GLM Parameterization of Classification Variables and Effects

Table 3.7 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 3.7: Available Types of Effects

Effect

Example

Description

Intercept

Default

Intercept (unless NOINT)

Regression

X Z

Continuous variables

Polynomial

X*Z

Interaction of continuous variables

Main

A B

CLASS variables

Interaction

A*B

Crossing of CLASS variables

Nested

A(B)

Main effect A nested within CLASS effect B

Continuous-by-class

X*A

Crossing of continuous and CLASS variables

Continuous-nesting-class

X(A)

Continuous variable X1 nested within CLASS variable A

General

X*Z*A(B)

Combinations of different types of effects


Table 3.8 shows some examples of MODEL statements that use various types of effects.

Table 3.8: 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