Ordinal Regression

What is Ordinal Regression?

Ordinal regression, also known as ordinal logistic regression or ordered logit, is a statistical method used to predict an ordinal variable, which is a type of categorical variable with a natural order. Ordinal regression models the relationship between a set of predictor variables and an ordinal response variable, allowing for the prediction of the probability of an observation falling into a specific category.

Example of Ordinal Regression

Suppose we have a dataset containing information about customers' satisfaction levels with a product, measured on a scale of “Very Dissatisfied,” “Dissatisfied,” “Neutral,” “Satisfied,” and “Very Satisfied.” We want to predict their satisfaction levels based on their age, gender, and purchase frequency. Since the satisfaction levels have a natural order, we can use ordinal regression to model the relationship between the predictor variables and the ordinal response variable (satisfaction levels).

Here’s a Python code example using the ordinal package:

import pandas as pd
import numpy as np
from ordinal import OrderedLogit

# Create a sample dataset
data = {'Age': [25, 32, 45, 28, 37, 41, 29, 33, 54],
        'Gender': ['M', 'F', 'M', 'F', 'M', 'F', 'F', 'M', 'F'],
        'PurchaseFrequency': [5, 12, 8, 10, 7, 15, 9, 11, 6],
        'Satisfaction': [3, 4, 2, 3, 4, 5, 3, 4, 1]}

df = pd.DataFrame(data)

# Convert categorical variable 'Gender' to numeric
df['Gender'] = df['Gender'].map({'M': 0, 'F': 1})

# Fit the ordinal regression model
model = OrderedLogit()
model.fit(df[['Age', 'Gender', 'PurchaseFrequency']], df['Satisfaction'])

# Make predictions
predictions = model.predict(df[['Age', 'Gender', 'PurchaseFrequency']])

In this example, we use the ordinal package to fit an ordinal regression model to the sample data and make predictions for the satisfaction levels based on the age, gender, and purchase frequency of the customers.

More resources to learn about Ordinal Regression