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3 Types of Logistic Regression

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In this article, we have explained the basic concept of Logistic Regression and presented the 3 different types of Logistic Regression.

Table of contents:

  1. Introduction to Logistic Regression
  2. 3 Types of Logistic Regression
    • Binary logistic regression
    • Multinomial logistic regression
    • Ordinal logistic regression
  3. Use cases of logistic regression

Introduction to Logistic Regression

Statistically, the connection between a dependent variable and one or more independent factors can be examined and modelled using logistic regression. Based on past data, it is frequently used in predictive modelling to ascertain the likelihood that a specific occurrence will occur. When the dependent variable has a binary or classified character, logistic regression is especially helpful.

Compared to other predictive modelling strategies, logistic regression has a number of benefits. First off, it is simple to use and understand. When all other variables are held fixed, the model's estimates can be understood as the impact of each independent variable on the likelihood of the dependent variable. Second, a variety of independent factors, such as continuous, classified, and binary variables, can be handled by logistic regression.

The logistic function is also known as the sigmoid function and can be written as:

P(Y=1 | X) = 1 / (1 + exp(-z))


  • P(Y=1 | X) is the probability of the dependent variable taking on a value of 1 given the predictor variables X
  • z is a linear combination of the predictor variables and their associated coefficients:
z = b0 + b1X1 + b2X2 + ... + bnXn


  • b0, b1, b2, ..., bn are the coefficients estimated by the logistic regression model
  • X1, X2, ..., Xn are the values of the predictor variables.

The logistic regression model is estimated using maximum likelihood estimation, which involves finding the set of coefficient values that maximize the likelihood of observing the data given the model.

Logistic regression is a widely used technique for binary classification problems, such as predicting the probability of a customer buying a product, the likelihood of a patient having a disease, or the probability of a borrower defaulting on a loan.

3 Types of Logistic Regression

There are 3 types of Logistic Regression:

  1. Binary logistic regression
  2. Multinomial logistic regression
  3. Ordinal logistic regression

We will dive into each type further.

Binary logistic regression

With this method, there are only two potential results for the response or dependent variable. (e.g. 0 or 1). It is frequently used to determine whether an email is junk or not, as well as whether a tumour is cancerous or not. This method is most frequently used in logistic regression, and it is also one of the most widely used models for binary categorization in general.



Total instances, chosen cases, and valid examples for each analysis. parameter coding for each category variable. factors added or subtracted, timeline of iterations, Observed groups and projected probabilities chart, residual chi-square, -2 log-likelihood, goodness of fit, Hosmer-Lemeshow goodness-of-fit measure, model chi-square, improvement chi-square, classification table, relationships between variables. Coefficient (B), standard error of B, Wald statistic, predicted odds ratio (exp(B)), confidence interval for exp(B), and log-likelihood if component is deleted from model are all given for each variable in the equation. Score statistics are used for each element left out of the calculation. Each instance includes the following information: observed group, expected chance, predicted group, residual, and standardised residual.


Block input of factors or any of the subsequent stepwise techniques can be used to estimate models: Backward conditional, Backward LR, Backward Wald, Forward conditional, Forward LR

Multinomial logistic regression

The dependent variable in this kind of logistic regression model has three or more potential values, but there is no established hierarchy between them.

For instance, in order to more effectively promote their films, movie companies want to forecast the type of film a viewer will likely watch. The company can find out how much of an impact a person's age, gender, and relationship status may have on the genre of movie they favour by using a multinomial logistic regression model.

The company can then target a particular movie's advertising effort at an audience that is most likely to go see it.

Ordinal logistic regression

Meaning of Ordinal: Something defined by a series.

When the response variable has three or more potential values—but in this instance, these values do have a specified order—this kind of logistic regression model is used. Grading systems from A to F or rating scales from 1 to 5 are two examples of ordinal answers.

A statistical analysis technique called ordinal logistic regression can be used to simulate the association between an ordinal answer variable and one or more explanatory factors. A category variable with a distinct ranking is called an ordinal variable.

Use cases of logistic regression

Logistic regression is commonly used for prediction and classification problems. Some of these use cases include:

Fraud detection:
Teams can spot data abnormalities that are indicative of fraud with the aid of logistic regression models. In order to better safeguard their customers, banking and other financial organisations may find that certain behaviours or characteristics are more frequently associated with fraudulent activities. In order to remove fake user accounts from their datasets when performing data analysis on company success, SaaS-based businesses have also begun to implement these practises.

Disease prediction:
This analytics strategy can be applied to medicine to forecast the probability of disease or illness in a particular community. Healthcare organisations can set up prophylactic treatment for people who have a greater risk of developing a particular disease.

Churn prediction:
Churn in various organisational roles may be indicated by certain behaviours. If top achievers are at danger of quitting the company, for instance, human resources and management teams may be interested in finding out. This type of information can spark discussions about the company's culture or pay practises. As an alternative, the sales team might want to find out which of their customers might decide to do business elsewhere. In order to prevent income loss, this may inspire teams to develop a retention plan.

With this article at OpenGenus, you must have the complete idea of different types of Logistic Regression.

3 Types of Logistic Regression
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