Logit

Graphical representation of the logit function logit ( p ) in the definition range from 0 to 1, where the base of the logarithm is e .

In statistics, a logit is the natural logarithm of an opportunity (probability by counter-probability ). The logit transformation is used in logistic regression as a specification of the coupling function. ${\displaystyle p}$ ${\displaystyle 1-p}$

definition

A logit is the natural logarithm of an opportunity (probability by counter-probability ): ${\displaystyle p}$ ${\displaystyle 1-p}$

${\displaystyle \operatorname {logit} (p):=\ln \left({\frac {p}{1-p}}\right)=\ln \left(\operatorname {odds} (p)\right)}$.

The inverse function of the logit is the logistic function :

${\displaystyle F_{\text{logistisch}}:=\operatorname {logit} ^{-1}(s)={\frac {\operatorname {exp} \left(s\right)}{1+\operatorname {exp} \left(s\right)}}={\frac {1}{1+\operatorname {exp} \left(-s\right)}}}$.

application

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The logit function can be used for linearization of sigmoidal curves are used and therefore has great significance for the evaluation of ELISA curves in biochemistry obtained. The logit transformation is central to logistic regression .

Individual evidence

1. ↑ Torsten Becker, et al .: Stochastic risk modeling and statistical methods. Springer Spectrum, 2016. p. 3010.