Mediation and Moderation Flashcards
Mediation:
- Occurs when the relationship between a predictor and an outcome, can be explained by their relationship to a third variable - the mediator
- With , mediation we’re looking at how variables are related, we’re attempting to further our understanding by explaining the relationship between the predictor and the outcome - we’re interested in pathways:
- Change in the predictor = change in the mediator = change in the outcome
Mediation 2:
- We can use a mediation model whenever we use a linear model
- A mediation is essentially a few linear models
- Can be used in correlational or experimental designs
- The mediator used and the pathways should be theoretically driven
- We can investigate further to check if our decisions are appropriate
- But we need to be careful with our interpretations and conclusions:
- With mediation were implying there is a directional path between our variables, but without a casual design, we cannot infer causality from our results
Mediation - pathways:
· We start with the Total Effect, which is the simple relationship between predictor and outcome, where we’re not adjusting for any other variables:
· It might help to think of it as being the overall relationship between your two variables…
· We then partition this Total Effect into:
- An Indirect Effect which is the effect of the predictor on the outcome, through the mediator
- & a Direct Effect which is the effect of the predictor on the outcome, after adjusting for the mediator
Mediation - partitions:
· The terms for each of these pathways can feel counter-intuitive…
· The Total Effect is comprised of the Indirect Effect AND the Direct Effect
· Even though we call it the Total Effect, it’s still just the simple relationship between predictor and outcome - we haven’t accounted for any other variables
· By adding in a mediator, we can see how much of this Total Effect is a Direct Effect of our predictor, and how much can be explained by our mediator (i.e., the Indirect Effect)
A mathsy mediation example:
· SES is a predictor of children’s maths aainment (Evans et al., 2018, 2020a, 2020b, 2020c)
· There are many possible mechanisms underlying this relationship, which is what we are trying to uncover with a mediation
· So, starting with the simple relationship between predictor and outcome, we have the Total Effect of SES on children’s maths ability:
· We can then include a mediator in our model to see how SES is related to children’s maths ability, and whether this relationship can be explained by another variable…
A mathsy mediation example 2:
· You should use theory and research to decide what the mediator might be in this scenario
· For today, parental involvement in educational activities seems to be a sensible mediator
· And so our mediation model is:
· We’re testing whether SES predicts maths ability, and if/how much of this relationship can be explained by parental involvement in education
Doing a mediation:
- Does the predictor predict the outcome (Total Effect)
· We could theoretically test this with a simple regression in R- Separate the Total Effect into an Indirect Effect (path ab) by first working out path
- Separate the Total Effect into an Indirect Effect (path ab) by first working out path a, and then path b, adjusting for the predictor:
· We could test this with a multiple regression in R where we adjust for our predictor
- We need to adjust for the predictor because if we don’t control for it the outcome and the mediator could be correlated just because our predictor is related to them both - See whether our predictor still predicts our outcome path c (the Direct Effect), after accounting for the Indirect Effect:
· We could test this with a multiple regression in R where we adjust for our mediator
Interpreting results:
· We can interpret the bs in the same way as we would with a linear model:
- Path a tells us the effect for the predictor on the mediator
- Path b tells us the effect for the mediator on the outcome adjusting for the predictor
- Path c (Direct Effect) tells us the effect for the predictor on the outcome adjusting for the mediator
- The Indirect Effect tells us whether there is a mediation
- The Total Effect tells us the effect of the predictor on the outcome, NOT adjusting for the mediator
Interpreting results 2:
· To see if we have a significant mediation, we look at the size, the confidence interval, and the p-value of the Indirect Effect
- If the confidence intervals do not contain 0 and if the p-value is less than .05 then we can say there is a mediation effect
· We can have different types of mediation:
- Partial mediation is when the Direct Effect (c) is reduced but still significant - there’s both an indirect and direct effect of the predictor on the outcome
- Full mediation is when Direct Effect (c) reduced to non-significance - the effect of the predictor on the outcomes goes entirely through the mediator
· It’s generally best to avoid thinking of mediations as being full or partial when based on p-values because of the all-or-nothing conclusions drawn from significance tests, instead, it’s beer to ask: is the size of the mediation effect substantial enough to care about it?
Moderation:
· With moderation were looking at when variables are related
· With moderation we can investigate whether the effect of our predictor is the same for all people or whether it differs under different conditions depending on the value of another variable - the moderator
· Differences could be the presence of an effect, the size of the effect, or the direction of the effect.
Moderation 2:
· A moderator is a variable that affects the relationship between two others - it modifies it
· Can be used in correlational or experimental designs with continuous or categorical variables
Moderation 3:
· The key conceptual difference is that you are implying a variable (the moderator) alters the relationship between the other two variables
· The moderator chosen should be theoretically driven - the same as a mediation
· However, the same issues around causation apply here too
· We are implying a directional relationship (i.e., the moderator modifies the relationship) but correlation does not equal causation unless you have a causal design
The catch:
· When using a linear model with multiple predictors, each of the effects (bs) are interpreted when the other variables in the model are 0
· So if we had parental maths anxiety and parental homework help as predictors in a non-moderated linear model, we would interpret the b of parental maths anxiety when parental homework help is at 0, and vice versa
· In some scenarios this interpretation isn’t problematic because 0 is a plausible and meaningful score
- I.e., a child could get a score of 0 on our maths anxiety measure meaning they have no anxiety at all
· But often it doesn’t make sense for a predictor to be interpreted in this way because a score of 0 isn’t possible or doesn’t make sense
- Imagine we measured parental anxiety by measuring heart rate, here, a score of 0 would indicate something is very wrong with our participant
· The interaction term in our moderation means that the bs for the main effects are usually uninterpretable..
Grand mean cutting:
· So, to make interpretation easier, we centre our variables by transforming them into deviations around a fixed point - in grand mean centring this ‘fixed point’ is the overall mean of that measure
· We can then interpret our effects at average levels of the other variable
· This applies to our predictor and moderator only
- We don’t need to centre our outcome because we interpret the effects of our predictors at specific values of our bs, with grand mean centring, this ‘specific value’ becomes the mean of the other variable(s)
· Centring is super easy to do in R with mutate() and mean(), we’re just taking the overall mean away from each participant individual score - we’ll go over the code in your skills lab this week
· So what happens is that our predictors and moderators now shift to have a mean of 0 but the overall distribution stays the same
Probing interactions:
· If we find a significant moderation effect, we need to follow it up to understand how the relationship between the predictor and the outcome changes at different values of the moderator
- Remember that a moderation can occur from differences in effect presence, size, direction or …
- Without probing the interaction further, we don’t know what’s actually happening in this relationship
· We can use two techniques to follow up a significant interaction effect:
- Simple slopes
- Johnson-Neyman interval
· These tell us the coefficient for our predictor (i.e., the effect it has on our outcome) at different values of our moderator
