Stochastic Moderated Regression: An Efficient Methodology for Estimating Parameters in Moderated Regression

In moderated regressions, the effect of a focal variable x1 depends on the level of a moderator variable x2. Moderation is estimated by introducing the product term of the two variables (x1x2) as an independent variable in the regression equation. Such moderator regressions often suffer from multicollinearity due to the usually high correlation between the product term and its components. The authors propose to recognize explicitly the stochastic nature of moderating effects to derive more efficient estimates of all the effects in the stochastic moderated regression model (SMR). Using Monte-Carlo simulations, the authors assess the ability to extract better inference about these effects under different conditions of stochasticity at different levels of the moderating effect. In addition, because of the inability to remove the collinearity inherent in the model specification itself (having a product term and its components in the same model), they evaluate the impact of introducing (or removing) terms in the model specification on the significance of these effects.