Main Effects
If a classification variable has m levels, the GLM parameterization generates m columns for its main effect in the model matrix. Each column is an indicator variable for a given level. The order of the columns is the sort order of the values of their levels and frequently can be controlled with the ORDER= option in the procedure or CLASS statement.
Table 19.4 is an example where 
denotes the intercept and A and B are classification variables with two and three levels, respectively.
Table 19.4: Example of Main Effects
|
Data |
I |
|
|
|||||||
|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
|
A1 |
A2 |
B1 |
B2 |
B3 |
|||
|
1 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
|||
|
1 |
2 |
1 |
1 |
0 |
0 |
1 |
0 |
|||
|
1 |
3 |
1 |
1 |
0 |
0 |
0 |
1 |
|||
|
2 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
|||
|
2 |
2 |
1 |
0 |
1 |
0 |
1 |
0 |
|||
|
2 |
3 |
1 |
0 |
1 |
0 |
0 |
1 |
|||
Typically, there are more columns for these effects than there are degrees of freedom to estimate them. In other words, the GLM parameterization of main effects is singular.