Introduction
In regression modelling, interaction terms play a crucial role. They are incorporated to capture the combined effect of two or more independent variables on the dependent variable. Often, the relationship between control and target variables isn’t just simple. Interaction terms become valuable when the effect of one independent variable on the dependent variable depends on the level of another independent variable. In this blog, we’ll explore interaction terms through a simulated e – commerce user – behavior scenario.
Learning Objectives
Understand how interaction terms enhance the predictive power of regression models. Learn to create and incorporate them in regression analysis. Analyze their impact on model accuracy with a practical example. Visualize and interpret their effects on predicted outcomes. Gain insights into when and why to apply them in real – world scenarios.
Understanding the Basics of Interaction Terms
In real life, variables don’t work in isolation. For instance, on an e – commerce platform, the time a user spends can be affected differently by adding items to the cart and then making a purchase. Adding interaction terms to a regression model acknowledges these intersections, improving the model’s ability to explain data patterns and predict the dependent variable. Mathematically, in a simple linear regression with two independent variables \(X_1\) and \(X_2\): \(Y=\beta_0+\beta_1X_1+\beta_2X_2+\epsilon\). To add an interaction term, we introduce \(X_1\cdot X_2\): \(Y = \beta_0+\beta_1X_1+\beta_2X_2+\beta_3(X_1\cdot X_2)+\epsilon\), where \(\beta_3\) represents the interaction effect.
How Interaction Terms Influence Regression Coefficients?
\(\beta_0\) is the intercept, \(\beta_1\) is the effect of \(X_1\) on \(Y\) when \(X_2 = 0\), \(\beta_2\) is the effect of \(X_2\) on \(Y\) when \(X_1 = 0\), and \(\beta_3\) shows the change in the effect of one variable on \(Y\) for a one – unit change in the other.
Simulated Scenario: User Behavior on an E – Commerce Platform
We created a simulated dataset with variables like added_in_cart, purchased, and time_spent. Our goal is to predict the time users spend on an e – commerce site based on adding items to the cart and making a purchase. First, we built an ordinary least square regression model without considering interaction effects, hypothesizing that each action separately affects the time spent. Then, we constructed a model with the interaction term between adding items to the cart and making a purchase.
Model Without an Interaction Term
The model without the interaction term had a mean squared error (MSE) of 2.11, accounting for about 80% (test R – squared) and 82% (train R – squared) of the variance in time_spent. While it was reasonably accurate, there was room for improvement, especially in capturing higher time_spent values.
Model With an Interaction Term
The model with the interaction term showed a better fit. The test R – squared increased from 80.36% to 90.46%, and the MSE decreased from 2.11 to 1.02. The predicted values were closer to the actual values, indicating that the interaction term helped express how user actions collectively affect the time spent.
Comparing Model Performance
Comparing the two models, the model without the interaction term had more dispersed predictions for higher actual time spent values. The model with the interaction term produced more accurate predictions, with points closer to the diagonal line.
Conclusion
Adding interaction terms can enhance a model’s performance. In our example, they captured additional information not evident from main effects alone. Considering interaction terms in regression models can lead to more accurate and insightful predictions in real – world applications.
