Interaction term

An interaction term lets the effect of one predictor depend on another. In

E [Y ∣ X, Z] = β_{0} + β_{1} X + β_{2} Z + β_{3} XZ,

(1)

the slope with respect to

X

β_{1} + β_{3} Z

Table of contents
- Coupling constant (physics) Interaction term
- Principle of marginality Interaction term

Coupling constant (physics, $g$ )

 0  0

A coefficient multiplying an interaction term controls its strength relative to the chosen field normalization. Its engineering dimension determines whether it is dimensionless, relevant or irrelevant. A renormalized coupling constant constant is specified at a renormalization scale; its change with that scale is described by the renormalization-group beta function.

Principle of marginality

 1  0

A hierarchical statistical model that contains an interaction term retains its associated lower-order effects. For two categorical predictors this means keeping both main effects when keeping their interaction. A nonsignificant averaged main effect may coexist with large opposite effects in different groups. Dropping its lower-order term while retaining the interaction can make the model depend on arbitrary factor coding.