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 within-subject factors) as well as the interactions of within-subject factors with independent variables in the MODEL statement (often called between-subject factors). The REPEATED statement provides multivariate and univariate tests as well as hypothesis tests for a variety of single-degree-of-freedom contrasts. There is no limit to the number of within-subject 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 left-hand 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 left-hand side of the equal sign in the MODEL statement), with the associated within-subject 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 45.9 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 within-subject 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 factor-name. With two repeated factors, you must specify the factor-name and number of levels (levels) for each factor. Optionally, you can specify the actual values for the levels (level-values), a transformation that defines single-degree-of-freedom contrasts, and options for additional analyses and output. When you specify more than one within-subject factor, the factor-names (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 45.10 summarizes the options available in the REPEATED statement.
Table 45.10: 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 within-subject variables |
|
Specifies the method of evaluating the test statistics |
|
Displays only univariate analyses results |
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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 analysis-of-variance 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 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. 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 Y1-Y12=group / nouni; repeated trt 3, time 4; run;
implies the following structure:
Dependent Variables |
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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.