Shared Statistical Concepts

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
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	XZA(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