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 44.16 in Chapter 44: 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 |
. |
. |
. |
You can specify the following mm-options after a slash (/):