| Multimember Effects |
A multimember effect is formed from one or more classification variables in such a way that each observation can be associated with one or more levels of the union of the levels of the classification variables. In other words, a multimember effect is a classification-type effect with possibly more than one nonzero column entry for each observation. Multimember effects are useful, for example, in modeling the following:
nurses’ effects on patient recovery in hospitals
teachers’ effects on student scores
lineage effects in genetic studies. See Example 40.16 in Chapter 40, The GLIMMIX Procedure, for an application with random multimember effects in a genetic diallel experiment.
The levels of a multimember effect consist of the union of formatted values of the variables that define this effect. Each such level contributes one column to the design matrix. For each observation, the value that corresponds to each level of the multimember effect in the design matrix is the number of times that this level occurs for the observation.
For example, the following data provide teacher information and end-of-year test scores for students after two semesters:
Student Score Teacher1 Teacher2 Mary 87 Tobias Cohen Tom 89 Rodriguez Tobias Fred 82 Cohen Cohen Jane 88 Tobias . Jack 99 . .
For example, Mary had different teachers in the two semesters, Fred had the same teacher in both semesters, and Jane received instruction only in the first semester.
You can model the effect of the teachers on student performance by using a multimember effect specified as follows:
CLASS teacher1 teacher2; EFFECT teacher = MM(teacher1 teacher2);
The levels of the teacher effect are Cohen, Rodriguez, and Tobias, and the associated design matrix columns are as follows:
Student Cohen Rodriguez Tobias
Mary 1 0 1
Tom 0 1 1
Fred 2 0 0
Jane 0 0 1
Jack . . .
requests a table that shows the levels of the multimember effect.
specifies that, for observations with all missing levels of the multimember variables, the values in the corresponding design matrix columns be set to zero. If, in the preceding example, the teacher effect is defined by
EFFECT teacher = MM(teacher1 teacher2 / noeffect);
then the associated design matrix columns values for Jack are all zero. This enables you to include Jack in the analysis even though there is no effect of teachers on his performance.
A situation where it is important to designate observations as having no effect due to a classification variable is the analysis of crossover designs, where lagged treatment levels are used to model the carryover effects of treatments between periods. Since there is no carryover effect for the first period, the treatment lag effect in a crossover design can be modeled with a multimember effect that consists of a single classification variable and the NOEFFECT option, as in the following statements:
CLASS Treatment lagTreatment; EFFECT Carryover = MM(lagTreatment / noeffect);
The lagTreatment variable contains a missing value for the first period. Otherwise, it contains the value of the treatment variable for the preceding period.
specifies that for each observation, the entries in the design matrix that corresponds to the multimember effect be scaled to have a sum of one.
specifies numeric variables used to weigh the contributions of each of the classification effects that define the constructed multimember effect. The number of variables in wght-list must match the number of classification variables that define the effect.