Moderation Recap

• With moderation we're looking at when variables are related

• 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 Recap

• 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

  • But don't forget: correlation does not equal causation unless you have a causal design!!

• We run a moderation in the same way as a linear model but with 3 predictors:

Moderation Recap

• With our 3 predictors: we have two main effects (i.e., 'lower-order effects'), and one interaction effect (i.e., 'higher-order effects') or in our case the moderation!

• When using a linear model with multiple predictors normally, each of the effects (bs) are interpreted when the other variables in the model are 0

• But the interaction term in our moderation analysis means that the bs for the main effects are usually uninterpretable unless we centre our predictors...

Step 1: Grand Mean Centring

• For continuous variables, we centre them by transforming them into deviations around a fixed point - in grand mean centring this 'fixed point' is the overall mean of that variable

• We can then interpret our effects at average levels of the other variable rather than at 0

• To center our predictor and moderator, the code is nice & easy!

data <- data %>% 
  dplyr::mutate(
    predictor_cent = predictor - mean(predictor, na.rm = TRUE),
    moderator_cent = moderator - mean(moderator, na.rm = TRUE))Copy Code

Step 1: Grand Mean Centring

• For continuous variables, we centre them by transforming them into deviations around a fixed point - in grand mean centring this 'fixed point' is the overall mean of that variable

• We can then interpret our effects at average levels of the other variable rather than at 0

• To center our predictor and moderator, the code is nice & easy!

data <- data %>% 
  dplyr::mutate(
    predictor_cent = predictor - mean(predictor, na.rm = TRUE),
    moderator_cent = moderator - mean(moderator, na.rm = TRUE))Copy Code

Step 2: Fitting our Model

• Once we've centred our predictor and moderator, we can fit our model!

• The code for fitting our model should be familiar to us:

my_model <- lm(outcome ~ predictor*moderator, data = data)Copy Code

• We can then summarise our model, which should also be familiar to us...

summary(my_model)
broom::tidy(my_model, conf.int = TRUE)
broom::glance(my_model)Copy Code

Moderations VS Interactions

• You might have noticed that the code to do a moderation analysis, is the exact same as interactions from last term! 🤯

• That's because they're essentially the same thing, except:

  • Interactions are used mainly with two categorical predictors

  • Moderations are used with at least one continuous predictor

• They also differ conceptually...

• In moderations we're implying that one of the variables is the driver of the differences in effects - one of our variables is the predictor, and one of them is the moderator

  • With interactions, we don't make that conceptual distinction - they're both seen as predictors

Step 3: Interpretation

• Now we've fit our model, we want to interpret the results!!

• The model summary tells us whether we have significant main effects of our predictor and moderator, and also if we have an interaction effect (a moderation)

• The Johnson-Neyman interval shows us a 'zone of significance'

• The Simple Slopes analysis compares the relationship between predictor and outcome, at low, average, and high values of the moderator

• The Interaction Plot visualises the Simple Slopes analysis

Interpretation: Code

For Simple Slopes & Johnson-Neyman interval:

interactions::sim_slopes(model_lm,
  pred = predictor,
  modx = moderator,
  jnplot = TRUE,
  confint = TRUE)Copy Code

For the Interaction Plot:

interactions::interact_plot(model_lm,
  pred = predictor,
  modx = moderator,
  x.label = "Predictor Label",
  y.label = "Outcome Label",
  legend.main = "Moderator Label")Copy Code

Categorical Moderators

• The process and interpretation is essentially the same for categorical moderators

• The only differences are that:

  • We can't grand mean centre the moderator (but we should with our predictor)

  • & we can't get a Johnson Neyman Interval

Different Slopes for Different Folks

• In our final model, we have two Main Effects but no Moderation effect suggesting that the slopes of attractiveness on dating potential are the same for funny and dull dates...

• But what if we did have a moderation? What might that look like? Give it a go on the next slide!!

That's all - happy moderating!