LMIXED Procedure

ESTIMATE Statement

ESTIMATE 'label' contrast-specification <(divisor=n)><, 'label' contrast-specification <(divisor=n)>> <, …> </ options>;

The ESTIMATE statement provides a mechanism for obtaining custom linear estimate of the fixed and/or random effects. As in the CONTRAST statement, the basic element of the ESTIMATE statement is the contrast-specification, which consists of MODEL and RANDOM effects and their coefficients. Specifically, a contrast-specification takes the form

< fixed-effect values …> < | random-effect values …>

Based on the contrast-specifications in your ESTIMATE statement, PROC LMIXED constructs the matrix , as in the CONTRAST statement, where is associated with the fixed effects and is associated with the G-side random effects. Each contrast-specification is referred to as a row in the matrix.

PROC LMIXED then produces for each row of an approximate t test of the hypothesis , where .

Note that multiple-row estimates are permitted. Unlike the CONTRAST statement, you need to specify a 'label' for every row of the multiple-row estimate, because PROC LMIXED produces one test per row.

PROC LMIXED checks the estimability of the fixed-effects portion in each row of the multiple-row estimate.

If one row is found to be nonestimable (see the SINGULAR= option), then the procedure displays missing values for that row.

PROC LMIXED uses the residual degrees of freedom that you define by specifying the DDFM=RESIDUAL option. You can modify the degrees of freedom by using the DF= option. If you select DDFM=NONE and do not modify the degrees of freedom by using the DF= option, PROC LMIXED uses infinite degrees of freedom, essentially computing approximate z tests.

If PROC LMIXED finds the fixed-effects portion of the specified estimate to be nonestimable, then it displays "Non-est" for the estimate entry.

The construction of the matrix for an ESTIMATE statement follows the same rules that are listed for the CONTRAST statement.

Table 5 summarizes the options available in the ESTIMATE statement.

Table 5: ESTIMATE Statement Options

Option	Description
ADJUST=	Specifies the method to use for multiple comparison adjustment of estimates
ALPHA=	Specifies the confidence level
CL	Constructs t-type confidence limits
DF=	Specifies the degrees of freedom
DIVISOR=	Specifies values to divide the coefficients
E	Displays the matrix coefficients
GROUP	Sets up random-effect contrasts between groups
LOWER	Performs one-sided, lower-tailed inference
SINGULAR=	Tunes the estimability checking
SUBJECT	Sets up random-effect estimates between subjects
UPPER	Performs one-sided, upper-tailed inference

Results from all ESTIMATE statements are displayed together in the Estimates ODS table.

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

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

performs a multiple comparison adjustment of the p-values and confidence limits for the estimates. The adjusted quantities are produced in addition to the unadjusted quantities. Adjusted confidence limits are produced if you specify the CL or ALPHA= option. For a description of the adjustments, see the ADJUST= option in the LSMEANS statement.

ALPHA=number

constructs a t-type confidence interval with confidence level . The value of number must be between 0 and 1, exclusive; the default is 0.05. If DDFM=NONE and you do not specify degrees of freedom by using the DF= option, PROC LMIXED uses infinite degrees of freedom, essentially computing a z interval.

CL

constructs t-type confidence limits. If DDFM=NONE and you do not specify degrees of freedom by using the DF= option, PROC LMIXED uses infinite degrees of freedom, essentially computing a z interval. By default, the confidence level is 0.95.

DF=number

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

DIVISOR=value-list

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 a value-list, a default value of 1.0 is assumed. Missing values in the value-list are converted to 1.0.

If the number of elements in the value-list exceeds the number of rows of the estimate, the extra values are ignored. If the number of elements in the value-list is less than the number of rows of the estimate, the last value in the value-list is carried forward.

If you specify a row-specific divisor as part of the specification of the estimate row, this value multiplies the corresponding divisor implied by the value-list. For example, the following statement divides the coefficients in the first row by 8 and divides the coefficients in the third and fourth rows by 3:

estimate 'One vs. two'   A [2 1] [-2 2] (divisor=2),
         'One vs. three' A [1 1] [-1 3]            ,
         'One vs. four'  A [3 1] [-3 4]            ,
         'One vs. five'  A [1 1] [-1 5] / divisor=4,.,3;

E

displays the matrix coefficients. In the ODS output, the name of this "L Matrix Coefficients" table is Coef.

GROUP coeffs

sets up random-effect contrasts between different groups when a GROUP= variable appears in the RANDOM statement. By default, ESTIMATE statement coefficients about random effects are distributed equally across groups. You can enter a multiple-row estimate, but you can enter only one row for the GROUP coefficients. For example, the following ESTIMATE statement has a GROUP option with two sets of brackets; these two sets of brackets apply to each row of the estimate.

estimate 'Trt 1 vs 2 @ x=0.4' trt [1 1] [-1 2] | x [0.4 1],
         'Trt 1 vs 3 @ x=0.4' trt [1 1] [-1 3] | x [0.4 1],
         'Trt 1 vs 2 @ x=0.5' trt [1 1] [-1 2] | x [0.5 1],
         'Trt 1 vs 3 @ x=0.5' trt [1 1] [-1 3] | x [0.5 1] /
                              group [1 1] [-1 2];

If the GROUP effect has two levels and random effect 'x' has one level, then the specified coefficient 0.4 in the first contrast row is expanded across two levels of the GROUP effect weighted by the GROUP coefficients. The resulting coefficients are

0.4 -0.4

LOWER LOWERTAILED

bases the p-value for the t test only on values less than the test statistic. A two-tailed test is the default. A lower-tailed confidence limit is also produced if you specify the CL or ALPHA= option.

SINGULAR=number

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

SUBJECT coeffs

sets up random-effect estimates between different subjects when a SUBJECT= variable appears in the RANDOM statement. By default, ESTIMATE statement coefficients about random effects are distributed equally across subjects. The rules for listing subject coefficients for an ESTIMATE statement with multiple rows are the same as the rules for listing GROUP coefficients.

UPPER UPPERTAILED

bases the p-value for the t test only on values greater than the test statistic. A two-tailed test is the default. An upper-tailed confidence limit is also produced if you specify the CL or ALPHA= option.

Last updated: June 22, 2026