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?
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asked Dec 7, 2014 at 18:44
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8$\begingroup$ Logistic regression belongs to the GLM family of models. $\endgroup$– Stéphane LaurentCommented Dec 7, 2014 at 19:04
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15$\begingroup$ You can use it to regress probabilities. $\endgroup$– EmreCommented Dec 7, 2014 at 22:38
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29$\begingroup$ 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. $\endgroup$– Glen_bCommented Dec 8, 2014 at 1:07
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6$\begingroup$ 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. $\endgroup$– Glen_bCommented Dec 8, 2014 at 1:14
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$\begingroup$ It's a regression modelling strategy and you'd be amazed by the number of people who use it without checking the linearity with the log odds assumption. $\endgroup$– SeanosapienCommented Sep 2, 2022 at 19:44
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4 Answers
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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:
- Classification is a decision. To make an optimal decision, you need to asses a utility function, which implies that you need to account for the uncertainty in the outcome, i.e. a probability.
- The costs of misclassification are not uniform across all units.
- Don't use cutoffs.
- Use proper scoring rules.
- The problem is actually risk estimation, not classification.
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.
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4$\begingroup$ 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? $\endgroup$– KuberCommented Dec 10, 2014 at 6:51
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9$\begingroup$ @Outlier Counterexample: SVM doesn't compute class probabilities at all, it just measures the distance between an observation and a hyperplane. $\endgroup$– Sycorax ♦Commented Dec 10, 2014 at 12:59
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$\begingroup$ @Outlier in ML these are called probabilistic classifiers; trees and random forest are not, xgboost is - at least with logloss) $\endgroup$– seanv507Commented May 25, 2019 at 6:46
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$\begingroup$ @SycoraxsaysReinstateMonica So is there any classification algorithm in the world? SVMs compute distance from the class boundary, Neural Networks compute some other continuous function... $\endgroup$– Igor F.Commented Dec 19, 2019 at 11:56
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2$\begingroup$ @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. $\endgroup$– Sycorax ♦Commented Dec 19, 2019 at 13:09
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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 $(Y|X=x)$.
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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.
if you want to read more please check this link for more detail https://ryxcommar.com/2020/06/27/why-do-so-many-practicing-data-scientists-not-understand-logistic-regression/
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$\begingroup$ Yes, and very often the probabilities predicted by a logistic regression model will not get as high as 0.5 so a decision must be made on a sensible threshold to use for classification. An excellent article by Frank Harrell on this matter that I re-read constantly: fharrell.com/post/classification $\endgroup$ Commented Sep 2, 2022 at 6:41
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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.
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$\begingroup$ what happens if u insert the outcome y of your linear model into another linear model (can think of it as an extreme case of sigmoid with very gentle change of gradient. Will that work for classification? If not why? $\endgroup$– SamCommented Feb 5, 2020 at 8:04