The factor-specification for the REPEATED statement can include any number of individual factor specifications, separated by commas, of the following form:

factor-name levels < (level-values) > < transformation >

where

factor-name

names a factor to be associated with the dependent variables. The name should not be the same as any variable name that already exists in the data set being analyzed and should conform to the usual conventions of SAS variable names.

When specifying more than one factor, list the dependent variables in the MODEL statement so that the within-subject factors defined in the REPEATED statement are nested; that is, the first factor defined in the REPEATED statement should be the one with values that change least frequently.

levels

specifies the number of levels associated with the factor being defined. When there is only one within-subject factor, the number of levels is equal to the number of dependent variables. In this case, levels is optional. When more than one within-subject factor is defined, however, levels is required, and the product of the number of levels of all the factors must equal the number of dependent variables in the MODEL statement.

(level-values)

specifies values that correspond to levels of a repeated-measures factor. These values are used to label output; they are also used as spacings for constructing orthogonal polynomial contrasts if you specify a POLYNOMIAL transformation. The number of level values specified must correspond to the number of levels for that factor in the REPEATED statement. Enclose the level-values in parentheses.

The following transformation keywords define single-degree-of-freedom contrasts for factors specified in the REPEATED statement. Since the number of contrasts generated is always one less than the number of levels of the factor, you have some control over which contrast is omitted from the analysis by which transformation you select. The only exception is the IDENTITY transformation; this transformation is not composed of contrasts, and it has the same degrees of freedom as the factor has levels. By default, the procedure uses the CONTRAST transformation.

CONTRAST<(ordinal-reference-level)>

 
generates contrasts between levels of the factor and a reference level. By default, the procedure uses the last level; you can optionally specify a reference level in parentheses after the keyword CONTRAST. The reference level corresponds to the ordinal value of the level rather than the level value specified. For example, to generate contrasts between the first level of a factor and the other levels, use

   contrast(1)

HELMERT

generates contrasts between each level of the factor and the mean of subsequent levels.

IDENTITY

generates an identity transformation corresponding to the associated factor. This transformation is not composed of contrasts; it has degrees of freedom for an -level factor, instead of . This can be used for doubly-multivariate repeated measures.

MEAN<(ordinal-reference-level)>

 
generates contrasts between levels of the factor and the mean of all other levels of the factor. Specifying a reference level eliminates the contrast between that level and the mean. Without a reference level, the contrast involving the last level is omitted. See the CONTRAST transformation for an example.

POLYNOMIAL

generates orthogonal polynomial contrasts. Level values, if provided, are used as spacings in the construction of the polynomials; otherwise, equal spacing is assumed.

PROFILE

generates contrasts between adjacent levels of the factor.

For examples of the transformation matrices generated by these contrast transformations, see the section Repeated Measures Analysis of Variance in Chapter 39, The GLM Procedure.

You can specify the following options in the REPEATED statement after a slash:

performs a canonical analysis of the and matrices corresponding to the transformed variables specified in the REPEATED statement.

specifies the method of evaluating the multivariate test statistics. The default is MSTAT=FAPPROX, which specifies that the multivariate tests are evaluated by using the usual approximations based on the distribution, as discussed in the "Multivariate Tests" section in Chapter 4, Introduction to Regression Procedures. Alternatively, you can specify MSTAT=EXACT to compute exact p-values for three of the four tests (Wilks’ lambda, the Hotelling-Lawley trace, and Roy’s greatest root) and an improved F-approximation for the fourth (Pillai’s trace). While MSTAT=EXACT provides better control of the significance probability for the tests, especially for Roy’s Greatest Root, computations for the exact p-values can be appreciably more demanding, and are in fact infeasible for large problems (many dependent variables). Thus, although MSTAT=EXACT is more accurate for most data, it is not the default method. For more information about the results of MSTAT=EXACT, see the section Multivariate Analysis of Variance in Chapter 39, The GLM Procedure.

displays only the results of the univariate analyses.

displays only the results of the multivariate analyses.

displays the matrix for each combination of within-subject factors, as well as partial correlation matrices for both the original dependent variables and the variables defined by the transformations specified in the REPEATED statement. In addition, the PRINTE option provides sphericity tests for each set of transformed variables. If the requested transformations are not orthogonal, the PRINTE option also provides a sphericity test for a set of orthogonal contrasts.

displays the (SSCP) matrix associated with each multivariate test.

displays the transformation matrices that define the contrasts in the analysis. PROC ANOVA always displays the matrix so that the transformed variables are defined by the rows, not the columns, of the displayed matrix. In other words, PROC ANOVA actually displays .

produces the characteristic roots and vectors for each multivariate test.

produces analysis-of-variance tables for each contrast defined by the within-subjects factors. Along with tests for the effects of the independent variables specified in the MODEL statement, a term labeled MEAN tests the hypothesis that the overall mean of the contrast is zero.