
ADJDFE=SOURCE
ADJDFE=ROW

specifies how denominator degrees of freedom are determined when pvalues and confidence limits are adjusted for multiple comparisons with the ADJUST= option. When you do not specify the ADJDFE= option or when you specify ADJDFE=SOURCE, the denominator degrees of freedom
for multiplicityadjusted results are the denominator degrees of freedom for the LSmean effect in the “Type III Tests of Fixed Effects” table.
The ADJDFE=ROW setting is useful if you want multiplicity adjustments to take into account that denominator degrees of freedom
are not constant across estimates. For example, this can be the case when the denominator degrees of freedom are computed
by the Satterthwaite or KenwardRoger method (Kenward and Roger, 1997) in a mixed model.
The ADJDFE= option is not supported by the procedures that perform chisquarebased inference (GENMOD, LOGISTIC, PHREG and
SURVEYLOGISTIC).

ADJUST=BON
ADJUST=SCHEFFE
ADJUST=SIDAK
ADJUST=SIMULATE<(simoptions)>
ADJUST=T

requests a multiple comparison adjustment for the pvalues and confidence limits for the LSmean estimates. The adjusted quantities are produced in addition to the unadjusted pvalues and confidence limits. Adjusted confidence limits are produced if the CL or ALPHA= option is in effect. For a description of the adjustments, see Chapter 42: The GLM Procedure, and Chapter 61: The MULTTEST Procedure, in addition to the documentation for the ADJUST= option in the LSMEANS statement.
Not all adjustment methods of the LSMEANS statement are available for the LSMESTIMATE statement. Multiplicity adjustments in the LSMEANS statement are designed specifically for differences of least squares means.
If you specify the STEPDOWN option, the pvalues are further adjusted in a stepdown fashion.

ALPHA=number

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

AT variable=value
AT (variablelist)=(valuelist)
AT MEANS

modifies the values of the covariates used in computing LSmeans. See the AT option in the LSMEANS statement for details.

BYLEVEL

requests that the procedure compute separate margins for each level of the LSMEANS effect.
The standard LSmeans have equal coefficients across classification effects. The BYLEVEL option changes these coefficients
to be proportional to the observed margins. 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 the input data set. In this case, the resulting LSmeans
are actually equal to raw means for fixedeffects models and certain balanced randomeffects models, but their estimated standard
errors account for the covariance structure that you have specified. If a WEIGHT statement is specified, the procedure uses
weighted margins to construct the LSmeans coefficients.
If the AT option is specified, the BYLEVEL option disables it.

CATEGORY=categoryoptions

specifies how to construct estimates and multiplicity corrections for models with multinomial data (ordinal or nominal). This option is also important for constructing sets of estimable functions
for F tests with the JOINT option.
The categoryoptions indicate how response variable levels are treated in constructing the estimable functions. Possible value for the categoryoptions are the following:

JOINT

computes the estimable functions for every nonredundant category and treats them as a set. For example, a threerow LSMESTIMATE
statement in a model with three response categories leads to six estimable functions.

SEPARATE

computes the estimable functions for every nonredundant category in turn. For example, a threerow LSMESTIMATE statement in
a model with three response categories leads to two sets of three estimable functions.

quotedvaluelist

computes the estimable functions only for the list of values given. The list must consist of formatted values of the response
categories.
For further details about using the CATEGORY= option in models for multinomial data, see the documentation for the CATEGORY= option in the ESTIMATE statement.
The CATEGORY= option is supported only by the procedures that support generalized linear modeling (GENMOD, LOGISTIC, and SURVEYLOGISTIC)
and by PROC PLM when it is used to perform statistical analyses on item stores that were created by these procedures.

CHISQ

requests that chisquare tests be performed in addition to F tests, when you request an F test with the JOINT option. This option has no effect in procedures that produce chisquare statistics by default.

CL

requests that t type confidence limits be constructed for each of the LSmeans. 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. But if you also specify STEPDOWN, then only pvalues are stepdown adjusted, not the confidence limits.

CORR

displays the estimated correlation matrix of the linear combination of the least squares means.

COV

displays the estimated covariance matrix of the linear combination of the least squares means.

DF=number

specifies the degrees of freedom for the tests and confidence limits. The option is not supported by the procedures that perform chisquarebased inference (GENMOD, LOGISTIC,
PHREG, and SURVEYLOGISTIC).

DIVISOR=valuelist

specifies a list of values by which to divide the coefficients so that fractional coefficients can be entered as integer numerators. If you do not specify valuelist, a default value of 1.0 is assumed. Missing values in the valuelist are converted to 1.0.
If the number of elements in valuelist exceeds the number of rows of the estimate, the extra values are ignored. If the number of elements in valuelist is less than the number of rows of the estimate, the last value in valuelist is carried forward.
If you specify a rowspecific divisor as part of the specification of the estimate row, this value multiplies the corresponding
value in the valuelist. For example, the following statement divides the coefficients in the first row by 8, and the coefficients in the third and
fourth row by 3:
lsmestimate A 'One vs. two' 8 8 divisor=2,
'One vs. three' 1 0 1 ,
'One vs. four' 3 0 0 3 ,
'One vs. five' 3 0 0 0 3 / divisor=4,.,3;
Coefficients in the second row are not altered.

E

requests that the coefficients of the estimable function be displayed. These are the coefficients that apply to the fixedeffect parameter estimates. The E option displays the coefficients
that you would need to enter in an equivalent ESTIMATE statement.

ELSM

requests that the matrix coefficients be displayed. These are the coefficients that apply to the LSmeans. This option is useful to ensure that you assigned the coefficients
correctly to the LSmeans.

EXP

requests exponentiation of the least squares means estimate. When you model data with the logit link function and the estimate represents a log odds ratio, the EXP option produces an
odds ratio. If you specify the CL or ALPHA= option, the (adjusted) confidence limits for the estimate are also exponentiated.
The EXP option is supported only by PROC PHREG, PROC SURVEYPHREG, the procedures that support generalized linear modeling
(GENMOD, LOGISTIC, and SURVEYLOGISTIC), and by PROC PLM when it is used to perform statistical analyses on item stores that
were created by these procedures.

ILINK

requests that the estimate and its standard error also be reported on the scale of the mean (the inverse linked scale). The computation of the inverse linked estimate depends on the estimation
mode. For example, if the analysis is based on a posterior sample when a BAYES statement is present, the inversely linked
estimate is the average of the inversely linked values across the sample of posterior parameter estimates. If the analysis
is not based on a sample of parameter estimates, the procedure computes the value on the mean scale by applying the inverse
link to the estimate.
The interpretation of the inversely linked quantity depends on the coefficients that are specified in your LSMESTIMATE statement
and the link function. For example, in a model for binary data with logit link the following LSMESTIMATE statement computes
where and are the least squares means that are associated with the first two levels of the classification effect A
:
proc logistic;
class A / param=glm;
model y = A / dist=binary link=logit;
lsmestimate A 1 1 / ilink;
run;
The quantity q is not the difference of the probabilities associated with the two levels,
The standard error of the inversely linked estimate is based on the delta method. If you also specify the CL or ALPHA= option, the procedure computes confidence intervals for the inversely linked estimate. These intervals are obtained by applying
the inverse link to the confidence intervals on the linked scale.
The ILINK option is supported only by the procedures that support generalized linear modeling (GENMOD, LOGISTIC, and SURVEYLOGISTIC)
and by PROC PLM when it is used to perform statistical analyses on item stores that were created by these procedures.

JOINT<(jointtestoptions)>

requests that a joint F or chisquare test be produced for the rows of the estimate. For more information about the simulationbased pvalue calculation, see the section Joint Hypothesis Tests with Complex Alternatives, the ChiBarSquare Statistic. You can specify the following jointtestoptions in parentheses:

ACC=

specifies the accuracy radius for determining the necessary sample size in the simulationbased approach of Silvapulle and
Sen (2004) for tests with order restrictions. The value of must be strictly between 0 and 1; the default value is 0.005.

EPS=

specifies the accuracy confidence level for determining the necessary sample size in the simulationbased approach of Silvapulle
and Sen (2004) for F tests with order restrictions. The value of must be strictly between 0 and 1; the default value is 0.01.

LABEL='label'

assigns an identifying label to the joint test. If you do not specify a label, the first nondefault label for the ESTIMATE
rows is used to label the joint test.

NOEST
ONLY

performs only the joint test and suppresses other results from the ESTIMATE statement. This option is useful for emulating
the CONTRAST statement that is available in other procedures.

NSAMP=n

specifies the number of samples for the simulationbased method of Silvapulle and Sen (2004). If n is not specified, it is constructed from the values of the ALPHA=, the ACC=, and the EPS= options. With the default values for , , and (0.005, 0.01, and 0.05, respectively), NSAMP=12,604 by default.

CHISQ

adds a chisquare test if the procedure produces an F test by default.

BOUNDS=valuelist

specifies boundary values for the estimable linear function. The null value of the hypothesis is always zero. If you specify
a positive boundary value z, the hypotheses are , with the added constraint that . The same is true for negative boundary values. The alternative hypothesis is then subject to the constraint . If you specify a missing value, the hypothesis is assumed to be twosided. The BOUNDS option enables you to specify sets
of one and twosided joint hypotheses. If all values in valuelist are set to missing, the procedure performs a simulationbased pvalue calculation for a twosided test.

LOWER
LOWERTAILED

requests that the pvalue for the t test be based only on values that are less than the test statistic. A twotailed test is the default. A lowertailed confidence limit is
also produced if you specify the CL or ALPHA= option.
Note that for ADJUST=SCHEFFE the onesided adjusted confidence intervals and onesided adjusted pvalues are the same as the corresponding twosided statistics, because this adjustment is based on only the right tail of
the F distribution.
If you request an F test with the JOINT option, then a onesided lefttailed order restriction is applied to all estimable functions, and the corresponding chibarsquare
statistic of Silvapulle and Sen (2004) is computed in addition to the twosided, standard, F or chisquare statistic. See the JOINT option for how to control the computation of the simulationbased chibarsquare statistic.

OBSMARGINS<=OMdataset>
OM<=OMdataset>

specifies a potentially different weighting scheme for the computation of LSmeans coefficients. The standard LSmeans have equal coefficients across classification effects; however,
the OM option changes these coefficients to be proportional to those found in the OMdataset. 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 OMdataset. See the OBSMARGINS option in the LSMEANS statement for further details.

PLOTS=plotoptions

produces ODS statistical graphics of the distribution of estimable functions if the procedure performs the analysis in a samplingbased mode. For example, this is the case when procedures support
a BAYES statement and perform a Bayesian analysis. The estimable functions are then computed for each of the posterior parameter
estimates, and the “Least Squares Means Estimates” table reports simple descriptive statistics for the evaluated functions. In this situation, the PLOTS= option enables you
to visualize the distribution of the estimable function. The following plotoptions are available:

ALL

produces all possible plots with their default settings.

BOXPLOT<(boxplotoptions)>

produces box plots of the distribution of the estimable function across the posterior sample. A separate box plot is generated
for each estimable function and all box plots appear on a single graph by default. You can affect the appearance of the box
plot graph with the following options:

ORIENTATION=VERTICAL  HORIZONTAL
ORIENT=VERT  HORIZ

specifies the orientation of the boxes. The default is vertical orientation of the box plots.

NPANELPOS=number

specifies how to break the series of box plots across multiple panels. If the NPANELPOS option is not specified, or if number equals zero, then all box plots are displayed in a single graph; this is the default. If a negative number is specified,
then exactly up to of box plots are displayed per panel. If number is positive, then the number of boxes per panel is balanced to achieve small variation in the number of box plots per graph.

DISTPLOT<(distplotoptions)>
DIST<(distplotoptions)>

generates panels of histograms with a kernel density overlaid. A separate plot in each panel contains the results for each
estimable function. You can specify the following distplotoptions in parentheses:

BOX  NOBOX

controls the display of a horizontal box plot below the histogram. The BOX option is enabled by default.

HIST  NOHIST

controls the display of the histogram of the estimable function’s distribution across the posterior sample. The HIST option
is enabled by default.

NORMAL  NONORMAL

controls the display of a normal density estimate on the graph. The NONORMAL option is enabled by default.

KERNEL  NOKERNEL

controls the display of a kernel density estimate on the graph. The KERNEL option is enabled by default.

NROWS=number

specifies the highest number of rows in a panel. The default is 3.

NCOLS=number

specifies the highest number of columns in a panel. The default is 3.

UNPACK

unpacks the panel into separate graphics.

NONE

does not produce any plots.

SEED=number

specifies the seed for the samplingbased components of the computations for the LSMESTIMATE statement (for example, chibarsquare statistics and simulated pvalues). The value of number must be an integer. The seed is used to start the pseudorandomnumber generator for the simulation. If you do not specify
a seed, or if you specify a value less than or equal to zero, the seed is generated from reading the time of day from the
computer clock. Note that there could be multiple LSMESTIMATE statements with SEED= specifications and there could be other
statements that can supply a random number seed. Since the procedure has only one random number stream, the initial seed is
shown in the SAS log.

SINGULAR=number

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

STEPDOWN<(stepdownoptions)>

requests that multiplicity adjustments for the pvalues of estimable functions be further adjusted in a stepdown fashion. Stepdown methods increase the power of multiple
testing procedures by taking advantage of the fact that a pvalue is never declared significant unless all smaller pvalues are also declared significant. The STEPDOWN adjustment combined with ADJUST=BON corresponds to the methods of Holm (1979) and “Method 2” of Shaffer (1986); this is the default. Using stepdownadjusted pvalues combined with ADJUST=SIMULATE corresponds to the method of Westfall (1997).
If the ESTIMATE statement is applied with a STEPDOWN option in a mixed model where the degreesoffreedom method is that of
Kenward and Roger (1997) or of Satterthwaite, then stepdownadjusted pvalues are produced only if the ADJDFE=ROW option is in effect.
Also, the STEPDOWN option affects only pvalues, not confidence limits. For ADJUST=SIMULATE, the generalized least squares hybrid approach of Westfall (1997) is used to increase Monte Carlo accuracy.
You can specify the following stepdownoptions in parentheses:

MAXTIME=n

specifies the time (in seconds) to be spent computing the maximal logically consistent sequential subsets of equality hypotheses
for TYPE=LOGICAL. The default is MAXTIME=60. If the MAXTIME value is exceeded, the adjusted tests are not computed. When this
occurs, you can try increasing the MAXTIME value. However, note that there are common multiple comparisons problems for which
this computation requires a huge amount of time—for example, all pairwise comparisons between more than 10 groups. In such
cases, try to use TYPE=FREE (the default) or TYPE=LOGICAL(n) for small n.

ORDER=PVALUE
ORDER=ROWS

specifies the order in which the stepdown tests are performed. ORDER=PVALUE is the default, with LSmean estimates being
declared significant only if all LSmean estimates with smaller (unadjusted) pvalues are significant. If you specify ORDER=ROWS, then significances are evaluated in the order in which they are specified.

REPORT

specifies that a report on the stepdown adjustment be displayed, including a listing of the sequential subsets (Westfall,
1997) and, for ADJUST=SIMULATE, the stepdown simulation results.

TYPE=LOGICAL<(n)>
TYPE=FREE

specifies how stepdown adjustment are made. If you specify TYPE=LOGICAL, the stepdown adjustments are computed by using
maximal logically consistent sequential subsets of equality hypotheses (Shaffer, 1986; Westfall, 1997). Alternatively, for TYPE=FREE, sequential subsets are computed ignoring logical constraints. The TYPE=FREE results are more
conservative than those for TYPE=LOGICAL, but they can be much more efficient to produce for many estimates. For example,
it is not feasible to take logical constraints between all pairwise comparisons of more than about 10 groups. For this reason,
TYPE=FREE is the default.
However, you can reduce the computational complexity of taking logical constraints into account by limiting the depth of the
search tree used to compute them, specifying the optional depth parameter as a number n in parentheses after TYPE=LOGICAL. As with TYPE=FREE, results for TYPE=LOGICAL(n) are conservative relative to the true TYPE=LOGICAL results. But even for TYPE=LOGICAL(0), they can be appreciably less conservative
than TYPE=FREE, and they are computationally feasible for much larger numbers of estimates. If you do not specify n or if n = –1, the full search tree is used.

TESTVALUE=valuelist
TESTMEAN=valuelist

specifies the value under the null hypothesis for testing the estimable functions in the LSMESTIMATE statement. The rules for specifying the valuelist are very similar to those for specifying the divisor list in the DIVISOR= option. If no TESTVALUE= is specified, all tests are performed as . Missing values in the valuelist also are translated to zeros. If you specify fewer values than rows in the LSMESTIMATE statement, the last value in valuelist is carried forward.
The TESTVALUE= option affects only pvalues from individual, joint, and multiplicityadjusted tests. It does not affect confidence intervals.
The TESTVALUE option is not available for the multinomial distribution, and the values are ignored when you perform a samplingbased
(Bayesian) analysis.

UPPER
UPPERTAILED

requests that the pvalue for the t test be based only on values that are greater than the test statistic. A twotailed test is the default. An uppertailed confidence limit is also
produced if you specify the CL or ALPHA= option.
Note that for ADJUST=SCHEFFE the onesided adjusted confidence intervals and onesided adjusted pvalues are the same as the corresponding twosided statistics, because this adjustment is based on only the right tail of
the F distribution.
If you request a joint test with the JOINT option, then a onesided righttailed order restriction is applied to all estimable functions, and the corresponding chibarsquare
statistic of Silvapulle and Sen (2004) is computed in addition to the twosided, standard, F or chisquare statistic. See the JOINT option for how to control the computation of the simulationbased chibarsquare statistic.