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Binary vs Multinomial vs Ordinal Logistic Regression
April 20, 2022 | Data science

In this article, we are going to take a look at logistic or logit regression, and we are going to learn the differences between binary, multinomial, and ordinal logistic regression.

What is logistic regression?

Like all other regression analyses (simple and multiple linear, polynomial or multinomial, and other regressions), logistic regression is a part of predictive analysis.

We use logistic regression when we want to explain the relationship between the dependent variable, which is binary or dichotomous (which means the possible answers to analysis are yes or no, present or absent, 0 or 1), and one or more independent variables, which can be nominal, ordinal, interval or ratio-level variable(s).

The main premises when using logistic regression are:

What are some examples from the life of when we can use logistic regression?

As already said, we use logistic regression when we want to predict what is the probability of a specific event happening.

Types of logistic regression

In general, there are three types of logistic regression:

When to use multinomial and when ordinal logistic regression?

On some occasions deciding between multinomial and ordinal logistic regression can be tricky in practice because both multinomial and ordinal models are used for categorical outcomes that contain more than two categories. The main decision criterium is that with the ordinal model we are dealing with variables that have some sort of categories of order (for example – bronze, silver, gold medal or uncomfortable, comfortable, very comfortable car seats etc.), while with the multinomial model the main criterium is that the outcome is nominal and the categories have no order.

However, sometimes things aren’t as simple as that.

We should bring out that there are quite a few ordinal outcomes that describe the ordering of the outcome categories in different ways, but only one logistic regression model suitable for nominal outcomes. Luckily, the majority of software offers only one model for each of the nominal and ordinal outcomes.

Another issue we should bring out regarding ordinal outcomes is the proportional odds model, which as the name suggests has an assumption that is rarely met in real-life data – that the odds assumption is proportional and the lines assumptions are parallel, which means that the predictors’ effect on the likelihood of shifting to a higher-order category along the scale is the same.

To sum up, if you are dealing with a nominal result, you should be careful not to run a model that is ordinal. That’s an obvious one. However, if you are dealing with an ordinal outcome with a proportional odds assumption, we recommend running the cumulative logit version of ordinal logistic regression. However, if you’re dealing with an ordinal outcome, but the proportional odds assumption isn’t met, you can run a different ordinal model, or surprisingly, you can still try running a nominal model if it answers your research question.