Added variable plots, also known as partial regression leverage plots or adjusted partial residual plots, are powerful tools in the field of statistical analysis. They allow data analysts to visualize the relationship between a predictor variable and the response, after adjusting for all other predictor variables in a multiple linear regression model. In this comprehensive guide, we’ll focus on the creation of added variable plots using R.
I. Introduction to Added Variable Plots
The added variable plot is a graphical tool that can illustrate the marginal effect of adding a variable to a regression model. Each plot gives a unique view of the relationship between the response variable and one predictor variable, accounting for the effects of all other predictor variables. This can help with tasks such as assessing linearity, detecting outliers, and understanding interactions in your data.
II. Understanding the Data for Added Variable Plots
For an added variable plot, you’ll typically work with a dataset containing one or more continuous predictor variables and a continuous response variable. You might use an added variable plot when you want to visualize how each predictor contributes to the prediction of the response, after taking into account the effects of other predictors.
For instance, consider a dataset with the salaries of individuals along with their years of experience, education level, and age. An added variable plot could help you visualize how much additional information each predictor (e.g., education level) brings to the model after accounting for the other predictors (e.g., years of experience and age).
III. Creating a Basic Added Variable Plot in R
To create added variable plots in R, we’ll use the ‘car’ package, which provides advanced regression diagnostics. If you haven’t installed it yet, you can do so with the command install.packages("car").
Let’s assume we have a dataset on salaries:
# Load the necessary package
library(car)
# Create a data frame
salary_data <- data.frame(
Salary = c(50, 60, 65, 70, 65, 55, 80, 75, 85, 95),
Experience = c(2, 4, 6, 8, 10, 1, 10, 12, 14, 16),
Education = c(3, 3, 4, 4, 5, 3, 5, 5, 6, 6),
Age = c(22, 25, 28, 30, 35, 24, 36, 38, 40, 42)
)
# Run a linear regression
model <- lm(Salary ~ Experience + Education + Age, data = salary_data)An added variable plot can be created using the avPlots() function:
# Create added variable plots
avPlots(model)
This will create a separate plot for each predictor in the model. Each plot shows the relationship between the response variable and one predictor, after adjusting for all other predictors.
IV. Customizing Added Variable Plots in R
Like other R functions, avPlots() allows for extensive customization to cater to specific visualization needs.
1. Selecting Specific Variables
To create an added variable plot for a specific predictor, use the variables argument:
# Create an added variable plot for the 'Experience' predictor
avPlots(model, variables = "Experience")2. Adjusting Plot Layout
You can adjust the layout of the plots using the layout argument:
# Create added variable plots with a custom layout
avPlots(model, layout = c(2, 2))Here, layout = c(2, 2) specifies that the plots should be arranged in a 2 by 2 grid.
3. Adding a Grid
You can add a grid to the plots using the grid argument:
# Create added variable plots with a grid
avPlots(model, grid = TRUE)V. Conclusion
Added variable plots can reveal a lot about the relationships in your data that might be missed with standard scatterplots or boxplots. They provide an excellent way to see how each predictor contributes to the response variable after adjusting for all other predictors in a multiple regression model.