GLM, GLZ, PLS, GDA, and MANOVA Syntax - Keyword Design

DESIGN = Design specifications;

Example 1. DESIGN = GROUP | GENDER | TIME | PAID;
Example 2. DESIGN = SEQUENCE + PERSON(SEQUENCE) +
  TREATMNT + SEQUENCE*TREATMNT;
Example 3. DESIGN = MULLET | SHEEPSHD | CROAKER @2;
Example 4. DESIGN = TEMPERAT | MULLET | SHEEPSHD | CROAKER
  - TEMPERAT;
Example 5. DESIGN = BLOCK + DEGREES + DEGREES*DEGREES +
  TIME + TIME*TIME + TIME*DEGREES;

Optional keyword; specify the design for the between group design (categorical and continuous predictors); default is NONE.

Simple terms and operators
To the right of the Design statement, list the effects separated by the + (plus) operator. Single effects can be specified as follows:
A Main effect for factor (categorical or continuous) predictor variable A.
A*B A by B interaction effect (for categorical or continuous predictor variables A and B).
A(B) A nested in B; the levels of categorical predictor (factor) A are nested within the levels of categorical predictor (factor) B.
Effect macros
Complete factorial designs, or standard nesting of factors can be specified via the following shortcuts:

Bar operator

A|B Complete factorial for factors A and B; this expression will be expanded (internally by the syntax interpreter) to A+B+A*B; complete higher order factorial designs can be specified analogously, for example, a complete 3-way design for factors A, B, and C can be specified as: A|B|C.

Factorial degree operator

A|B|C @2 The complete factorial for factors A, B, and C, up to degree 2; this expression will be expanded (internally by the syntax interpreter) to A + B + C + A*B + A*C + B*C; i.e., a factorial design will be constructed only up to the requested degree (to the second degree in this example; the three-way interaction will not be added).

Grouping-of-terms-operator

A | (B+C) The complete factorial for factors A and (main effects) B + C, this expression will be expanded (internally by the syntax interpreter) to A + B + C + A*B + A*C; note that the three-way interaction term A*B*C is not included in this model.
Deletion operator
The deletion operator (-) can be used to remove effects from a factorial design specified via the bar operator (|); :
A|B|C-C Complete factorial for factors A, B, and C without the main effect for C; this expression will be expanded (internally by the syntax interpreter) to A + B + A*B + A*C + B*C + A*B*C (note that main effect C is missing).
A|B|C-|C Complete factorial for factors A, B, and C without all interactions that involve factor C; this expression will be expanded (internally by the syntax interpreter) to A + B + C + A*B (note that all interactions involving effect C are missing).
A|B|C-(A*C) Complete factorial for factors A, B, and C without the A by C interaction; this expression will be expanded (internally by the syntax interpreter) to A + B + C + A*B + B*C + A*B*C; note that the A by C interaction is missing.
A|B|C-|(A*C) Complete factorial for factors A, B, and C without all higher order interactions that involve the A by C interaction; this expression will be expanded (internally by the syntax interpreter) to A + B + C + A*B + A*C + B*C; note that the only higher-order interaction involving A by C is the three-way interaction, which will is missing.

Applies to. GLM, GLZ, PLS, GDA, ANOVA/MANOVA, GC&RT, and GCHAID.