Ordinal Regression

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21 Aug, 2024

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Ordinal Regression is a statistical method designed to explore the relationship between one or more independent variables and an ordinal-level dependent variable in a meaningful order. This approach is utilized for comprehending and predicting the behavior of ordinal variables concerning independent ones.

It leverages generalized linear models to fit cutoff and coefficient vectors to the data set, making it a valuable tool for causal analysis and predictive modeling. It finds applications in various fields, including healthcare, psychology, and marketing, where it aids in predicting outcomes influenced by factors like patient response to treatments, student performance, and customer satisfaction.

What Is Ordinal Regression ?

Ordinal regression is a statistical technique for modeling the relationship between one or more independent variables and an ordinal-level dependent variable, with the goal of understanding and predicting the behavior of the ordinal variable.
It assumes ordinal dependent variables, independent variables of any type, no multicollinearity, and proportional odds.
It manages ordered outcomes but assumes linearity, which may not be accurate.
It forecasts ordinal dependent variables, whereas logistic regression predicts binary dependent variables, highlighting the contrast in their applications.

Ordinal Regression Method Explained

The ordinal regression model is a statistical method used to predict the behavior of an ordinal dependent variable while considering a set of independent variables. An ordinal variable consists of distinct categories with a meaningful order, although the intervals between these categories are not necessarily uniform. It places ordinal regression between classification and conventional regression methods, making it particularly suitable for analyzing ordinal-level dependent variables.

Ordinal regression employs a generalized linear model (GLM) to estimate thresholds and coefficients for the dataset. When applied to a set of observations, it models the relationship between an ordinal dependent variable and one or more independent variables by fitting a coefficient vector and a set of thresholds. This technique uncovers the relationship between independent variables and the dependent variable by forecasting the probability of falling into a specific category of the dependent variable.

In the realm of ordinal data analysis, tools like ordinal regression in SPSS and interpreting ordinal regression results in SPSS, ordinal regression in R, and ordinal regression Python are valuable resources for researchers and data analysts. It assumes that as independent variables increase, the probability of a higher category occurring also increases. This concept is known as the cumulative logit model. Its applications span causal analysis, trend prediction, and forecasting effects. For instance, it assists in credit analysis, where various credit rating agencies evaluate a business's creditworthiness on an ordinal scale.

It is also instrumental in customer preference analysis within the art market, determining socioeconomic factors affecting households and investigating the factors influencing risk tolerance among investors. It is used for predicting outcomes related to voter turnout, student performance, employee engagement, and patient responses to treatment. Banks rely on it to assess the likelihood of a customer defaulting on a loan, considering their credit score and debt-to-income ratio.

Assumptions

Before conducting an analysis, it is essential to consider several key assumptions. These assumptions are fundamental to the methodology and should be well understood:

The dependent variable should be assessed using an ordinal scale, where categories exhibit a meaningful order but lack fixed intervals.
Independent variables can encompass a range of types, including continuous, categorical, or ordinal variables, depending on the research context.
It is essential to ensure that there is no multicollinearity among the independent variables. Multicollinearity refers to a high degree of correlation between independent variables, which can affect the model's stability and interpretability.
This method relies on the proportional odds assumption. It means that each pair of outcome groups shares the same association with the independent variables. In practical terms, the coefficients describing the relationship between the lowest category of the dependent variable and all higher categories should be identical to those describing the relationship between the next lowest category and all higher categories, and so on.

Examples

Let us use a few examples to understand the topic.

Example #1

The study, published on August 16, 2020, aims to investigate how individuals sustained their optimism throughout the COVID-19 pandemic. The research delved into the connections between various positive factors, including physical, mental, and social well-being, preventive actions, and leisure activities. These factors were assessed on a 5-point Likert scale.

The results of the study revealed significant associations between people's positive responses during the lockdown and their income levels, participation in online book clubs/quizzes, and staying informed through newspapers, mobile apps, television, or the internet. This research underscores the importance of maintaining optimism during challenging times like a pandemic and highlights the influence of personal choices in nurturing a positive outlook.

Example #2

In a hypothetical scenario, ordinal regression was used by Jane, a marketing analyst at Fictional Insights Inc. in Rivertown, a busy metropolis, to gauge client happiness during her work there. She studied information gathered from a hypothetical chain of coffee shops named Brewville that was present in several places. Jane assessed customer satisfaction using a 5-point Likert scale and determined that a number of variables, including service caliber, coffee flavor, atmosphere, and cost, had an impact. By using this method, she discovered that while price and coffee flavor had less of an influence, service quality had a considerably favorable impact on customer satisfaction.

Thanks to this realization, Brewville was able to concentrate on raising customer pleasure, enriching the whole customer experience, and improving service quality, which eventually resulted in a rise in customer loyalty and company success in Rivertown and beyond.

Advantages And Disadvantages

For using this method, it is essential to know its pros and cons:

Advantages	Disadvantages
Manages ordered outcomes	Makes a significant assumption that could not be true in every situation
Fewer parameters compared to other multiclass regression models	Prone to lots of the same mistakes that other models of regression make
Has Interpretable coefficients	Information loss during ordering
It has coefficients that are really understandable and clarify the connection between the characteristics and the result variable	Sometimes, estimates could be more realistic
Suitable for trend forecasting, causal analysis, and effect forecasting	Using the wrong models can lead to more severe issues than those that these techniques were intended to address.
Strong analytical tool for data including a number of independent variables and an ordinal dependent variable	Reduced statistical power
Numerous uses across a range of industries, including finance	Frequently, responses are so limited in scope relative to the topic that they introduce or amplify bias not taken into account in the survey

Ordinal Regression vs Logistic Regression

Although both are part of a regression family, they differ in certain aspects. Their significant differences are listed in the table below:

Basis	Ordinal Regression	Logistic Regression
Purpose	Forecasting ordinal dependent variables	Forecasting binary dependent variables
Management of Results	Handles ordered outcomes	Handles unordered outcomes
Number of Parameters	Fewer parameters compared to other multiclass regression models	More variables compared to ordinal regression
Assumption on Result Groups	Assumes that every pair of result groups has the same connection with one another	Assumes a linear connection between predictor and result
Information Loss during Ordering	Some information was lost during the ordering process	No information loss throughout the ordering process
Realism of Estimates	Sometimes, estimates may not be realistic	Less likely for estimates to be unrealistic
Statistical Power	Reduced statistical power	Statistical power remains unaffected

Frequently Asked Questions (FAQs)

1. When to use ordinal regression?

It can be used when:
• The level of the dependent variable becomes ordinal.
• There are two types of independent variables: continuous and categorical.
• The influence of every independent variable over the dependent variable remains uniform throughout every category of the dependent variable, according to the proportional odds premise.

2. How to interpret ordinal regression in SPSS?

In SPSS, interpret ordinal regression results by examining coefficients, p-values, and odds ratios. Positive coefficients indicate an increase in the dependent variable, p-values indicate statistical significance, and odds ratios indicate a change in the dependent variable category.

3. How to report ordinal regression results?

The following details have to be included when presenting the findings of this method:
• The kind of ordinal regression model that was applied (e.g., cumulative logit model, proportional odds model).
• Each independent variable's coefficients, p-values, plus odds ratios.
• Any more pertinent data, such as sample size along with model goodness-of-fit.

4. What is ordinal regression analysis?

Ordinal regression analysis is a statistical technique used to model the relationship between an ordinal-level dependent variable and one or more independent variables. It is a type of logistic regression, but it is designed explicitly for ordinal-level dependent variables.