Moderation & Mediation

Types of regression models

General linear model, generalized linear model, generalized linear mixed model

General linear regression model

Methods for data that’s normally distributed

Examples of general linear regression models

t-test, ANOVA, simple/multiple regression

Generalized linear regression model

Methods for DV that is NOT normally distributed

Examples of generalized linear regression models

Logistic regression

Generalized linear mixed regression models

Methods for nested data (=hierarchical levels of grouped data)E

Examples of generalized linear mixed regression models

HLM

HLM

Advanced regression model for nested data (=the predictor variables are varying at hierarchical levels). Separates the effect of IVs by level, in data analysis

This graph is depicting what concept?

Hierarchical levels

Nested data

Hierarchical levels of grouped data. Data cases in a lower level are included in only one higher level group

Nested data typically violates this assumption

Independence of observations

Mediation analysis

Tests hypothetical causal chain where one variable X affects a second variable M and, in turn, that variable affects a third variable Y

Mediators

“How/why” of a relationship between two other variables. Indirect effect

TRUE/FALSE: Both mediators and third variables can be detected using multiple regression

TRUE

_______ are external to the bivariate correlation (problematic & spurious correlation), whereas ______ are internal to the causal variable (not problematic)

third variables; mediators

The most popular method to detect mediators

Baron & Kenny’s (1986) 4-step indirect effect

Step 1 of Baron & Kenny’s (1986) 4-step indirect effect method

Estimate the relationship btwn IV on DV. Path “C” must be significantly different from 0

Step 2 of Baron & Kenny’s (1986) 4-step indirect effect method

Estimate the relationship btwn IV on M. Path “A” must be significantly different from 0.

Step 3 of Baron & Kenny’s (1986) 4-step indirect effect method

Estimate the relationship btwn M on DV controlling for IV. Path “B” must be significantly different from 0

Step 4 of Baron & Kenny’s (1986) 4-step indirect effect method

Estimate the relationship btwn DV on IV controlling for M. Path “C’” should be non-significant and nearly 0

TRUE/FALSE: If there is no relationship between THE IV and DV, there is nothing to mediate

TRUE

TRUE/FALSE: If IV and M have no relationship, M is just a third variable that may or may not be associated with DV

TRUE

TRUE/FALSE: If a mediation exists, the effect of the IV on the DV will disappear (or at least weaken) when M is included in the regression. The effect of the IV on the DV goes through M.

TRUE

M is a full mediator

b4 is non-significant

M is a partial mediator

b4 is significant but becomes smaller

ACME (Average Casual Mediation Effects)

Represents the indirect (mediated) causal effect. Expected change in Y when X changes the mediator M, holding the direct path constant. When this is significant, it indicates a statistically meaningful X → M → Y pathway

ADE (Average Direct Effects)

Represents the direct effect. The expected change in Y when X changes while the mediator M is held constant. If this is significant, it suggests the direct effect of X on Y is statistically meaningful

Total effect

Represents the sum of the direct and indirect effects. A significant total effect is not required for mediation to existP

Prop. Mediated (Proportion Mediated)

ACME / Total Effect. Describes the relative contribution of the indirect effect. Can be unstable or uninterpretable when the total effect is small or changes sign. Should be interpreted cautiously.

Interpretation if ACME is significant and ADE is non-significant

Full mediation (indirect-only)

Interpretation if both ACME and ADE is significant

Partial mediation

Interpretation if ACME is non-significant and ADE is significant

Direct effect only (no mediation)

Interpretation if ACME is significant but both ADE and Total Effect are non-significant

Indirect-only / suppression

Bootstrap

Simulation method to estimate the variability of a statistic by repeatedly resampling the observed data. Especially more suitable for small sample sizes.

Why do we use Bootstrapping in Mediation Analysis?

Indirect effect of mediation is often not normally distributed and the Sobel test assumes normality. Bootstrapping does not assume a specific distribution and provides a more accurate and robust confidence intervals for the indirect effect

Bootstrapping helps us determine

What the sampling distribution of the test statistic would be if the null hypothesis were actually true

Null hypothesis when testing the regression coefficient β

H₀: β = 0. This means the regression coefficient is zero, implying that changes in X do not affect Y. In other words, X does not contribute to predicting Y

95% Confidence Interval includes 0 when H₀: β = 0

Fail to reject null hypotheses; not statistically significant

95% Confidence Interval does not include 0 when H₀: β = 0

Reject the null hypothesis; statistically significant

Moderation analysis

Tests whether a variable (Z) affects the direction and/or strength of the relation between an IV (X) and a DV (Y). Tests for interactions that affect WHEN (under what conditions) relationships between variables occur

_______ designs can be used to test whether an IV affects different kinds of people in different situations in the same way

Factorial

Describe the relationship shown within the graph

The effect of talking on a cell phone did not depend on age

Describe the relationship shown within the graph

The effect of talking on a cell phone varies between ages

In simple terms, moderators can be described as the _______ whereas mediators can be described as the ________

when; how/why

TRUE/FALSE: Some variables can not be a moderator and/or a mediator depending on questions

FALSE

How can moderation analysis be tested?

By looking for significant interactions between the moderating variable (Z) and the IV (X)

Method to reduce multicollinearity and make moderation analysis interpretation easier

Centering for both moderator and IV

Centering

Transforms variable so that it mean becomes 0 by subtracting the mean of a variable from each value in that variable

Moderation exists if the _______ term is significant

interaction

TRUE/FALSE: A significant interaction does not require significant main effects

TRUE

TRUE/FALSE: Centering does not change the result - it stabilizes estimation and makes coefficients interprtable

TRUE

What does this model depict?

Moderated mediation

Moderated mediation

The mechanism differs depending on the person or condition. X → M → Y, but the strength of this process depends on W. Indirect effect is conditional on W

Mediated moderation

Explaining why an interaction occurs. Interaction between X and W affects Y, but this effect operates through M. Goal is to explain why interaction effect occurs.

TRUE/FALSE: Depending on what the researcher aims to explain, the same statistical model may be described as “moderated mediation” or “mediated moderation”

TRUE

Assumptions from the “gvlma” package for mod/med analysis in R

Global stat, skewness and kurtosis, link function, and heteroskedasticity

Global stat assumption

Checks whether the relationship between the dependent and independent relationship is roughly linear

Skewness and kurtosis assumption

Checks if the distribution of the residuals is normal

Link function assumption

Checks if the DV is continuous or categorical

Heteroskedasticity assumption

Checks if error variance is equally random

Simple slopes analysis

Examines how the effect of the IV changes at different levels of the moderator when the moderation is significant. Helps determine how the moderator influences the relationship between the IV and the DV by analyzing three regression lines at different levels of the moderator: Mean (M), Mean - 1SD, Mean + 1SD

Buffering effect

When the moderator weakens the IV-DV relationship, the slow follows this pattern: -1SD (steep) → Mean (moderate) → +1SD (shallow)

Enhancing effect

When the moderator strengthens the IV-DV relationship, the slope follows this pattern: -1SD (shallow) → Mean (moderate) → +1SD (steep)

When the moderator is at its mean (M = 0), the simple slope is what?

Generally equal to the regression coefficient (b1) of the IV in the moderation analysis

Rockchalk function

Automatically plots the simple slopes of the moderating effect

Black line in rockchalk function

When moderator is low

Red line in rockchalk function

Mean of the moderator

Green line in rockchalk function

When moderator is high