Moderation using Multiple Regression

Discuss Moderated Mediation vs Mediated Moderation

- Differ in terms of whether the focus is on direct or indirect effects - Mediated Moderation (Direct Effect focus) - Moderated Mediation (Indirect Effect focus) - Type of analysis is determined by the research question - Essential computations are the same for both analyses - It's all regression, just regression layered upon regression... - Purpose here is to just show how additional complexity can be built in - The sucky terminology has been recognized - People are shifting to just describing these as "conditional effects"

Define moderation

- Direct effect of a Predictor variable on an Outcome that is influenced by a third variable (the Moderator) - Unlike the other "third variable" situations, in Moderation, the third variable is influencing a pre-existing relationship between two variables (i.e., the Moderator affects the strength of an effect in data) - Moderator can enhance or attenuatethe Predictor-Outcome relationship - Unlike Mediation, Moderation focuses on the direct effect of the Predictor on the Outcome

Q1 addressed by moderation: Is the relationship between the Predictor and Outcome affected by the Moderator variable?

- Does the interaction between Predictor and Moderator affect the Outcome over and above the effects of each variable in isolation? - Interaction is the product of Predictor and Moderator scores - Evaluating the Interaction Term - Two-stage Regression Analysis (Hierarchical Regression) - Stage 1: Add Predictor and Moderator as predictor variables - Stage 2: Add Interaction as a third predictor variable - Evaluate change in R2--- does inclusion of Interaction significantly improve the fit of the regression model? - "If it improves the fit, moderation is legit." - Significant interaction term implies that the effect of the Predictor on the Outcome is different depending on the level of the Moderator

Q2 addressed by moderation: How does the moderator variable affect the Predictor-Outcome relationship?

- How do the slopesof the Predictor-Outcome relationship different at high vs. low levels of the Moderator? - We now know that the effect of the Predictor on the Outcome is different at different levels of the Moderator variable - Evaluated via simple slopes analysis - Separate regression analyses at low and high values of the Moderator - By convention "low" and "high" are ± 1 SD from the mean of the Moderator - Note the points at which simple slopes are evaluated are chosen arbitrarily!

List necessary hypotheses for moderation

- Hypothesize a significant interaction term in the first regression analysis - Hypotheses about the effect of the Moderator are theory-dependent - Is the Moderator expected to enhance, attenuate, or even reverse the relationship between the Predictor and the Outcome? - Simple slopes can be significant or non-significant - e.g., Predictor-Outcome might be unrelated at one level of the Moderator

List steps in conducting moderated multiple regression

- Mean center Predictor and Moderator variables - Mean Centered Score = Score - Mean - Reduces collinearity with Interaction term - Compute the Interaction variable - Conduct a Hierarchical Regression - Block 1: Predictor and Moderator as predictor variables in regression - Block 2: Add Interaction term as a third predictor - If interaction term is significant, examine simple slopes - Separate regression analyses for high and low values of Moderator - Plot the slopes

List Key Questions Addressed by Moderation

- Mediation asks the question of what mechanism underlies the relationship between a predictor and outcome variable - Moderation asks the question of whether an effect applies (at all or to differing degrees) for different subsets of people - Subsets of people are identified by different levels of the Moderator variable - As the moderator variable goes from a low value to a high value, does the strength of the direct effect change at all?

Discuss regression in relation to moderation

- Moderated Multiple Regression is most often used when the 3rdvariable is measured (rather than manipulated—but both are OK) - Continuous or categorical 3rd variable - Predictor variable can be measured or manipulated - Continuous or categorical is fine - Outcome variable determines what kind of regression is used - Continuous—linear regression - Categorical—logistic regression

Give a summary of moderation

- Moderation can help us identify boundary conditions of effects - At what point does an effect "turn off"? - Addresses situations where strength of an effect differs across people - Multi-stage analysis (like Mediation Analysis) - But focuses on direct, rather than indirect effects - Has been automated via the PROCESS macro (see Blackboard for details) - Mediation and Moderation can co-exist in a data set

Discuss the hellish cross-overs between mediation and moderation.

- Possible for Mediation and Moderation to occur simultaneously - Process involves a minimum of 4 variables * Moderated Mediation - The indirect effect is the main research focus - 1) The strength of the indirect effect is changed by the Moderator - 2) Different indirect effects are engaged at different levels of the Moderator * Mediated Moderation - The direct effect is the main research focus - 1) Moderation effect is controlled by a fourth mediating variable