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Logit

14/12/2022

What is a logit function?

The logit function (also called logit, logit model or logistic regression) belongs to the regression analyses. A Regression indicates the relationship between two or more variables. A logit makes it possible to explain a dependent binary variable and also to make a prediction about the probability of an event occurring.

The approach of logistic regression largely corresponds to linear regression. The main difference is in the dependent variable. In linear regression it is metric (for example, amounts of money) and in logistic regression it is binary (there are exactly two expressions, for example, male and female, coded as 0 and 1).

The logit function is:

logit(p):= In (p / p-1)

Where "p" is the probability and "p-1" is the counter probability.

Applications of logit functions

  • Predicting the purchase decision: Does a person buy a certain product?
  • Brand awareness: Does a person know a certain brand?
  • Creditworthiness: Can a person repay a certain amount of credit?
  • Party preference: If there were a federal election on Sunday, would a person vote for a certain party?
  • Audience ratings: Did a person watch a particular programme?

What are the requirements for using this function?

  1. The dependent variable is binary, in other words coded as 0 and 1.
  2. The model should show no or little multicollinearity (two or more explanatory variables have a very strong correlation to each other) and be as simple as possible.
  3. There is a linear relationship between the independent variables and the "log odds" (the chances of occurrence of the characteristic expression of the dependent variable under consideration).
  4. A fairly large sample size is needed.

What are alternatives to the logit function?

Logistic regression is used in machine learning as a classification algorithm to predict the probability of a dependent variable. It is uncomplicated, but does not work properly with highly complex models.

In such cases, other classification options should be used, for example:

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