Moderation Analysis Overview

Moderation Analysis

• Requires an independent variable (IV), dependent variable (DV), and moderating variable (MV)
• IV and DV must be continuous, MV can be continuous or categorical
• If IV is categorical, use ANOVA
• If DV is categorical, use logistic regression

Moderation Analysis Steps

• Step 1: Estimate the interaction effect.
• Step 2: Conduct a statistical inference test.
• Step 3: If the interaction is significant, probe the interaction by doing a simple slopes analysis.

Moderation Analysis in Jamovi

• Click on "+ Modules" and search for "medmod".

Possible Conclusions for Moderation Analysis

• Main Effects are Present: The significant simple slopes indicate a meaningful relationship between the predictor (IV) and outcome (DV) at different levels of the moderator. This means the IV consistently affects the DV, regardless of the moderator.
• Lack of Interaction: The non-significant interaction effect implies the relationship between the IV and DV doesn't change significantly across different levels of the moderator.

Mediation Analysis

• Examines causal hypotheses where an initial variable (IV) influences an outcome variable (DV) through a mediating variable (M).
• This is a causal chain where IV affects M, which in turn affects DV.
• A variable is considered a mediator if it carries the influence of the IV onto the DV.
• For mediation to occur, the following must be true:
  • IV significantly affects M.
  • IV significantly affects DV in the absence of M.
  • M has a significant unique effect on DV.
  • The effect of IV on DV shrinks upon the addition of M to the model.

Mediation Analysis: Path Diagrams

• Each arrow in a path diagram represents a causal relationship between two variables, with an assigned coefficient or weight.
• These coefficients are standardized regression coefficients (betas) showing the direction and magnitude of the effect of one variable on the other.

Summary of Moderation and Mediation

• Used to explore interrelationships among three variables.
• If only two variables are being studied, a simple correlation or linear regression can be used instead.
• Mediation and moderation are tests of association, specifically designed to answer particular questions.
• Both require a theory, model, or principle.

Mediation Concepts

• Exogenous Variable: A variable that has no explicit causes within the model (no arrows pointing to it). This is the independent variable.
• Endogenous Variable: A variable that is causally affected by other variables in the model (has arrows pointing to it). This is the dependent variable.
• From a regression standpoint, an equation should be fitted for every endogenous variable in the model.

Mediation Analysis Assumptions

• Continuous Measurements: All variables should be measured on a continuous scale.
• Normality: All variables should follow a normal distribution.
• Independence: The errors associated with one observation should not be correlated with the errors of any other observation.
• Linearity: Relationships among variables should be linear.

Simple Mediation Analysis Steps

• Step 1: Estimate direct and indirect effects using regression analysis.
  • Direct Effect: Path C
  • Indirect Effect (or Mediation Effect): Path a x Path b
• Step 2: Conduct a statistical inference test (p-value) by performing a significance test for the indirect effect or by calculating a bootstrap confidence interval.

Testing for Mediation: Baron and Kenny (1986) Approach

• A four-step approach:
  • Step 1: Confirm the significance of the relationship between the initial IV and DV (X → Y).
  • Step 2: Confirm the significance of the relationship between the initial IV and the mediator (X → M).
  • Step 3: Confirm the significance of the relationship between the mediator and the DV in the presence of the IV (M|X → Y).
  • Step 4: Confirm the insignificance (or meaningful reduction) of the relationship between the initial IV and the DV in the presence of the mediator (X|M → Y).

Three Main Types of Mediation

• Indirect Effect: Predicts no direct effect from X to Y. X directly affects the mediator, and the mediator directly affects Y. This hypothesis can only be supported if the direct effect of X to Y is insignificant before testing for indirect effects.
• Partial Mediation: Predicts significant direct and indirect effects from X to Y. The unmediated relationship is significant, as well as the X to the mediator and mediator to Y relationships.
• Full Mediation: Predicts that the direct effect of X to Y will be significant only if the mediator is absent. When the mediator is present, this direct effect becomes insignificant, while the indirect effect is significant.

Reporting Mediation Analysis Results

• Use a table to present the results.
• Explain the total effect of the IV on the DV.
• Describe the effect of the IV on the DV with the mediator included.
• Report the indirect effect of the IV on the DV through the mediator.
• State whether the relationship between the IV and DV is fully, partially, or not mediated.

This quiz explores the key concepts and steps involved in moderation analysis, including the roles of independent, dependent, and moderating variables. It covers necessary statistical tests and provides guidance on performing analysis using Jamovi. Test your understanding of moderation analysis fundamentals.