Moderation Model

A moderating variable...

Moderates, interferes, and alters the effect of predicting variable on criterion variable.
Specifies the conditions under which a given effect occurs, as well as the conditions under which the direction (nature) or strength of an effect vary.
Affects the relationship between two variables, so that the nature of the effect of the predictor on the criterion varies according to the level or value of the moderator (Holmbeck, 1997).
The presence of a moderator modifies the original relationship between predictor & criterion variable.
Interacts with the predictor in such a way as to have an impact on the level of the criterion variable.

"A qualitative (e.g., sex, race, class) or quantitative variable ... that affects the direction and/or strength of a relation between an independent or predictor variable and a dependent or criterion variable ... A basic moderator effect can be presented as an interaction between a focal independent variable and a factor (the moderator) that specifies the appropriate conditions for its operation... Moderator variables are typically introduced when there is an unexpectedly weak or inconsistent relation between a predictor and a criterion variable"

(Baron & Kenny, 1986).

Examples

Moderating Effect

Main Effect:

Y = a + b.X + c.M

Interaction Effect:

Y = a + (b + d.M).X + c.M

Y = a + b.X + c.M + d(X.M)

Moderating Effect when Running an Analysis

Hypothesis

Should I hypothesize the form of the interactions in advance?

YES, not only should the existence of an interaction effect be predicted, but also its form. In particular, whether a moderator increases or decreases the association between two other variables should be specified as part of the a priori hypothesis (Dawson, 2014)

Example:

H₁: The positive relationship between satisfaction and loyalty will be stronger when perceived image is high.

H₂: The positive relationship between satisfaction and loyalty would be stronger for male compared to female.

H₁: Body Mass Index (BMI) moderates the relationship between exercise and weight loss, such that for those with a low BMI, the effect is negative (i.e., you gain weight muscle mass), and for those with a high BMI, the effect is positive (i.e., exercising leads to weight loss).