Shared Statistical Concepts

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 can be controlled by the ORDER= option in the CLASS statement.

Table 4.9 is an example where $\beta _0$ denotes the intercept and A and B are classification variables that have two and three levels, respectively.

Table 4.9: Example of Main Effects

Data

 

I

 

A

 

B

A

B

 

$\beta _0$

 

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


There are usually 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.