Moderation (statistics)

In statistics, moderation occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator variable or simply the moderator ^[1]. The effect of a moderating variable is characterized statistically as an interaction^[1]; that is, a qualitative (e.g., sex, race, class) or quantitative (e.g., level of reward) variable that affects the direction and/or strength of the relation between dependent and independent variables. Specifically within a correlational analysis framework, a moderator is a third variable that affects the zero-order correlation between two other variables. In analysis of variance (ANOVA) terms, a basic moderator effect can be represented as an interaction between a focal independent variable and a factor that specifies the appropriate conditions for its operation (Baron and Kenny, 1986: p. 1174).

Moderation analysis in the behavioral sciences involves the use of linear multiple regression analysis or causal modelling^[1]. To quantify the effect of a moderating variable in multiple regression analyses, regressing random variables Y on X, an additional term is added to the model. This term is the interaction between X and the proposed moderating variable ^[1].

Thus, for a response Y and two variables x₁ and moderating variable x₂,:

$Y = b_0 + b_1x_1 + b_2x_2 + b_3(x_1\times x_2) + \varepsilon \,$

In this case, the role of x₂ as a moderating variable is accomplished by evaluating b₃, the parameter estimate for the interaction term^[1]. See linear regression for discussion of statistical evaluation of parameter estimates in regression analyses.

Moderation should not be confused with mediation.

See also

• Omitted-variable bias

References

1. ^ ^{a b c d e} Cohen, Jacob; Cohen, Patricia; Leona S. Aiken; West, Stephen H. (2003). Applied multiple regression/correlation analysis for the behavioral sciences. Hillsdale, N.J: L. Erlbaum Associates. ISBN 0-8058-2223-2. 

• Baron, R. M., & Kenny, D. A. (1986). "The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations." Journal of Personality and Social Psychology, Vol. 51, No. 6, pp. 1173–1182.
• Hayes, A. F., & Matthes, J. (2009). "Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations." Behavior Research Methods, Vol. 41, pp. 924-936.