 30, "The GLM Procedure."
requests that a t-type confidence interval be constructed for
each of the LS-means with confidence level 1-number.
The value of number must be between 0 and 1; the default is 0.05.
- AT variable = value
- AT (variable-list) = (value-list)
- AT MEANS
enables you to modify the values of the covariates 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.
If there is an effect containing two or more covariates, the AT
option sets the effect equal to the product of the individual means
rather than the mean of the product (as with standard LS-means
calculations). The AT MEANS option sets covariates equal to their
mean values (as with standard LS-means) and incorporates this
adjustment to cross products of covariates.
As an example, consider the following invocation of PROC MIXED:
model Y = A X1 X2 X1*X2;
lsmeans A / at means;
lsmeans A / at X1=1.2;
lsmeans A / at (X1 X2)=(1.2 0.3);
For the first two LSMEANS statements, the LS-means coefficient for
X1 is (the mean of X1) and for
(the mean of X2). However, for the first LSMEANS
statement, the coefficient for X1*X2 is , but for
the second LSMEANS statement, the coefficient is
. The third LSMEANS statement
sets the coefficient for 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.
If a WEIGHT variable is present, it is used in processing AT
variables. Also, observations with missing dependent
variables are included in computing the covariate means,
unless these observations form a missing cell and the
FULLX option in the MODEL statement is
not in effect. You can use the E
option in conjunction with the AT option to
check that the modified LS-means coefficients are the ones
The AT option is disabled if you specify the
requests PROC MIXED to process the OM data set
by each level of the LS-mean effect (LSMEANS effect)
in question. For more details, see the OM
option later in this section.
requests that t-type confidence limits be constructed for each
of the LS-means. The confidence level is 0.95 by default; this can
be changed with the ALPHA= option.
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 denominator degrees of
freedom taken from the "Tests of Fixed Effects" table
corresponding to the LS-means effect.
requests that differences of the LS-means be displayed. The optional
difftype specifies which differences to produce, with possible
values being ALL, CONTROL, CONTROLL, and CONTROLU. The
difftype ALL requests all pairwise differences, and it is the
default. The difftype CONTROL requests the differences with a
control, which, by default, is the first level of each of the
specified LSMEANS effects.
To specify which levels of the effects are the controls, list the
quoted formatted values in parentheses after the keyword CONTROL.
For example, if the effects A, B, and C are class
variables, each having two levels, 1 and 2, the following LSMEANS
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 ordering of the list is significant, and
you should check the output to make sure that the controls
Two-tailed tests and confidence limits are associated with the
CONTROL difftype. For one-tailed results, use either the
CONTROLL or CONTROLU difftype. The CONTROLL difftype
tests 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. Conversely, the CONTROLU difftype tests 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.
If you want to perform multiple comparison adjustments on the
differences of LS-Means, use the ADJUST= option. For DIFF=ALL (the
default), ADJUST=TUKEY is the default method, and in all other
instances, the default ADJUST= option is DUNNETT. If there is a
conflict between the DIFF= and ADJUST= options, the ADJUST= option
The differences of the LS-means are displayed in a table titled
"Differences of Least Squares Means." For ODS purposes, the
table name is "Diffs."
requests that the L matrix coefficients for all LSMEANS effects
be displayed. For ODS purposes, the label of this
"L Matrix Coefficients" table is "Coefficients".
specifies a potentially different weighting scheme for the
computation of LS-means coefficients. The standard LS-means have
equal coefficients across classification effects; however, the OM
option changes these coefficients to be proportional to those found
in OM-data-set. This adjustment is reasonable when you want
your inferences to apply to a population that is not necessarily
balanced but has the margins observed in OM-data-set.
By default, OM-data-set is the same as the analysis data set.
You can optionally specify another data set that describes the
population for which you want to make inferences. This data set must
contain all model variables except for the dependent variable (which
is ignored if it is present). In addition, the levels of all CLASS
variables must be the same as those occurring in the analysis data
set. Specifying an OM-data-set enables you to construct
arbitrarily weighted LS-means.
In computing the observed margins, PROC MIXED uses all observations
for which there are no missing or invalid independent variables,
including those for which there are missing dependent variables.
Also, if OM-data-set has a WEIGHT variable, PROC MIXED uses
weighted margins to construct the LS-means coefficients. If
OM-data-set is balanced, the LS-means are unchanged by the OM option.
The BYLEVEL option modifies the observed-margins LS-means.
Instead of computing the margins across all of OM-data-set,
PROC MIXED computes separate margins for each level of the LSMEANS
effect in question. The resulting LS-means are actually
equal to raw means in this case, but their estimated standard errors
account for the covariance structure that you have specified.
If the AT option is specified, the BYLEVEL option disables it.
You can use the E option in conjunction with either the OM or
BYLEVEL option to check that the modified LS-means
coefficients are the ones you desire. It is possible that the
modified LS-means are not estimable when the standard
ones are, or vice versa. Nonestimable LS-means are
noted as "Non-est" in the output.
is the same as the DIFF option.
tunes the estimability
checking as documented on the "CONTRAST Statement" section.
- SLICE= fixed-effect
- SLICE= (fixed-effects)
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 code 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
using them to form an F-test. See the "Inference and Test Statistics" section
for more information on this F-test.
The SLICE option produces a table titled "Tests of Effect Slices."
For ODS purposes, the table name is "Slices."
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.