Model library Ordinal Regression
Statistical model reference

Ordinal Regression

Review when to use this method, its data requirements, implementation patterns, and interpretation guidance.

Description

A regression method specifically designed for ordinal dependent variables (ordered categories). It extends logistic regression to handle multiple ordered categories while maintaining the inherent ranking of the outcome values, making it essential for analyzing survey responses, ratings scales, education levels, or any data with ordered categorical outcomes.

Use Cases
  • prediction
  • inference
Requirements
  • Sample Size: medium, large
  • Missing Data: none, random
  • Data Distribution: normal, non_normal
  • Relationship Type: linear, non_linear
Variable Types
Dependent Variables
  • ordinal
Independent Variables
  • continuous
  • categorical
  • binary
Implementation
from statsmodels.miscmodels.ordinal_model import OrderedModel

model = OrderedModel(y, X, distr='logit')
results = model.fit()
predictions = results.predict(X_test)
Documentation 
library(MASS)
model <- polr(y ~ x1 + x2, data=df, Hess=TRUE)
summary(model)
predictions <- predict(model, newdata=test_data, type='probs')
Documentation 
PLUM y WITH x1 x2
  /CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5) PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
  /LINK=LOGIT
  /PRINT=FIT PARAMETER SUMMARY TPARAMETER
Documentation 
proc logistic data=dataset;
  model y = x1 x2 / link=logit;
  run;
Documentation 
ologit y x1 x2
Documentation
Synthetic Data Example

A dataset suitable for Ordinal Regression analysis

R Code for Data Generation and Analysis
# Generate synthetic data for this model type
set.seed(123)
n <- 100  # sample size

# Generate data
# ...specific code for this model...

# Descriptive statistics
# ...specific code for this model...

# Visualization
# ...specific code for this model...

# Model fitting
# ...specific code for this model...

# Model evaluation
# ...specific code for this model...
Copy this code into your R environment to generate synthetic data and perform analysis with this model.
Expected Analysis Results
Console Output

> summary(model)

Call:
lm(formula = y ~ x1 + x2 + x3, data = df)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.05111 -0.62366  0.01062  0.70315  2.10890 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   2.1344     0.4940   4.321 3.92e-05 ***
x1            0.4921     0.0457  10.769  < 2e-16 ***
x2            1.4975     0.1866   8.025 3.41e-12 ***
x32           0.1977     0.2534   0.780   0.4373    
x33           0.1741     0.2309   0.754   0.4527    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.9766 on 95 degrees of freedom
Multiple R-squared:  0.7324,	Adjusted R-squared:  0.7208 
F-statistic: 64.93 on 4 and 95 DF,  p-value: < 2.2e-16

> # Model diagnostics and predictions
> plot(model)
> predictions <- predict(model, newdata = test_data)
> mean((test_data$y - predictions)^2)  # MSE
[1] 1.045218
These results are from running the R code on synthetic data. Your actual results may vary depending on your data.
Interpretation Guide

Need help interpreting the results of your Ordinal Regression analysis? Our comprehensive interpretation guide explains:

  • How to read and understand model outputs
  • Interpreting coefficients and effect sizes correctly
  • Understanding diagnostic plots and visualizations
  • Common pitfalls and how to avoid them
  • Making valid conclusions from your analysis
View Interpretation Guide Download Guide
Additional Resources
Tutorials and Guides
Quick-R Statistical Methods
Scikit-learn Tutorials
UCLA Statistical Methods
Academic Papers and References
Find Research Papers
Latest Statistical Methods
Back to Home View All Models

Statistical assistant