What is a moderating variable?

Answer 1

A moderator variable is the independent qualitative or quantitative variable that affects the relationship of the dependent and independent variables. In correlation, a moderator is a third variable that affects the correlation of two variables. In a casual relationship, if x is the predictor variable and y is a cause variable, then z is the moderator variable that affects the casual relationship of x and y. Most of the moderator variables measure casual relationship using regression coefficient. In ANOVA, the moderator variable effect is represented by the infraction effect between the dependent variable and the factor variable.

Assumptions:

1. Casual assumption: When x variable is not randomized, then causation must be assumed. The moderator variable can reversely effect the causation, if the causation between x and y is not presumed.
2. Casual variable relationship: The two variables, the moderator variable and the casual variable, should be independent. If x is a manipulated variable, then there should be no correlation between the moderator variable and the casual variable.
3. Measurement: Usually, the moderation effect is represented by the interaction effect between the x and z variable. In a multiple regression equation, the moderator variable is as follows:

In this equation, the interaction effect between X and Z (or coefficient) measures the moderation effect.