Shared Concepts and Topics

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 4 is an example where denotes the intercept and A and B are classification variables with two and three levels, respectively.

Table 4: Example of Main Effects

Data			I		A			B
A	B				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.