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.
In this equation, the interaction effect between X and Z (or coefficient) measures the moderation effect.
Linear vs. non-linear measurement: In a regression equation, when the relationship between the dependent variable and the independent variable is linear, then the dependent variable may change when the value of the moderator variable changes. In a linear relationship, the following equation is used to represent the effect:
In this equation, the relationship is linear and represents the interaction effect. When the relationship is non-linear, the following equation shows the effect of the moderator variable effect:
In this equation, the relationship between the dependent and the independent variable is non-linear, so and shows the interaction effect. In a repeated measure design moderator, the variable can also be used. In multi-level modeling, if a variable predicts the effect size, that variable is called the moderator variable.
Methods for identifying:
In this equation, if is not statistically significant, then Z is not a moderator variable, it is just an independent variable. If is statistically significant, then Z will be a moderator variable.