Ordinal Logistic Regression vs. Simple Logistic Regression

Attribute	Ordinal Logistic Regression	Simple Logistic Regression
Number of response variables	More than 2	Binary (2)
Model type	Ordinal	Binary
Assumption	Ordered categories	Binary outcome
Output	Ordered categories	Binary outcome
Interpretation	Ordinal relationship between categories	Probability of belonging to a category

Introduction

Logistic regression is a popular statistical method used for predicting the probability of a binary outcome based on one or more predictor variables. There are different types of logistic regression models, including simple logistic regression and ordinal logistic regression. While both models are used for similar purposes, they have distinct attributes that make them suitable for different types of data and research questions.

Simple Logistic Regression

Simple logistic regression is used when the dependent variable is binary, meaning it has only two possible outcomes. In this model, the relationship between the dependent variable and one or more independent variables is estimated using the logistic function. The output of a simple logistic regression model is the probability of the dependent variable being in one of the two categories based on the values of the independent variables.

One of the key assumptions of simple logistic regression is that the relationship between the independent variables and the logit of the dependent variable is linear. This means that the effect of the independent variables on the log odds of the dependent variable is constant. Simple logistic regression is often used in situations where the outcome variable is dichotomous, such as predicting whether a customer will buy a product or not based on their demographic characteristics.

• Used for binary outcome variables
• Assumes a linear relationship between independent variables and logit of the dependent variable
• Output is the probability of the dependent variable being in one of two categories

Ordinal Logistic Regression

Ordinal logistic regression, on the other hand, is used when the dependent variable is ordinal, meaning it has more than two ordered categories. In this model, the relationship between the dependent variable and the independent variables is estimated using the cumulative logit function. The output of an ordinal logistic regression model is the odds of the dependent variable falling into one of the categories relative to the reference category.

Unlike simple logistic regression, ordinal logistic regression does not assume a linear relationship between the independent variables and the logit of the dependent variable. Instead, it allows for the relationship to be non-linear, making it more flexible for modeling ordinal outcomes. Ordinal logistic regression is commonly used in research areas where the outcome variable has multiple ordered categories, such as levels of satisfaction or agreement.

• Used for ordinal outcome variables
• Does not assume a linear relationship between independent variables and logit of the dependent variable
• Output is the odds of the dependent variable falling into one category relative to the reference category

Comparison of Attributes

While both simple logistic regression and ordinal logistic regression are used for modeling categorical outcomes, they differ in several key attributes. One of the main differences is the type of outcome variable they can handle. Simple logistic regression is limited to binary outcomes, while ordinal logistic regression can handle ordinal outcomes with multiple categories.

Another difference between the two models is the assumption of linearity. Simple logistic regression assumes a linear relationship between the independent variables and the logit of the dependent variable, while ordinal logistic regression does not make this assumption. This makes ordinal logistic regression more flexible in modeling non-linear relationships between variables.

Furthermore, the output of the two models also differs. In simple logistic regression, the output is the probability of the dependent variable being in one of two categories, while in ordinal logistic regression, the output is the odds of the dependent variable falling into one category relative to the reference category. This difference in output reflects the different types of outcome variables each model is designed to handle.

Overall, the choice between simple logistic regression and ordinal logistic regression depends on the nature of the outcome variable and the research question being addressed. If the outcome variable is binary and the relationship with the independent variables is assumed to be linear, simple logistic regression may be more appropriate. On the other hand, if the outcome variable is ordinal and the relationship is non-linear, ordinal logistic regression would be the preferred choice.