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.