Skills Lab 09: Moderation

.title[
# Skills Lab 09: Moderation
]
.subtitle[
## <i>Different Slopes for Different Folks</i>
]
.author[
### Dr Danielle Evans
]
.date[
### 23 March 2022
]

---

## Overview

**Continuous Moderators & Categorical Moderators**

- Step 1: Centring

- Step 2: Fit Model

- Step 3: Interpretation
  
  + Johnson Neyman Interval
  
  + Simple Slopes Analysis
  
  + Interaction Plot

---

## 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:

<br>

---

## 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** (__*b*s__) are interpreted when the other variables in the model are **0**

- But the interaction term in our moderation analysis means that the *b*s 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!

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

<div class="tu" style="font-size:90%">
<p><b>Top Tip!</b> We only need to centre our <b>predictor</b> & <b>moderator</b> - not the <b>outcome</b>! </p>
</div>

---

## 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!

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

<div class="pc" style="font-size:90%">
<p><b>Demo!</b> Grand Mean Centring! </p>
</div>

---

## 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:

```r
my_model <- lm(outcome ~ predictor*moderator, data = data)
```

<br>

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

```r
summary(my_model)

broom::tidy(my_model, conf.int = TRUE)
broom::glance(my_model)
```

<div class="pc" style="font-size:90%">
<p><b>Demo!</b> Fitting & summarising our model! </p>
</div>

---

## 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**:

```r
interactions::sim_slopes(model_lm,
  pred = predictor,
  modx = moderator,
  jnplot = TRUE,
  confint = TRUE)
```

For the **Interaction Plot**:

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

<div class="pc" style="font-size:90%">
<p><b>Demo!</b> Interpreting our model! </p>
</div>
---

## 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**

<div class="pc" style="font-size:90%">
<p><b>Demo!</b> Fitting, summarising & interpreting our second model! </p>
</div>

---

## 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!!

---

## Different Slopes for Different Folks

- We already have the line for the **funny** group, let's try drawing a line for the **dull** group if we *did* have a moderation!

<br>

---

## *That's all - happy moderating!*

[Give session feedback here!](https://forms.gle/ZyXAB7kZzUUyct9n6) 😀

]