PSYC3010 – Moderated Multiple Regression Lecture

A comprehensive set of question-and-answer flashcards covering definitions, procedures, interpretation, and example results for moderated multiple regression as presented in the PSYC3010 lecture.

What does moderated multiple regression (MMR) test for?

Whether the relationship between a focal predictor (X) and a criterion (Y) changes as a function of another predictor, the moderator (W).

In MMR, what name is given to the variable that changes the X–Y relationship?

The moderator (W).

Which three hypothesis tests are run in a moderated multiple regression?

(1) Direct effect of X on Y, (2) direct effect of W on Y, and (3) the XW interaction effect on Y.

MMR is conceptually equivalent to what analysis when both predictors are categorical?

A two-way factorial ANOVA.

Write the regression model that includes an interaction term for predictors X and W.

Ŷ = bX·X + bW·W + bXW·(XW) + a

What is the purpose of Step 1 in a hierarchical MMR analysis?

Enter only the predictors (X and W) to test their additive direct effects on Y.

What statistic is examined to see if adding the interaction term improves the model?

The change in R² (R²change) assessed with an Fchange test.

Why are predictor variables mean-centred before creating the interaction term?

To reduce multicollinearity between the predictors and their interaction and to make coefficients interpretable as effects at the mean of the other predictor.

How is the interaction term (XW) created after mean-centring?

By multiplying each participant’s mean-centred X score with their mean-centred W score.

In mean-centred models, what does the slope bX represent?

The relationship between X and Y when W is at its average (0 after centring).

List the four practical steps for moderation testing in SPSS.

(1) Mean-centre X and W; (2) create XW interaction; (3) run hierarchical regression: Step 1 X & W, Step 2 XW; (4) if interaction is significant, probe simple slopes.

What is a ‘simple slope’ in the context of MMR?

The regression slope of X predicting Y at a specific value (usually low or high) of the moderator W.

Common numeric definitions for ‘low’ and ‘high’ levels of a continuous moderator are .

–1 SD (low) and +1 SD (high) from the mean.

When plotting an interaction from MMR, what variable is placed on the x-axis?

The focal predictor (X).

In an interaction plot, how is the moderator W represented?

By separate lines, typically one for low W and one for high W.

What does a significant XW interaction imply about the X–Y relationship?

That the slope of X predicting Y differs across levels of W (stronger, weaker, non-existent, or reversed).

True or False: Significant main (direct) effects are required for an interaction to be significant.

False. Direct effects and interactions are conceptually distinct.

What percentage of relationship-satisfaction variance was explained by external stressors and communication quality together in the lecture example (additive model)?

82 % (R² = .82).

How much additional variance did the interaction term explain in the example?

8 % additional variance (R²_change = .08).

Give the standardised regression equation from the example after including the interaction.

zŶ = –.328·zX + .719·zW + .312·zXW

When communication quality was low, what was the simple slope (β) of external stressors on relationship satisfaction?

β = –.66 (significantly negative).

When communication quality was high, what was the simple slope (β) of external stressors on relationship satisfaction?

β ≈ .00 (nonsignificant).

What does mean-centring do to the means and standard deviations of predictors?

Sets the mean to 0 while leaving the standard deviation unchanged.

Explain multicollinearity in the context of interactions without mean-centring.

X, W, and XW would be highly correlated, inflating standard errors and making coefficients unstable.

State two key statistics reported for overall model fit in MMR.

R² and the F statistic (with associated p value).

Which statistics are typically reported for individual predictors in MMR?

Standardised beta (β), squared semi-partial correlation (sr²), t value, and p value.

Describe how to compute W_low (–1 SD centred) from a mean-centred W variable.

Wlow = Wcentered – (–1 SD) or W_centered + 1 SD.

After creating Wlow and Whigh, what additional variables must be created for simple slopes?

Interaction terms XWlow and XWhigh (Xcentered × Wlow / W_high).

During simple slopes analysis, which coefficient in Step 2 indicates the slope of X at a specific W level?

The b (or β) for X, because W and XW have been recoded for that moderator level.

In the example, what was the unique variance (sr²) explained by external stressors when communication quality was low?

sr² = .29 (29 %).

What graphical evidence supports an attenuated relationship at high communication quality in the example?

The flat (near-zero slope) line for high W on the interaction plot.

Name two advantages of visualising simple slopes.

(1) Easier interpretation of interaction patterns; (2) clear communication of where effects are present or absent.

Why are 3-D interaction plots rarely used in journal articles?

They are confusing to read and difficult to reproduce on paper; 2-D simple-slope plots are clearer.

What is meant by ‘follow-up’ of a significant interaction in MMR?

Conducting simple slopes analysis to test X–Y relationships at specific values of W.

If R²_change is not significant after adding XW, how should the interaction be interpreted?

As nonsignificant; no evidence that X–Y relationship varies with W.

How does mean-centring aid interpretation of main effects in presence of an interaction?

Coefficients for X and W then represent their effects at the average level of the other predictor, making them meaningful.

Provide one SPSS command type used to compute centred variables or interactions.

Compute (via syntax), e.g., COMPUTE c_stress = stress – 5.3.

Which upcoming lecture topic was announced after MMR?

Mediation & Indirect Effects.

What are the two primary regression types reviewed before introducing MMR?

Standard multiple regression and hierarchical multiple regression.

In factorial ANOVA terms, what is a ‘simple effect’ analogous to in regression?

A simple slope.

What are boundary conditions in the context of moderation?

Specific levels of a moderator at which a predictor’s effect on an outcome strengthens, weakens, disappears, or reverses.

True or False: Regression can only use categorical predictors for moderation.

False. Regression can use continuous, categorical, or mixed predictor types.

What practical assessment accompanied the tutorials following the MMR lecture?

Practical Test 7 (Moderated Multiple Regression I).

At what step of hierarchical MMR is the interaction’s sr² equal to R²_change?

Step 2, because the interaction is the only new variable entered at that step.

What is the usual sample size advice regarding interactions?

Larger samples are recommended because interaction effects are often smaller and require more power to detect.