Alternative ways to show impact of interaction term

As a data analyst or researcher, communicating the results of your statistical models to others can be a challenging task. When working with interaction terms in regression analysis, it’s essential to choose an appropriate visualization method to effectively convey the relationship between variables.

In this article, we’ll explore alternative ways to visualize the impact of an interaction term in regression analysis. We’ll start by examining the original code provided and then delve into various methods for presenting interaction effects in a clear and concise manner.

Understanding Interaction Terms

Before diving into visualization techniques, it’s crucial to understand what interaction terms represent. In regression analysis, an interaction term is used when two or more continuous variables are modeled together. The product of these variables represents the effect of each variable on the outcome while controlling for the other variables.

For example, in the provided R code:

ex <- lm(Sepal.Length ~ (Sepal.Width + Petal.Length)^2, data = iris_scaled)

The interaction term (Sepal.Width + Petal.Length)^2 indicates that we’re modeling the effect of Sepal.Width and Petal.Length separately while also accounting for their combined effect.

Original Code

Let’s examine the original code provided:

iris_scaled <- iris %>% 
  mutate_at(vars(-Species), my_scale)

ex <- lm(Sepal.Length ~ (Sepal.Width + Petal.Length)^2, data = iris_scaled)

GGally::ggcoef(ex, conf.level = 0.90, exclude_intercept = TRUE) + 
  ggtitle("Interaction of sepal width and petal length associated with 
smaller sepal length") +
  theme_classic()

The GGally package is used to generate a confidence interval for the interaction term using a graphical approach.

Alternative Methods

Quantizing Continuous Variables

One way to visualize interactions is by quantizing one of the continuous variables into example bins. This can help show how the slope of the first variable changes over that range.

library(broom)

augment(
  lm(Sepal.Length ~ (Sepal.Width + Petal.Length)^2, data = iris),
  newdata = 
    expand.grid(Sepal.Width  = range(iris$Sepal.Width),
                Petal.Length = quantile(iris$Petal.Length))
) %>% 
ggplot(aes(Sepal.Width, .fitted, color = Petal.Length)) + 
geom_line(aes(group = Petal.Length)) +
geom_point(data = iris, aes(y = Sepal.Length)) +
scale_color_gradient(low = "blue", high = "green") +
theme_classic()

In this example, we’re creating a new data frame with expand.grid that includes bins for both Sepal.Width and Petal.Length. We then use the augment function to add predicted values from the model. The resulting plot shows how the slope of Sepal.Length changes as Sepal.Width increases, while controlling for Petal.Length.

However, be cautious not to misinterpret these plots. You must explicitly label them as conditional model predictions and indicate which variable is being “conditioned on.”

Inverting Visualization

The previous plot can also be turned around by reversing the roles of Sepal.Width and Petal.Length. This demonstrates how the interaction effect changes when the variables are swapped.

augment(
  lm(Sepal.Length ~ (Petal.Length + Sepal.Width)^2, data = iris),
  newdata = 
    expand.grid(Petal.Length = range(iris$Petal.Length),
                Sepal.Width = quantile(iris$Sepal.Width))
) %>% 
ggplot(aes(Petal.Length, .fitted, color = Sepal.Width)) + 
geom_line(aes(group = Sepal.Width)) +
geom_point(data = iris, aes(y = Sepal.Length)) +
scale_color_gradient(low = "blue", high = "green") +
theme_classic()

In this example, the plot shows how the slope of Sepal.Length changes as Petal.Length increases, while controlling for Sepal.Width.

Conclusion

When working with interaction terms in regression analysis, choosing an appropriate visualization method is crucial. By quantizing one of the continuous variables or inverting the roles of the variables, you can present the interaction effect in a clear and concise manner.

However, it’s essential to carefully label these plots as conditional model predictions and indicate which variable is being “conditioned on.” This ensures that your audience understands the context and meaning behind the plot.

By exploring alternative visualization techniques, you can effectively communicate the results of your statistical models to others. Whether working with the GGally package or creating custom plots, there are many ways to present interaction effects in a way that’s easy to digest.

Additional Resources

For more information on working with interactions in regression analysis, we recommend checking out the following resources:

Broom: A package for tidy statistical modeling.
GGally: A package for producing informative and attractive statistical graphics.
Tidyverse documentation: Official documentation for the Tidyverse packages.

I hope this article has provided you with a deeper understanding of alternative ways to show impact of interaction term. If you have any questions or need further clarification, please don’t hesitate to ask.

Last modified on 2024-09-15