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The MIXED Procedure |

**CONTRAST***'label' < fixed-effect values ...>*

< | random-effect values ...> , ...< / options >**;**

You can test the hypothesis , where

In the CONTRAST statement,

*label*- identifies the contrast in the table. A label is required for every contrast specified. Labels can be up to 20 characters and must be enclosed in single quotes.
*fixed-effect*- identifies an effect that appears in the MODEL statement. The keyword INTERCEPT can be used as an effect when an intercept is fitted in the model. You do not need to include all effects that are in the MODEL statement.
*random-effect*- identifies an effect that appears in the RANDOM statement. The first random effect must follow a vertical bar (|); however, random effects do not have to be specified.
*values*- are constants that are elements of the
**L**matrix associated with the fixed and random effects.

If PROC MIXED finds the fixed-effects portion of the specified contrast to be nonestimable (see the SINGULAR= option), then it displays "Non-est" for the contrast entries.

The following CONTRAST statement reproduces the

contrast 'A broad' A 1 -1 0 A*B .5 .5 -.5 -.5 0 0 , A 1 0 -1 A*B .5 .5 0 0 -.5 -.5 / df=6;

Note that no random effects are specified in the preceding contrast; thus, the inference space is broad. The resulting

contrast 'A narrow' A 1 -1 0 A*B .5 .5 -.5 -.5 0 0 | A*Block .25 .25 .25 .25 -.25 -.25 -.25 -.25 0 0 0 0 , A 1 0 -1 A*B .5 .5 0 0 -.5 -.5 | A*Block .25 .25 .25 .25 0 0 0 0 -.25 -.25 -.25 -.25 ;

The preceding contrast does not contain coefficients for B and Block because they cancel out in estimated differences between levels of A. Coefficients for B and Block are necessary when estimating the mean of one of the levels of A in the narrow inference space (see Example 41.1).

If the elements of

If too many values are specified for an effect, the extra ones are ignored; if too few are specified, the remaining ones are set to 0. If no random effects are specified, the vertical bar can be omitted; otherwise, it must be present. If a SUBJECT effect is used in the RANDOM statement, then the coefficients specified for the effects in the RANDOM statement are equitably distributed across the levels of the SUBJECT effect. You can use the E option to see exactly what

The SUBJECT and GROUP options in the CONTRAST statement are useful for the case when a SUBJECT= or GROUP= variable appears in the RANDOM statement, and you want to contrast different subjects or groups. By default, CONTRAST statement coefficients on random effects are distributed equally across subjects and groups.

PROC MIXED handles missing level combinations of classification variables similarly to the way PROC GLM does. Both procedures delete fixed-effects parameters corresponding to missing levels in order to preserve estimability. However, PROC MIXED does not delete missing level combinations for random-effects parameters because linear combinations of the random-effects parameters are always estimable. These conventions can affect the way you specify your CONTRAST coefficients.

The CONTRAST statement computes the statistic

The numerator degrees of freedom in the

You can specify the following options in the CONTRAST statement after a slash (/).

**CHISQ**-
requests that -tests be performed in addition to any
*F*-tests. A -statistic equals its corresponding*F*-statistic times the associate numerator degrees of freedom, and this same degrees of freedom is used to compute the*p*-value for the -test. This*p*-value will always be less than that for the*F*-test, as it effectively corresponds to an*F*-test with infinite denominator degrees of freedom. **DF=***number*-
specifies the denominator degrees of freedom for the
*F-*test. The default is the denominator degrees of freedom taken from the "Tests of Fixed Effects" table and corresponds to the final effect you list in the CONTRAST statement. **E**-
requests that the
**L**matrix coefficients for the contrast be displayed. For ODS purposes, the label of this "L Matrix Coefficients" table is "Coefficients". **GROUP***coeffs***GRP***coeffs*-
sets up random-effect contrasts between different groups
when a GROUP= variable appears in
the RANDOM statement. By default, CONTRAST statement
coefficients on random effects are distributed equally
across groups.
**SINGULAR=***number*-
tunes the estimability checking. If
**v**is a vector, define ABS(**v**) to be the absolute value of the element of**v**with the largest absolute value. If ABS(**K**'-**K**'**T**) is greater than C**number*for any row of**K**' in the contrast, then**K**is declared nonestimable. Here**T**is the Hermite form matrix (**X**'**X**)^{-}**X**'**X**, and C is ABS(**K**') except when it equals 0, and then C is 1. The value for*number*must be between 0 and 1; the default is 1E-4. **SUBJECT***coeffs***SUB***coeffs*-
sets up random-effect contrasts between different subjects
when a SUBJECT= variable appears
on the RANDOM statement. By default, CONTRAST statement
coefficients on random effects are distributed equally
across subjects.

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