Practice Set: Interactions

Multiple Regression

Let’s take a look at the iris data set!

##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa
##   Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
##  Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100  
##  1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300  
##  Median :5.800   Median :3.000   Median :4.350   Median :1.300  
##  Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199  
##  3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800  
##  Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500  
##        Species  
##  setosa    :50  
##  versicolor:50  
##  virginica :50  
##                 
##                 
##

You Try!

  • Build a multiple regression model with Petal Length as the outcome and Sepal Length and Sepal Width as predictors.
  • Name it mod_cont.

Let’s interpret those coefficients!

  • What does the estimate for the intercept mean?
  • What do the coefficients for each variable mean?
  • If the Estimate for Sepal Length was 2 and the Standard Error was 0.5, what would the t-value be?
  • What do the p-values mean?
  • What does the \(R^2\) stand for?

You try!

  • Let’s build a multiple regression model with Petal Length as the outcome and Sepal Length and Species as predictors.
  • Name it mod_cat.

Let’s interpret those coefficients!

  • What is the reference (base) category?
  • What does the estimate for the intercept mean?
  • What do the coefficients for each variable mean?

Continuous Predictors Interacting

You try!

  • Let’s build a regression model with Petal Length as the outcome and Sepal Length and Sepal Width as predictors that interact.
  • Name it mod1.
  • We’ll reference mod1throughout the assignment, so don’t forget what it stands for!

Let’s interpret those coefficients!

  • What does the estimate for the intercept mean?
  • What do the coefficients for each variable mean?
  • What happened to the coefficient of Sepal Length compared to the multiple regression model mod_cont?

Quick Quiz

☝️ Good job! You can work with continuous variable interactions!

Simple Slopes

A great way of understanding interactions is by visualizing them!

Example 1:

First, choose which package you want to use. We’ll start with sjPlot.

library(sjPlot)

Plug in your regression model(we’ll use mod1) and plot the interaction!

plot_model(mod1, type = "pred",terms = c("Sepal.Width","Sepal.Length"))

Now, we’ll look at these interactions for mod1 when Sepal.Width equals 2 and 3.

plot_model(mod1, type = "pred", terms = c("Sepal.Width", "Sepal.Length[2,3]"))

You try!

  • Let’s visualize this model: Sepal.Width ~ Sepal.Length*Petal.Length using the sjPlot package
  • Name your regression model mod_width
  • Then let’s visualize this models when Sepal.Length is 4 and 6

Let’s look at these interactions across Species. For this, we’ll need to create a new regression model first.

mod1_species<-lm(Petal.Length~Sepal.Length*Sepal.Width+Species, data=iris)

plot_model(mod1_species, type = "pred", terms = c("Sepal.Length", "Sepal.Width", "Species"))

Example 2:

There are many ways of exploring an interaction. Now we’re going to try using the reghelper package to look at the significance of our simple slopes at specific levels.

Using mod1, let’s see if Sepal Width is a significant predictor of Petal Length at different levels of Sepal Length (specifically when Sepal Length is 5 and 6).

simple_slopes(mod1, levels = list(Sepal.Length = c(5,6)))
##   Sepal.Length Sepal.Width Test Estimate Std. Error  t value  df  Pr(>|t|) Sig.
## 1            5      sstest       -1.6709     0.1631 -10.2436 146 < 2.2e-16  ***
## 2            6      sstest       -1.1652     0.1326  -8.7874 146 3.842e-15  ***
# what do these results mean?

You try!

  • Now let’s see if Sepal Length is a significant predictor of Sepal Width at different levels of Petal length (specifically when Petal Length is 4 and 6).
  • Please use the reghelper package
  • HINT: check slide 53

Example 3:

Just like how there are many ways of exploring simple slopes, there are also many ways of visualizing interactions!

Let’s visualize mod1 using the package ggeffects.

predict<- ggpredict(mod1, terms =
                      c("Sepal.Width","Sepal.Length"))

plot(predict)

There’s something cool about this function, though. Check out the data that ggpredict creates!

predict
## # Predicted values of Petal.Length
## 
## # Sepal.Length = 5.02
## 
## Sepal.Width | Predicted |        95% CI
## ---------------------------------------
##        2.00 |      4.09 | [ 3.71, 4.48]
##        2.40 |      3.43 | [ 3.16, 3.70]
##        2.80 |      2.77 | [ 2.59, 2.95]
##        3.20 |      2.10 | [ 1.96, 2.25]
##        3.60 |      1.44 | [ 1.23, 1.64]
##        4.40 |      0.11 | [-0.31, 0.53]
## 
## # Sepal.Length = 5.84
## 
## Sepal.Width | Predicted |       95% CI
## --------------------------------------
##        2.00 |      5.09 | [4.82, 5.36]
##        2.40 |      4.59 | [4.41, 4.78]
##        2.80 |      4.09 | [3.98, 4.21]
##        3.20 |      3.60 | [3.49, 3.70]
##        3.60 |      3.10 | [2.93, 3.27]
##        4.40 |      2.10 | [1.76, 2.44]
## 
## # Sepal.Length = 6.67
## 
## Sepal.Width | Predicted |       95% CI
## --------------------------------------
##        2.00 |      6.10 | [5.65, 6.55]
##        2.40 |      5.77 | [5.47, 6.07]
##        2.80 |      5.44 | [5.27, 5.61]
##        3.20 |      5.11 | [4.95, 5.27]
##        3.60 |      4.78 | [4.51, 5.05]
##        4.40 |      4.12 | [3.54, 4.69]

What does this output mean?

Make it pretty!

What is this graph telling you?

Massive shout out to the Fall 2022 AI Selin Toprakkiran for creating this excellent Practice Set!