The concept of moderation and tests for interaction effects were introduced in Week 5 under the Analysis of Covariance (ANCOVA) assumption of homogeneity of slopes. Recall that we tested the null hypothesis that the slopes (regression coefficients) of the relationship between acoun (counseling; IV) and recovery (DV) were not significantly different for females as compared to males. We also tested the null hypothesis that the regression slopes for the relationship between ddepre (depression; IV) and recovery (DV) were homogeneous across different racial/ethnic groups. The SPSS module Analyze General Linear Model Univariate allows for various interaction terms to be added to linear models by including these terms in the Model specification window.
This week, we will extend the application of moderation analysis to (1) explore interactions involving two or more continuous variables, (2) examine the practice of centering the main effects prior to calculating the interaction term, and (3) become familiar with a new SPSS module called PROCESS, developed by Dr. Andrew Hayes, that performs both moderation and mediation analysis.
Interactions Involving Continuous Variables
Thus far our examination of interaction effects (moderation) has been limited to two categorical variables (e.g. 2-way ANOVA) or a categorical and continuous variable (e.g. homogeneity of slopes in ANCOVA). Here we will look at moderation involving two continuous variables. The principles governing the interaction between two continuous variables are identical to those governing categorical variables. One variable serves as the independent variable (X) and the other serves as the moderator variable (M). In moderation analysis, the null hypothesis is that the relationship between the independent variable (X) and the dependent variable (Y) is not significantly different at different levels of M. The alternative hypothesis is therefore that the relationship between X and Y is significantly different at different levels of M. Conceptually, we can represent a moderation effect with the following path diagram.