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

Creating the Interaction Term

Product indicator approach.
Orthogonalizing approach.
Two-stage approach.

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).

Moderating Effect Assessment

i = interaction model; m = main effect model

Suggested by Cohen (1988), f² is assessed as:

0.02 Small

0.15 Medium

0.35 Large

“Even a small interaction effect can be meaningful under extreme conditions, if the resulting beta changes are meaningful, then it is important to take these conditions into account” (Chin, Marcolin & Newsted, 2003; p. 211).

Interaction Plots

The relationship between satisfaction and customer loyalty is stronger when Image is low…

Look at the gradient!

Why Plot?

However, it is not entirely clear how it differs. If you get a positive coefficient, the positive coefficient of the interaction term suggests that it becomes more positive as Image increases; however, the size and precise nature of this effect is not easy to difine from examination of the coefficients alone, and becomes even more so when one or more of the coefficients are negative, or the standard deviations of X (IV) and Z (Moderator) are very different (Dawson, 2013).

Caveat

An important consideration about categorical moderators is that they should only be used when the variable was originally measured as categories.

Continuous variables should never be converted to categorical variables for the purpose of testing interactions. Doing so reduces the statistical power of the test, making it more difficult to detect significant effects (Stone-Romero and Anderson 1994; Cohen et al. 2003), as well as throwing up theoretical questions about why particular dividing points should be used (Dawson, 2013).

Some Online Sources

Interpreting interaction effects. Please click here.

Interaction. Please click here.

Moderation (Interaction Effect) Material. Please click here.

Excel Template

Interaction plot for the categorical data moderator. Click here to download.

Interaction plot for the continuous data moderator. Click here to download.