# Why isn't Logistic Regression called Logistic Classification?

Since Logistic Regression is a statistical classification model dealing with categorical dependent variables, why isn't it called Logistic Classification? Shouldn't the "Regression" name be reserved to models dealing with continuous dependent variables?

• Logistic regression belongs to the GLM family of models. – Stéphane Laurent Dec 7 '14 at 19:04
• You can use it to regress probabilities. – Emre Dec 7 '14 at 22:38
• While logistic regression can certainly be used for classification by introducing a threshold on the probabilities it returns, that's hardly its only use - or even its primary use. It was developed for - and continues to be used for - regression purposes that have nothing to do with classification. I'd argue that this is still easily what it's mostly used for, but I suppose it depends on what you look at. – Glen_b -Reinstate Monica Dec 8 '14 at 1:07
• You might find this paper on the development of logistic regression interesting, particularly since it does give some sense of the kinds of problems that it is used for as a regression technique. – Glen_b -Reinstate Monica Dec 8 '14 at 1:14

Logistic regression is emphatically not a classification algorithm on its own. It is only a classification algorithm in combination with a decision rule that makes dichotomous the predicted probabilities of the outcome. Logistic regression is a regression model because it estimates the probability of class membership as a (transformation of a) multilinear function of the features.

Frank Harrell has posted a number of answers on this website enumerating the pitfalls of regarding logistic regression as a classification algorithm. Among them:

If I recall correctly, he once pointed me to his book on regression strategies for more elaboration on these (and more!) points, but I can't seem to find that particular post.

• If that's the case, all(or most) the classifiers predicts the probabilities to belong in a class first(as far as I know) and then transform this prob to classes.. Don't they? – Outlier Dec 10 '14 at 6:51
• @Outlier Counterexample: SVM doesn't compute class probabilities at all, it just measures the distance between an observation and a hyperplane. – Sycorax says Reinstate Monica Dec 10 '14 at 12:59
• @Outlier in ML these are called probabilistic classifiers; trees and random forest are not, xgboost is - at least with logloss) – seanv507 May 25 '19 at 6:46
• @SycoraxsaysReinstateMonica So is there any classification algorithm in the world? SVMs compute distance from the class boundary, Neural Networks compute some other continuous function... – Igor F. Dec 19 '19 at 11:56
• @IgorF. Any algorithm with a decision rule discretizing the output as classes is a classifier. Logistic regression is properly named because it's a regression of class probabilities. – Sycorax says Reinstate Monica Dec 19 '19 at 13:09

Abstractly, regression is the problem of calculating a conditional expectation $E[Y|X=x]$. The form taken by this expectation is different depending on the assumptions of how the data were generated:

• Assuming (Y|X=x) to be normally distributed yields with classical linear regression.
• Assuming a Poisson distribution yields Poisson regression.
• Assuming a Bernoulli distribution yields logistic regression.

The term "regression" has also been used more generally than this, including approaches like quantile regression, which estimates a given quantile of $(Y|X=x)$.

Apart from already provided good answers, another view is that Logistic regression predicts probabilities (which is continuous value) that have got range from 0 to 1. 