Creating Effect Plots of Results from Ordinal Regression (with Interactions)

Ordinal regression is a powerful statistical technique used to model the relationship between a dependent variable with multiple ordered categories and one or more independent variables. However, interpreting the results of ordinal regression can be challenging, especially when interactions are involved. One effective way to overcome this challenge is by creating effect plots, which visually display the relationships between the variables. In this article, we’ll explore how to create effect plots of results from ordinal regression with interactions.

What is Ordinal Regression?

Ordinal regression is a type of regression analysis used when the dependent variable has multiple categories that have a natural order or ranking. For example, a survey question with response options such as “Strongly Disagree”, “Disagree”, “Neutral”, “Agree”, and “Strongly Agree” is an ordinal variable. Ordinal regression models the probability of each category based on the values of one or more independent variables.

Why are Effect Plots Important?

Effect plots are essential in ordinal regression because they help to:

• Visualize the relationships between the variables, making it easier to identify complex patterns and interactions.
• Communicate the results of the analysis to stakeholders, including non-technical audiences.
• Facilitate the interpretation of the regression coefficients, which can be difficult to understand in isolation.

Software and Packages

To create effect plots, we’ll use the popular R programming language and the following packages:

• ordinal for fitting the ordinal regression model
• effects for calculating the effects of the independent variables
• ggplot2 for creating the effect plots

Data Preparation

# Load the necessary packages
library(ordinal)
library(effects)
library(ggplot2)

# Load the data
data(ordinal_example)

# Structure of the data
str(ordinal_example)

# Summary statistics
summary(ordinal_example)

Fitting the Ordinal Regression Model

# Fit the ordinal regression model
ordinal_model <- clm(rating ~ age + sex + age:sex, data = ordinal_example)

# Summary of the model
summary(ordinal_model)

Calculating the Effects

# Calculate the effects of the independent variables
ordinal_effects <- allEffects(ordinal_model, xlevels = list(age = 20:60, sex = c("Male", "Female")))

# Print the effects
ordinal_effects

Creating the Effect Plots

We’ll create two types of effect plots: (1) marginal effect plots and (2) interaction effect plots.

Marginal Effect Plots

# Create a marginal effect plot for age
ggplot(data = ordinal_effects, aes(x = age, y = fit, group = rating, color = rating)) + 
  geom_line() + 
  labs(x = "Age", y = "Predicted Probability", color = "Rating") + 
  theme_classic()

# Create a marginal effect plot for sex
ggplot(data = ordinal_effects, aes(x = sex, y = fit, group = rating, color = rating)) + 
  geom_line() + 
  labs(x = "Sex", y = "Predicted Probability", color = "Rating") + 
  theme_classic()

Interaction Effect Plots

# Create an interaction effect plot for age and sex
ggplot(data = ordinal_effects, aes(x = age, y = fit, group = sex, color = sex)) + 
  geom_line() + 
  facet_wrap(~ rating) + 
  labs(x = "Age", y = "Predicted Probability", color = "Sex") + 
  theme_classic()

Interpreting the Effect Plots

The effect plots provide valuable insights into the relationships between the variables. The marginal effect plots show the change in the predicted probability of each rating category as the independent variables change, while holding all other variables constant. The interaction effect plot reveals how the effect of one independent variable (age) on the predicted probability of each rating category changes depending on the level of another independent variable (sex).

Conclusion

In this article, we demonstrated how to create effect plots of results from ordinal regression with interactions using R. Effect plots are essential tools for visualizing and communicating the complex relationships between variables in ordinal regression models. By following the steps outlined in this article, you can create informative and engaging effect plots to facilitate the interpretation of your ordinal regression results.

Keyword	Frequency
Creating effect plots	5
Ordinal regression	6
Interactions	4

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