W6 Flashcards by Eline Olmos van Velden

Moderation Definition

A moderator (V2) changes the strength or direction of the effect of an independent variable (V1) on a dependent variable (Y). The moderator “interferes” with the relationship between IV and DV.

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Moderation Examples

Effect of salary (IV) on job intention (DV) depends on age (moderator), - Effect of advertisement (IV) on sales (DV) depends on message clarity, - Effect of discount (IV) on sales (DV) depends on whether it’s in-store or online (moderator) (moderator)

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How Moderators Work

Strengthening: A high value of moderator makes the IV effect stronger (more positive or more negative), - Weakening: A high value of moderator makes the IV effect weaker (less positive or less negative)

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Graphical Representation of Moderation

Two regression lines are used when a moderator is present (e.g. low vs. high moderator), - The difference in slopes shows how the moderator changes the relationship between IV and DV

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Strengthening Effect

Moderator increases slope steepness (absolute value), - Sign of moderation is the same as the sign of the main effect

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Buffering Effect

Moderator decreases slope (absolute value), - Sign of moderation is opposite to the sign of the main effect

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Antagonistic Effect

Moderator reverses the sign of the relationship (slopes go in opposite directions), - High and low levels of moderator flip the relationship between IV and DV

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Summary of Types of Moderation

No moderation = parallel lines, - Strengthening = steeper slope for higher moderator, - Weakening = flatter slope for higher moderator, - Antagonistic = slope changes direction between levels of moderator

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Moderation - Foundation

Moderation occurs when the effect of an independent variable (IV) on a dependent variable (DV) depends on a third variable (moderator). It can strengthen or weaken the effect.

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Strengthening vs Weakening Effects

Strengthening: Moderator increases the IV → DV effect., - Weakening: Moderator decreases the IV → DV effect.

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Buffering and Antagonistic Effects

Buffering: Effect remains in same direction but becomes weaker., - Antagonistic: Effect changes direction (e.g. positive to negative).

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Visualising Moderation Effects

Different slopes on regression lines: - Steeper slope with moderator = strengthening, - Flatter = buffering, - Opposite slope = antagonistic

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One-Way Interaction Regression

Use formula: Y = b0 + b1IV + b2Mod + b3*(IV×Mod) + error. The b3 term shows how the moderator alters the IV’s effect.

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Dummy Variables as Moderators

Dummy variables coded 0 or 1. Interaction terms formed as IV × dummy. R handles this automatically with lm() by including IV*Mod in the formula.

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Interpreting R Output

Look for significance (p < 0.05) in the interaction term. Positive value = strengthening, negative = weakening.

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Example: Price Discount & Ads

IV = price discount, Mod = feature ad, - Interaction term is +11.675 and significant, - Conclusion: Feature ads strengthen the effect of discounts.

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Detecting Moderation Types

Check direction and significance of IV and interaction term: - Both positive = strengthening, - Opposite signs = antagonistic/weakening

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Graph Interpretation

Higher moderator = steeper line if strengthening, - Shallower slope = buffering, - Crossed lines = antagonistic

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One-way Interaction with Metric Variables

Used when both the independent variable (IV) and moderator are continuous (metric). Example: Advertising spend (IV) and individualism score (moderator).

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Regression Formula

Y = b₀ + b₁ × V₁ + b₂ × V₂ + b₃ × (V₁ × V₂) + error, Where V₁ is the IV, V₂ is the moderator, and V₁ × V₂ is the interaction term.

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Scenario Overview

The researcher wants to see how advertising affects intention to adopt, and whether this depends on individualism scores.

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R Output Interpretation

b₁: Effect of advertising, b₂: Effect of individualism, b₃: Interaction effect (how individualism moderates the impact of advertising)

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What the Coefficients Mean

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Example output:Advertising = –0.037 (not significant), Individualism = 0.010, Interaction = –0.013 (significant), → This suggests higher individualism weakens the effect of advertising (i.e. antagonistic).

Effect Interpretation

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1 pt increase in advertising = –0.038 – 0.013 × individualism, 1 pt increase in individualism = 0.010 – 0.013 × advertising

Predicted Value Formula

Example: Argentina (0.03 advertising, 46 individualism), Prediction = 5.912 – 0.04 × 0.03 + 0.01 × 46 – 0.013 × (0.03 × 46)

Comparing Countries

To find predicted differences between Argentina and Australia, plug in both countries’ values into the formula and subtract. This includes both main and interaction effects.

Pure Effect of Moderation

If only interested in how individualism moderates the effect of advertising: Calculate: b₁(V₁ₐ – V₁_b) + b₃[(V₁ₐ × V₂ₐ) – (V₁_b × V₂_b)], (e.g. Argentina vs. Australia)

What is a one-way interaction with mixed variables?

It’s when a metric variable (like number of customers) interacts with categorical variables (like seasons) in a regression.

How does season moderate the effect of customers on sales?

Winter and summer significantly change the effect of customers on sales compared to autumn (the reference).

What is mean-centering in regression?

It’s subtracting the mean of a variable from each value so that the variable has a mean of 0.

Why is mean-centering useful?

It helps interpret the intercept, reduces multicollinearity, and clarifies interaction terms.

How do you mean-center a variable?

Subtract the mean of the variable from each individual value. For example, 115 – 110 = 5.

How does R handle mean-centering?

You can create centered variables manually or use R to generate them with commands like MC_X.

What does the intercept represent after mean-centering?

It shows the expected value of the dependent variable when all predictors are at their mean.

Does mean-centering change the effect of variables?

No, it doesn’t change the coefficients — it just helps with interpretation.

When should you NOT use mean-centering?

When predictors already have a meaningful value at 0 or you’re not using interaction terms.

What does a buffering effect look like in a graph?

The slope becomes flatter, showing that the moderator weakens the effect of the predictor.

What is mediation in regression?

Mediation explains why an independent variable (IV) affects a dependent variable (DV) through a third variable (mediator M).

Examples of mediation

E.g. Ad attitude → Brand attitude → Purchase intention. The mediator (brand attitude) helps model the effect process.

How is mediation tested?

Use regression to estimate: - Direct effect: IV → DV (path c), - Indirect: IV → M → DV (a and b), - Total effect = a×b + c′, - Total effect = a×b + c′

What is the 'a×b' path?

'a' is the effect of IV on M, 'b' is M on DV. Their product (a×b) is the indirect effect.

Full vs. Partial Mediation

Full: Only indirect effect matters, direct not significant. Partial: Both direct and indirect effects are significant.

Why do we use bootstrapping?

Because indirect effects (a×b) have no standard error. Bootstrapping helps build a confidence interval.

How does bootstrapping work?

Resample the dataset many times (with replacement), calculate a×b for each sample, and use the results to get an empirical distribution.

Steps in bootstrapping

1. Sample with replacement 2. Estimate a and b 3. Multiply a×b each time 4. Repeat (e.g. 1000x) and build a confidence interval.

What does mediation show us?

It shows how or why a relationship occurs — not just that it exists. It explains the process behind the effect.

What is the first step in setting up mediation in R using lavaan?

Define your variables: IV (X), Mediator (M), and DV (Y). Put them into a new data frame.

What do you need to specify in the lavaan model?

The direct effect (Y ~ X), the paths from X to M and M to Y (M ~ X, Y ~ M), and use := to define indirect (a*b) and total effects (a*b + c).

What function do you use to run the model?

Use sem() with the model and dataset, and summary() to see the output.

How do you check if mediation is significant?

Look at the indirect effect (a*b) and check if its p-value is less than 0.05.

What indicates full mediation?

Indirect effect is significant, but the direct effect (c path) is not.

What indicates partial mediation?

Both the indirect (a*b) and direct (c) effects are significant.

What was the result of the example given (attitude → brand → purchase intention)?

The indirect effect (0.257) was significant (p < 0.05), and the direct effect was not → full mediation.

How do you interpret the path diagram?

Each arrow shows a regression effect. For example, attitude → brand (0.76), brand → intention (0.325). Multiply them to get the indirect effect.

In the second exercise, how do you identify IV, M, and DV?

IV = Attitude, M = Intention, DV = Behavior.

What confirms significance of the mediator effect?

The ab path (a*b) has a p-value less than 0.05.

W6 Flashcards

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