Calculating Marginal Effects for GLM (Logistic) Models in R

Introduction

In logistic regression analysis, marginal effects refer to the change in the predicted probability of an event occurring as a result of a one-unit change in a predictor variable, while holding all other predictor variables constant. Calculating marginal effects is essential for understanding the relationship between predictor variables and the response variable.

In this article, we will explore two popular packages used in R for calculating marginal effects: margins and mfx. We’ll delve into their features, strengths, and limitations, providing a comprehensive overview of how to use each package to calculate marginal effects for logistic regression models.

Background

Logistic regression is a type of regression analysis that predicts the probability of an event occurring based on one or more predictor variables. The model is characterized by a log-odds ratio, which represents the change in the log-odds of the response variable as a result of a one-unit change in a predictor variable.

In logistic regression, marginal effects are calculated using the partial derivative of the log-odds function with respect to each predictor variable. This partial derivative represents the change in the log-odds of the response variable as a result of a one-unit change in the predictor variable, while holding all other predictor variables constant.

The `margins` Package

The margins package is one of the most widely used packages for calculating marginal effects in R. It provides a simple and intuitive interface for calculating marginal effects, interaction terms, and odds ratios.

Installation

To install the margins package, use the following command:

install.packages("margins")

Loading the Package

Load the margins package using the following code:

library(margins)

Calculating Marginal Effects

To calculate marginal effects using the margins package, use the margins() function and specify the model formula as an argument. For example:

logit <- glm(y ~ x1 + x2, data = mydata)
margins(logit, variable = "x1", control = list(fraction = 0.05))

In this code, logit is the logistic regression model, and x1 is the predictor variable of interest. The margins() function calculates the marginal effects for x1, while holding all other predictor variables constant.

The `mfx` Package

The mfx package provides an alternative method for calculating marginal effects in R. It uses a different approach, which involves computing the change in the predicted probabilities of the response variable as a result of a one-unit change in each predictor variable.

Installation

To install the mfx package, use the following command:

install.packages("mfx")

Loading the Package

Load the mfx package using the following code:

library(mfx)

Calculating Marginal Effects

To calculate marginal effects using the mfx package, use the mfx() function and specify the model formula as an argument. For example:

logit <- glm(y ~ x1 + x2, data = mydata)
mfx(logit, variable = "x1")

In this code, logit is the logistic regression model, and x1 is the predictor variable of interest.

Comparison of `margins` and `mfx`

Both packages provide similar functionality for calculating marginal effects. However, there are some key differences between them:

Interpretation: The margins package provides an odds ratio interpretation for the marginal effects, while the mfx package provides a probability interpretation.
Computational Approach: The margins package uses a different computational approach to calculate marginal effects, which involves computing the partial derivative of the log-odds function. In contrast, the mfx package uses an alternative method that computes the change in predicted probabilities.

Criticism of Other Packages

As mentioned earlier, the author of the margins package criticized other packages used for calculating marginal effects as they do not account for interaction terms properly. However, this criticism does not necessarily imply that these packages are incorrect or unreliable.

Other packages, such as calibration, provide an alternative approach to calculating marginal effects that accounts for interaction terms and other complexities of logistic regression analysis. These packages can be useful tools in the statistical toolkit, but they require careful consideration and interpretation to ensure accurate results.

Conclusion

Calculating marginal effects is a crucial step in understanding the relationship between predictor variables and the response variable in logistic regression analysis. Both margins and mfx packages provide reliable methods for calculating marginal effects, with different strengths and limitations.

By choosing the right package and using them correctly, researchers can gain valuable insights into the relationships between predictor variables and the response variable. Additionally, by considering alternative approaches and interpretations, researchers can ensure that their results are accurate and reliable.

Example Use Case

Suppose we have a logistic regression model that predicts the probability of a customer making a purchase based on their age and income:

# Create a sample dataset
set.seed(123)
n <- 1000
age <- rnorm(n, mean = 40, sd = 10)
income <- rnorm(n, mean = 50000, sd = 20000)
y <- ifelse(age > 50 | income > 60000, 1, 0)

# Fit the logistic regression model
logit <- glm(y ~ age + income, data = mydata)

To calculate marginal effects for this model using the margins package:

# Calculate marginal effects
margins(logit, variable = "age", control = list(fraction = 0.05))
margins(logit, variable = "income", control = list(fraction = 0.05))

This code calculates the marginal effects for age and income, while holding all other predictor variables constant.

To calculate marginal effects using the mfx package:

# Calculate marginal effects
mfx(logit, variable = "age")
mfx(logit, variable = "income")

This code provides an alternative approach to calculating marginal effects for age and income.

Last modified on 2025-03-22