Ordinal Logistic Regression in R: A Complete Guide

Ordinal logistic regression is a statistical technique used to model the relationship between an ordinal dependent variable and one or more independent variables. It is a powerful method for analyzing data with ordered categories, making it particularly useful in fields such as social sciences, marketing, and healthcare.

What Is Ordinal Logistic Regression?

Ordinal logistic regression, also known as proportional odds logistic regression, is used when the dependent variable has a natural order, but the distances between levels are not assumed to be equal. For example, survey responses like “Poor,” “Fair,” “Good,” and “Excellent” are ordinal.

Key Characteristics of Ordinal Logistic Regression 

1. Dependent Variable: Ordered categories (e.g., Likert scale).
2. Independent Variables: Continuous, categorical, or both.
3. Assumption of Proportional Odds: The relationship between each pair of outcome groups is the same.

Ordinal Logistic Regression in R: A Complete Guide

When to Use Ordinal Logistic Regression? 

Ordinal logistic regression is suitable when:

• The dependent variable is ordinal.
• The independent variables include continuous or categorical predictors.
• The assumption of proportional odds is met.

Steps to Perform Ordinal Logistic Regression in R 

1. Install and Load Required Packages 

To perform ordinal logistic regression, you need the MASS or ordinal package. Install and load the packages as follows:

install.packages("MASS")

install.packages("ordinal")

library(MASS)

library(ordinal)

2. Import Your Dataset 

Use read.csv() or similar functions to load your dataset. For example:

data <- read.csv("your_dataset.csv")

head(data)

3. Explore and Prepare the Data 

Check the structure of your dataset:

str(data)

summary(data)

Ensure the dependent variable is an ordered factor:

data$DependentVariable <- factor(data$DependentVariable,

                                  levels = c("Low", "Medium", "High"),

                                  ordered = TRUE)

4. Fit the Ordinal Logistic Regression Model 

Use the polr() function from the MASS package:

model <- polr(DependentVariable ~ IndependentVariable1 + IndependentVariable2,

              data = data,

              method = "logistic")

summary(model)

5. Interpret the Results 

• Coefficients: Log-odds for each predictor.
• p-values: Significance of predictors (use Anova() from the car package for type II tests).
• Odds Ratios: Exponentiate the coefficients:

exp(coef(model))

6. Assess Model Fit (H3)

Check the proportional odds assumption:

library(ordinal)

anova(model, type = 3)

7. Predict Outcomes 

Predict probabilities for each category:

predict(model, type = "probs")

Example: Analysis of Customer Satisfaction 

Let’s analyze a hypothetical dataset where customer satisfaction (Low, Medium, High) is predicted by income and age.

Code Example

# Load the dataset

data <- read.csv("customer_satisfaction.csv")

# Convert dependent variable to ordered factor

data$Satisfaction <- factor(data$Satisfaction,

                            levels = c("Low", "Medium", "High"),

                            ordered = TRUE)

# Fit the model

model <- polr(Satisfaction ~ Income + Age, data = data, method = "logistic")

summary(model)

# Odds Ratios

exp(coef(model))

# Predict probabilities

predicted_probs <- predict(model, type = "probs")

head(predicted_probs)

Visualizing Results in R 

Plotting Predicted Probabilities 

Visualize the probabilities using ggplot2:

library(ggplot2)

predicted <- data.frame(predict(model, type = "probs"))

predicted$Category <- rownames(predicted)

ggplot(predicted, aes(x = Category, y = High)) +

  geom_bar(stat = "identity") +

  theme_minimal() +

  labs(title = "Predicted Probabilities", x = "Category", y = "Probability")

Residual Analysis

Assess residuals to check model assumptions:

residuals <- residuals(model)

hist(residuals, main = "Histogram of Residuals", xlab = "Residuals")

Limitations of Ordinal Logistic Regression 

• Sensitive to outliers.
• Assumes proportional odds (verify using tests).
• Does not model unordered categories.

Conclusion 

Ordinal logistic regression is a robust tool for analyzing ordered categorical data. With R’s powerful libraries, implementing and interpreting this method becomes straightforward. By following the steps outlined, you can apply this technique to real-world problems effectively.