Shared Concepts
Class Variable Parameterization with Unbalanced Designs
Procedures in this book initially parameterize the CLASS variables by looking at the levels of the variables across the complete data set. If you have an unbalanced replication of levels across variables or BY groups, then the design matrix and the parameter interpretation might be different from what you expect. For example, suppose you have a model that has one CLASS variable A with three levels (1, 2, and 3), and another CLASS variable B with two levels (1 and 2). If the third level of A occurs only with the first level of B, if you use the EFFECT parameterization, and if your model contains the effect A(B) and an intercept, then the design for A within the second level of B is not a differential effect. In particular, the design looks like the following:
| Design Matrix | |||||||
|---|---|---|---|---|---|---|---|
| A(B=1) | A(B=2) | ||||||
| B | A | A1 | A2 | A1 | A2 | ||
| 1 | 1 | 1 | 0 | 0 | 0 | ||
| 1 | 2 | 0 | 1 | 0 | 0 | ||
| 1 | 3 | –1 | –1 | 0 | 0 | ||
| 2 | 1 | 0 | 0 | 1 | 0 | ||
| 2 | 2 | 0 | 0 | 0 | 1 | ||
Procedures in this book detect linear dependency among the last two design variables and set the parameter for A2(B=2) to 0, resulting in an interpretation of these parameters as if they were reference- or dummy-coded. The REFERENCE or GLM parameterization might be more appropriate for such problems.