LMIXED Procedure
MODEL Statement
MODEL dependent = <fixed-effects></ options>;
The MODEL statement names a single dependent variable and the fixed effects, which determine the 
matrix of the mixed model. The MODEL statement is required.
An intercept is included in the fixed-effects model by default. If no fixed effects are specified, only this intercept term is fit. You can remove the intercept by using the NOINT option. You cannot explicitly specify an intercept by using the keyword INTERCEPT as an effect in MODEL statement.
Table 9 summarizes options in the MODEL statement. These are subsequently discussed in detail in alphabetical order.
Table 9: Summary of Important MODEL Statement Options
| Option | Description |
|---|---|
| Model Building | |
| NOINT | Excludes the fixed-effect intercept from the model |
| Statistical Computations | |
ALPHA= | Determines the confidence level ( ) for fixed effects |
| DDF= | Specifies the denominator degrees of freedom |
| DDFM= | Specifies the method for computing the denominator degrees of freedom |
| Statistical Output | |
| CL | Displays confidence limits for fixed-effects parameter estimates |
| DENSESOL | Displays dense-type fixed-effects parameter estimates |
| SOLUTION | Displays fixed-effects parameter estimates |
You can specify the following options in the MODEL statement after a slash (/):
-
ALPHA=
sets the confidence level to be
for each confidence interval of the fixed-effects parameters, where must be a number between 0 and 1. By default, ALPHA=0.05. - CL
constructs that t-type confidence limits for each of the fixed-effects parameter estimates. The confidence level is 0.95 by default; this can be changed by specifying the ALPHA= option.
- DDF=value-list
-
enables you to specify your own denominator degrees of freedom for the fixed effects. The value-list is a list of numbers or missing values (.) separated by commas. The degrees of freedom should be listed in the order in which the effects appear in the MODEL statement. If you want to retain the default degrees of freedom for a particular effect, use a missing value for its location in the list. For example, the following statement assigns 3 denominator degrees of freedom to
Aand 4.7 toA*B, while those forBremain the same:model Y = A B A*B / ddf=3,.,4.7; - DDFM=CONTAIN | NONE | RESIDUAL
-
specifies the method of computing the denominator degrees of freedom for the tests of fixed effects. You can specify the following methods:
- CONTAIN
-
invokes the containment method to compute denominator degrees of freedom (DDF). The containment method is carried out as follows: Denote the fixed effect in question
A, and search the effect list that you specify in the RANDOM statement for the effects that syntactically containA. For example, the random effectB(A) containsA, but the random effectCdoes not, even if it has the same levels asB(A).Among the random effects that contain
A, compute their rank contribution to the (
) matrix. The DDF that is assigned to Ais the smallest of these rank contributions. If no effects are found, the DDF forAis set equal to the residual degrees of freedom,
. This choice of DDF matches the tests that are performed for balanced split-plot designs and should be adequate for moderately unbalanced designs. The DDFM=CONTAIN option is supported only when DMMETHOD=DENSE.
Caution: If you have a
matrix that contains a large number of columns, the overall memory requirements and the computing time after convergence can be substantial for the containment method. If they are too great, you might want to use the DDFM=RESIDUAL option instead. - NONE
does not apply any denominator degrees of freedom. PROC LMIXED then essentially assumes that infinite degrees of freedom are available in the calculation of p-values. The p-values for t tests are then identical to p-values that are derived from the standard normal distribution.
- RESIDUAL
performs all tests by using the residual degrees of freedom,
, where n is the number of observations that are used.
By default, DDFM=RESIDUAL.
- DENSESOL
-
produces the solutions for the fixed-effects parameters that match the solutions when you specify DMMETHOD=DENSE in the PROC LMIXED statement. The DENSESOL option changes only the ODS table ParameterEstimates.
Note that this option consumes extra computer memory. The DENSESOL option is valid only when DMMETHOD=SPARSE. It is designed specifically for users who need a solution for the fixed-effects parameters to match the solutions when DMMETHOD=DENSE in the PROC LMIXED statement.
- NOINT
requests that no intercept be included in the model. (An intercept is included by default.)
-
SOLUTION
S -
produces a solution for the fixed-effects parameters. Using notation from the section Linear Mixed Models Theory, the fixed-effects parameter estimates are
and their approximate standard errors are the square roots of the diagonal elements of 
. Along with the estimates and their approximate standard errors, a t statistic is computed as the estimate divided by its standard error. The Pr
|t| column contains the two-tailed p-value that corresponds to the t statistic and associated degrees of freedom. You can use the CL option to request confidence intervals for all of the parameters; they are constructed around the estimate by using a radius that is the product of the standard error times a percentage point from the t distribution.