Understanding Categorical Variables in Logistic Regression with R

Introduction

Logistic regression is a widely used statistical model for predicting the probability of an event occurring based on one or more predictor variables. In many cases, these predictor variables can be categorical, making it essential to understand how to handle them correctly in logistic regression.

In this article, we will delve into the world of categorical variables in logistic regression using R as our programming language of choice. We will explore what makes a variable categorical and provide practical examples on how to implement categorical variables in your logistic regression models.

What Makes a Variable Categorical?

A categorical variable is one that takes on distinct categories or values, rather than being continuous. For instance:

• Gender: Male/Female
• Professional Fields: Student, Worker, Teacher, Self-Employed

These are all examples of categorical variables because they have discrete values.

The Problem with Not Handling Categorical Variables Correctly

When we don’t handle categorical variables correctly in logistic regression, it can lead to misleading results and poor model performance. This is often due to the fact that these variables do not have a true zero value, making it impossible for the model to determine when the variable should be treated as zero or non-zero.

Creating Dummy Variables: A Common Approach

One common approach to handle categorical variables in logistic regression is to create dummy (or indicator) variables. These are new variables created from the original categorical variable by including only one level of the category and setting all other levels to zero.

For example, let’s say we want to model the influence of professional fields on the probability of a purchase using the following data:

To create dummy variables for x3, we can use the following R code:

set.seed(123)
y <- round(runif(100,0,1))
x1 <- round(runif(100,0,1))
x2 <- round(runif(100,20,80))
x3 <- factor(round(runif(100,1,4)), labels = c("student", "worker", "teacher", "self-employed"))

# Create dummy variables
dummies <- cbind(x1, x2, x3)

However, using this approach can result in a large number of coefficients in our model, which can be computationally expensive and may lead to overfitting.

Alternative Approach: Factor Variables

A more efficient alternative is to treat categorical variables as factor variables. This means we no longer create dummy variables for each category but instead include the original categorical variable directly into our model.

In R, we can achieve this by modifying our code as follows:

set.seed(123)
y <- round(runif(100,0,1))
x1 <- round(runif(100,0,1))
x2 <- round(runif(100,20,80))
x3 <- factor(round(runif(100,1,4)), labels = c("student", "worker", "teacher", "self-employed"))

# Fit the logistic regression model
test <- glm(y ~ x1 + x2 + x3, family = binomial(link = "logit"))
summary(test)

Conclusion

In this article, we explored how to handle categorical variables in logistic regression using R. We discussed what makes a variable categorical and provided practical examples on how to implement them correctly.

We also compared the use of dummy variables versus factor variables and found that factor variables are often a better choice for modeling categorical variables due to their ease of interpretation and computation efficiency.

By following these best practices, you can ensure that your logistic regression models provide accurate results and robust conclusions.

Last modified on 2023-12-11