Editing Logit (section)

{{Short description|Function in statistics}}
{{About|the binary logit function|other types of logit|discrete choice|the basic regression technique that uses the logit function|logistic regression|standard magnitudes combined by multiplication|logit (unit)}}
{{Distinguish|log probability}}
[[Image:Logit.svg|thumbnail|upright=1.3|Plot of logit(''x'') in the domain of 0 to 1, where the base of the logarithm is ''e''.]]

In [[statistics]], the '''logit''' ({{IPAc-en|ˈ|l|oʊ|dʒ|ɪ|t}} {{respell|LOH|jit}}) function is the [[quantile function]] associated with the standard [[logistic distribution]]. It has many uses in [[data analysis]] and [[machine learning]], especially in [[Data transformation (statistics)|data transformations]].

Mathematically, the logit is the [[inverse function|inverse]] of the [[logistic function|standard logistic function]] <math>\sigma(x) = 1/(1+e^{-x})</math>, so the logit is defined as
: <math>\operatorname{logit} p = \sigma^{-1}(p) = \ln \frac{p}{1-p} \quad \text{for} \quad p \in (0,1).</math>

Because of this, the logit is also called the '''log-odds''' since it is equal to the [[logarithm]] of the [[odds]] <math>\frac{p}{1-p}</math> where {{mvar|p}} is a probability. Thus, the logit is a type of function that maps probability values from <math>(0, 1)</math> to real numbers in <math>(-\infty, +\infty)</math>,<ref>{{Cite web|url=http://www.columbia.edu/~so33/SusDev/Lecture_9.pdf|title=Logit/Probit}}</ref> akin to the [[probit|probit function]].