# 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. Dec 7, 2014 at 19:04
• You can use it to regress probabilities.
– Emre
Dec 7, 2014 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. Dec 8, 2014 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. Dec 8, 2014 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? Dec 10, 2014 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
Dec 10, 2014 at 12:59
• @Outlier in ML these are called probabilistic classifiers; trees and random forest are not, xgboost is - at least with logloss) May 25, 2019 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... Dec 19, 2019 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
Dec 19, 2019 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 $(Y|X=x)$.

Blockquote The U.S. Weather Service has always phrased rain forecasts as probabilities. I do not want a classification of “it will rain today.” There is a slight loss/disutility of carrying an umbrella, and I want to be the one to make the tradeoff. Blockquote

Dr. Frank Harrell, https://www.fharrell.com/post/classification/

Classification is when you make a concrete determination of what category something is a part of. Binary classification involves two categories, and by the law of the excluded middle, that means binary classification is for determining whether something “is” or “is not” part of a single category. There either are children playing in the park today (1), or there are not (0).

Although the variable you are targeting in logistic regression is a classification, logistic regression does not actually individually classify things for you: it just gives you probabilities (or log odds ratios in the logit form). The only way logistic regression can actually classify stuff is if you apply a rule to the probability output. For example, you may round probabilities greater than or equal to 50% to 1, and probabilities less than 50% to 0, and that’s your classification.