### GLM Parameterization of Classification Variables and Effects

Subsections:

Table 4.7 shows the types of effects that are available in high-performance statistical procedures; they are discussed in more detail in the following sections. Let `A`, `B`, and `C` represent classification variables, and let `X` and `Z` represent continuous variables.

Table 4.7: Available Types of Effects

Effect

Example

Description

Default

Intercept (unless NOINT)

X Z

Continuous variables

X*Z

Interaction of continuous variables

A B

CLASS variables

A*B

Crossing of CLASS variables

A(B)

Main effect A nested within CLASS effect B

X*A

Crossing of continuous and CLASS variables

X(A)

Continuous variable X1 nested within CLASS variable A

X*Z*A(B)

Combinations of different types of effects

Table 4.8 shows some examples of MODEL statements that use various types of effects.

Table 4.8: Model Statement Effect Examples

Specification

Type of Model

`model Y=X;`

Simple regression

`model Y=X Z;`

Multiple regression

`model Y=X X*X;`

Polynomial regression

`model Y=A;`

One-way analysis of variance (ANOVA)

`model Y=A B C;`

Main-effects ANOVA

`model Y=A B A*B;`

Factorial ANOVA with interaction

`model y=A B(A) C(B A);`

Nested ANOVA

`model Y=A X;`

Analysis of covariance (ANCOVA)

`model Y=A X(A);`

Separate-slopes regression

`model Y=A X X*A;`

Homogeneity-of-slopes regression