REPEATED
factorspecification </ options> ;
When values of the dependent variables in the MODEL statement represent repeated measurements on the same experimental unit, the REPEATED statement enables you to test hypotheses about the measurement factors (often called withinsubject factors) as well as the interactions of withinsubject factors with independent variables in the MODEL statement (often called betweensubject factors). The REPEATED statement provides multivariate and univariate tests as well as hypothesis tests for a variety of singledegreeoffreedom contrasts. There is no limit to the number of withinsubject factors that can be specified.
The REPEATED statement is typically used for handling repeated measures designs with one repeated response variable. Usually, the variables on the lefthand side of the equation in the MODEL statement represent one repeated response variable. This does not mean that only one factor can be listed in the REPEATED statement. For example, one repeated response variable (hemoglobin count) might be measured 12 times (implying variables Y1 to Y12 on the lefthand side of the equal sign in the MODEL statement), with the associated withinsubject factors treatment and time (implying two factors listed in the REPEATED statement). See the section Examples for an example of how PROC GLM handles this case.
Designs with two or more repeated response variables can, however, be handled with the IDENTITY transformation; see the description of this transformation in the following section, and see Example 42.9 for an example of analyzing a doubly multivariate repeated measures design.
When a REPEATED statement appears, the GLM procedure enters a multivariate mode of handling missing values. If any values for variables corresponding to each combination of the withinsubject factors are missing, the observation is excluded from the analysis.
If you use a CONTRAST or TEST statement with a REPEATED statement, you must enter the CONTRAST or TEST statement before the REPEATED statement.
The simplest form of the REPEATED statement requires only a factorname. With two repeated factors, you must specify the factorname and number of levels (levels) for each factor. Optionally, you can specify the actual values for the levels (levelvalues), a transformation that defines singledegreeoffreedom contrasts, and options for additional analyses and output. When you specify more than one withinsubject factor, the factornames (and associated level and transformation information) must be separated by a comma in the REPEATED statement.
These terms are described in the following section, “Syntax Details.”
Table 42.10 summarizes the options available in the REPEATED statement.
Table 42.10: REPEATED Statement Options
Option 
Description 

Performs a canonical analysis of the and matrices 

Specifies the type of the matrix used for analysis 

Generates the overall arithmetic means of the withinsubject variables 

Specifies the method of evaluating the test statistics 

Displays only univariate analyses results 

Displays only multivariate analyses results 

Displays and partial correlation matrices for multivariate tests, and prints sphericity tests 

Displays the matrices for multivariate tests 

Displays the transformation matrices that define tested contrasts 

Displays characteristic roots and vectors for multivariate tests 

Produces analysisofvariance tables for univariate tests 

Specifies the F test adjustment for univariate tests 
You can specify the following terms in the REPEATED statement.
When specifying more than one factor, list the dependent variables in the MODEL statement so that the withinsubject 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. For example, assume that three treatments
are administered at each of four times, for a total of twelve dependent variables on each experimental unit. If the variables
are listed in the MODEL statement as Y1
through Y12
, then the REPEATED statement in
proc glm; class group; model Y1Y12=group / nouni; repeated trt 3, time 4; run;
implies the following structure:
Dependent Variables 














Value of 
1 
1 
1 
1 
2 
2 
2 
2 
3 
3 
3 
3 
Value of 
1 
2 
3 
4 
1 
2 
3 
4 
1 
2 
3 
4 
The REPEATED statement always produces a table like the preceding one. For more information, see the section Repeated Measures Analysis of Variance.