5 introduction to moderation analysis

Question 1

What is moderation analysis?

Answer 1

when, under what circumstances, for what types of people that effect exists

interaction

if the effect of X on Y is moderated, then X and W interact

Xs effect on Y depends on W in some way

size or direction of effect varies in some way with W

Question 2

What are two examples of moderation analyses?

Answer 2

e.g. compared to a traditional therapy, a new therapy (X) might be effective at reducing symptoms of depression (Y), but that effect might be smaller, or perhaps the therapy is even harmful, among people suffering from anxiety (W)

e.g. traumatic experiences (X) may reduce how satisfied people are with their relationships (Y), but social support (W) might buffer negative effects

Question 3

What is the basic equation for a moderation model?

Answer 3

X effect on Y is fixed -b1- regardless of W
→ constraints

needs to be released
→ specifying Xs effect to be a function of W: b1 + b3W

is the weight for W in the linear function different than zero?

if b3 not zero → Xs effect on Y varies with W

Y = iy + b1X + b2W + b3(XW) + e

b1 = effect of X on Y when W is 0
b2 = effect of W on Y when X is 0
b3 = coefficient for interaction term, how does effect change with a one-unit change in W

Question 4

What questions are asked to establish a possible moderation effect?

Answer 4

If the regression coefficient for the product of XW is statistically significant, this means only that the effect of X on Y depends on W

how does Xs effect vary with W?

combinations of X and W → produces what estimates of Y?

Question 5

What does standardisation of X and W / mean centering of X and W mean?

Answer 5

Mean centering X or W = subtracting the mean from each value so that the new mean is zero

Question 6

Why could one consider mean centering of X and W?

Answer 6

• helps make the interpretation of b1 and b2 more intuitive. After mean centering, b1 represents the effect of X on Y when W is at its mean, and b2 represents the effect of W on Y when X is at its mean.
• This adjustment makes the “conditional” nature of these effects more relevant and easier to understand because the reference point (the mean) is often more meaningful than zero, particularly for variables where zero is an arbitrary or non-central value.

they now describe the effects of X and W on Y at the average level of the other variable.

Question 7

What is multicollinearity?

Answer 7

two or more predictor variables are highly correlated
-> can make it difficult to identify the individual effects of each X on Y

Question 8

Should mean centering be done to reduce negative effects of multicollinearity?

Answer 8

it does reduce it:

• values represent deviations from their mean
  -> reduces shared variance (interaction term and its constituent variables X and W)
  -> makes interpretation more meaningful
  oneunit change in X when W is at its mean, not zero

BUT
not necessary
- does not affect statistical tests or significance
- mathematically equivalent to non-centered variables
- what is the primary interest? if there are no issues in interpretation, not necessary

Question 9

Does moderation require hierarchical variable entry?

Answer 9

No

the significance of XW is tested by either

p-value

change in R2

-> mathematical identity
therefore, order of entry is arbitrary

Question 10

Does W need to be uncorrelated to X?

Answer 10

No

it is all but assured in social sciences

interpretationally convenient, but doesn’t need to be a mathematical requirement

focus on interaction term!! XW

individual effects are statistically controlled for

interpretation of interaction remains intact

Question 11

What type of effect are b1 and b2?

Answer 11

NOT main effects
= average effect of a factor at all levels of another factor

conditional effects
-> for a specific W value

not just a straightforward main effect like in ANOVA (simple regression, no interaction term)

Question 12

How should b1 and b2 be interpreted?

Answer 12

When there’s an interaction term in the model, b1 represents the effect of X on Y when W is zero. Similarly, b2 represents the effect of W on Y when X is zero. These interpretations become less intuitive, especially when zero is not a meaningful or central value for X or W.

Question 13

How would statistical testing roughly go in moderation analysis?

Answer 13

how to formally test a hypothesis about the size of the effect of X on Y at those values

simple slopes analysis, pick-a-point approach, spotlight analysis

→ pick two or more values of the moderator, estimate the conditional effects of X on Y

→ test whether those conditional effects are different from zero

SE is needed to complete the inference (is the conditional effect of X on Y at that value of W different from zero?)

Question 14

How can the standard error be estimated?

Answer 14

SE = root of (seb12 + 2W(COVb1b2) + W2seb32)
covariance between b1 and b3 = COV

Question 15

What is regression centering implementation?

Answer 15

centering W around the value chosen prior to computing the product when regressing Y and X, centered W, and X multiplied by the centered W.

using existing macros for SPSS and SAS
MODPROBE, RLM, PROCESS

Question 16

What are some drawbacks for statistical inference?

Answer 16

• W is continuous → no clear rationale for choosing specific values of the moderator
• use of arbitrary conventions invites inconsistencies
  different operationalisation of the same thing
  results might appear different, but are essentially the same
  • → use population norms
  • but those may not be available
  • Jonhynson-Neyman technique
    floodlight analysis
    → analytically derives the values from W and identifies points of transition along the continuum → regions of significance
    no requirement of picking categories of W

Question 17

Does anything change if X or W are not dichotomous but multicategorical?

Answer 17

NO

regression analysis methods can account for it!

Question 18

What is moderated mediation?

Answer 18

As an indirect effect (mediation) is an effect, and effects can be contingent (moderation), it follows that an indirect effect can be contingent.

-> the size of an indirect effect can be dependent on another variable

e.g. a therapeutic method might indirectly influence later symptoms by changing people’s cognitive appraisals, which in turn influences
symptoms experienced, but this mechanism might be stronger in people who have more social support.

Question 19

What is conditional process analysis?

Answer 19

collection of analytical
strategies that focuses on examining the contingencies of mechanisms and test hypotheses about how processes can vary between people or across contexts

the indirect effect of X on Y through one or more mediators M is no longer fixed to be a single number but, instead, becomes a function of one or more moderators.

Question 20

What are key statistics for moderation analysis?

Answer 20

Effect of X on Y

As with Mediation Analyses, investigating the relationship between X and Y variables is important to Moderation Analysis. The output from the Moderation Analysis will tell you if a relationship exists between X and Y and what type of relationship it is (i.e. positive or negative).

Interaction effect of X and W on Y (the moderator effect)

If your Moderator variable moderates the relationship between your X and Y variables, then your output will show a significant interaction effect. This tells us that the relationship between X and Y changes depending on the value of the third variable. In Moderation, the third variable is the Moderator in our model.

Question 21

How should moderation analysis be conducted in SPSS?

Answer 21

options → generate code for visualising interactions
→ -1, mean, SD

Int_1 → interaction term

X and W interaction

p-value → significant? → moderating effect!

• what is the moderating effect?
  
  • look at conditional effects of the focal…
    is there a significant p for the different W conditions?
  • scatterplot
    more detailled depiction of interaction

Question 22

What are the main conceptual differences between mediation and moderation?

Answer 22

Mediation examines the mechanism or the process through which X affects Y. The mediator (M) is a variable through which the independent variable exerts its effect on the dependent variable.

-> M is another related variable of X-Y

Moderation focuses on how or when X affects Y. The moderator (W) changes the strength and/or direction of the relationship between X and Y.

-> alters X-Y

Question 23

What questions do you ask in mediation and moderation analysis?

Answer 23

Mediation is about the process (how X leads to Y), whereas moderation is about the condition (when or under what circumstances X leads to Y).

Question 24

What pathways are examined in medation and moderation analysis?

Answer 24

In mediation, the interest is in the causal pathway through M. In moderation, the interest is in how the X-Y relationship varies at different levels of W.

Question 25

What is the nature of the third variable in mediation and moderation analysis?

Answer 25

In mediation, M is a variable that is influenced by X and, in turn, influences Y. In moderation, W is a variable that alters the impact of X on Y, but it’s not necessarily in a causal pathway from X to Y.

Question 26

How do moderation and mediation differ in their relationship with the independent variable X?

Answer 26

M is correlated with X

W is uncorrelated with X

Question 27

How do moderation and mediation differ in their sequence of operation?

Answer 27

X - M - Y

W preceedes both X and Y

Question 28

How do moderation and mediation differ in their role that causal relationships play?

Answer 28

M
dual roles
Y for X
X for Y

W
auxiliary X for Y

Question 29

How do moderation and mediation differ in their control design?

Answer 29

M
manipulated or observed

W
simply observed

Question 30

How do moderation and mediation differ in their application?

Answer 30

both: when causal effect is found

W
also when it is not found
-> not homogeneous for a specific variable

Question 31

How do moderation and mediation differ in their analogies?

Answer 31

M
dominos

W
dimmer switch for lighting

Question 32

How do moderation and mediation differ in their function?

Answer 32

M
links a cause and an effect
-> state

W
third variable that modifies a causal effect
-> trait

Question 33

What is my phrasing of the differences between mediation and moderation?

Answer 33

can you say that moderation is:
how does the relationship between X and Y change when a specific condition is administered that it appears in?

and mediation would be more like, is the relationship influenced by another variable that can also explain the effect X has on Y?

Question 34

So finally, what was chatgpts summary of the processes ongoing in moderation and mediation analysis?

Answer 34

moderation
1. X and Y relationship
2. introduction of W
3. change in relationship

mediation
1. direct relationship
2. introduction of M
3. path analysis
4. indirect effect

Question 35

What is a good example to understand the difference between mediation and moderation?

Answer 35

X - hope
Y - QoL

M - depression
M - resilience

W - sex

=> Sex was the moderator on the direct path between hope and QOL. The relationship between hope and QOL was mediated by resilience and depression in both sexes. When compared with female patients, the effect of hope on QOL was completely mediated by resilience and depression in males. In female patients, the model was partially mediated, and the direct effect of hope on QOL was significantly negatively correlated with the level of hope.